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Business Process Improvement 281-304-9504
20314 Lakeland Falls www.spcforexcel.com
Cypress, TX 77433
Instruction Manual for SPC for MS Excel V3.0
Capability Analysis
LSL=60 USL=80Nominal=70
0
5
10
15
20
25
30
35
57 62 67 72 77 82 87
Measurement
Fre
qu
en
cy
Statistics
Cp=1.34
Cpk= 0.59
Cpu= 0.59 (3.84%)
Cpl= 2.09 (0%)
Est. Sigma= 2.49
Pp=1.31
Ppk= 0.57
Ppu= 0.57 (4.36%)
Ppl= 2.04 (0%)
Sigma= 2.55
Average=75.63
Count=96
No. Out of Spec=5 (5.21%)
Kurtosis=0.62
Skewness=0.71
Thank you for selecting our software package. This program was written by Dr. William H. McNeese
and is distributed by Business Process Improvement (Cypress, Texas). This program cannot be copied or
used unless under license with Business Process Improvement. Business Process Improvement is not
liable for any decisions made based on the use of this software package.
Requirements: This program is a Microsoft Excel® add-in. You must Microsoft Excel® for this program
to work. This program supports any version of Excel from 2000 on.
Business Process Improvement
20314 Lakeland Falls
Cypress, TX 77433
281-304-9504
www.spcforexcel.com
2 ©2007 Business Process Improvement
SPC for MS Excel V3.0
Table of Contents
Instructions Manual for SPC for MS Excel V3.0 ......................................................................................... 1 Installation..................................................................................................................................................... 4 Pareto Diagrams ............................................................................................................................................ 6 Histograms .................................................................................................................................................. 10 Attribute Control Charts ............................................................................................................................. 13
p Charts ................................................................................................................................................... 13 np Control Charts .................................................................................................................................... 16 c Control Charts ...................................................................................................................................... 18 u Control Charts ...................................................................................................................................... 20
Variable Control Charts .............................................................................................................................. 22
X -R Control Chart ................................................................................................................................. 22 Control Limit Option ............................................................................................................................... 26
X -s Control Charts ................................................................................................................................. 27 X-MR (Individuals) Control Charts ........................................................................................................ 28 Moving Average/Moving Range (MA/MR) Charts ................................................................................ 30 Table X-MR (Individuals) Chart............................................................................................................. 31 Run Charts .............................................................................................................................................. 32 Subgroup Maker: Make Subgroups from Column of Numbers .............................................................. 32
Process Capability ....................................................................................................................................... 33 Advanced Process Capability...................................................................................................................... 38 Scatter Diagram .......................................................................................................................................... 40 Updating Charts .......................................................................................................................................... 43 Changing Chart Options ............................................................................................................................. 43 Single Point Actions ................................................................................................................................... 44 All Points Action......................................................................................................................................... 46 Cause and Effect Diagram .......................................................................................................................... 47 Measurement Systems Analysis.................................................................................................................. 48
ANOVA Method ..................................................................................................................................... 53 Range Method for Gage R&R ................................................................................................................ 55 Bias – Independent Sample Method ....................................................................................................... 57 Bias – Control Chart Method .................................................................................................................. 59 Linearity .................................................................................................................................................. 61 Attribute Gage R&R ............................................................................................................................... 62
Transfer Charts to PowerPoint or Word ..................................................................................................... 65 Regression ................................................................................................................................................... 66
Changing the Variables in the Regression .............................................................................................. 69 Miscellaneous ............................................................................................................................................. 70
Descriptive Statistics ............................................................................................................................... 70 Confidence Interval Around a Mean ....................................................................................................... 71 Confidence Interval Around a Variance ................................................................................................. 73 Confidence Interval for the Difference in Two Means ........................................................................... 74 Confidence Interval for Multiple Processes ............................................................................................ 76 Paired Sample Comparison ..................................................................................................................... 78 Analysis of Means ................................................................................................................................... 79 Correlation Coefficients .......................................................................................................................... 81 Failure Mode and Effect Analysis .......................................................................................................... 82
3 ©2007 Business Process Improvement
Box and Whisker Plots ............................................................................................................................ 83 Sample Size Calculator ........................................................................................................................... 85 Side by Side Histogram .......................................................................................................................... 86 Plot Multiple Y Variables Against One X Variable................................................................................ 88
Select Cells.................................................................................................................................................. 89 Frequently Asked Questions ....................................................................................................................... 90
What out of control tests does the program use? .................................................................................... 90 Do all out of control tests apply to all the charts? ................................................................................... 90 How do I know if the chart has any out of control points? ..................................................................... 90 Can I remove the out of control points from the calculations? ............................................................... 90 Can I change the name of the worksheet tab containing the chart? ........................................................ 90 How come I can’t see the name of one of my charts in the list of charts to be updated? ....................... 90 How can I change the title or the x and y labels on an existing chart? ................................................... 91
4 ©2007 Business Process Improvement
Installation
The necessary files to run the program are installed when you run the installation program. The
installation file is the .exe program you downloaded or received on the CD. Running the setup.exe file
creates the following directory (there are slight differences for Excel 2007):
C:\Documents and Settings\{username}\Application Data\SPC_for_MS_Excel
The following program files are installed into this directory:
spcforexcelv3.xla
spcfor2007excelv3.xlam
installspcforexcelv3.exe
The installation process may leave uninstallation files such as unins001.exe and unins001.dat in this
directory. During operation, the program may save user preferences and other settings in one or more text
or binary files in this directory. The user is discouraged from altering any of these files and from storing
any work files in this directory.
The program also creates the following directory:
C:\Documents and Settings\{username}\My Documents\SPC for MS Excel
The following sample data files and instruction manual are installed into this directory:
Gage R&R Example Workbook.xls
SPC Example Data V3.xls
SPC for MS Excel V3.0 Instructions.pdf
The user is encouraged to use these files to learn how SPC for MS Excel works. If you also purchased the
PowerPoint training modules, they will be installed this directory as well.
The program is installed as an add-in. It will open whenever Excel is opened. In Excel 2000 to Excel
2003, SPC for Excel will appear on the Worksheet and Chart Menus next to Window. There is also a free
standing toolbar that can be placed anywhere in the window. Both are shown below.
5 ©2007 Business Process Improvement
In Excel 2007, SPC for Excel appears on the ribbon next to Home as shown below. The SPC Menu to the
right lists all the buttons.
The menu and toolbar allows you to access the various components of the program:
The data entry requirements to run each component of this program are given below. All the examples
are in the workbook SPC Example Data V3.0.xls and Gage R&R V3 Example Workbook.xls. This
instruction manual is intended to demonstrate how the program is used.
To learn more about SPC, please refer to one of the many books on the subject. The best reference is
probably Understanding Statistical Process Control by D. Wheeler and D. Chambers, SPC Inc., 1986 or
any of the later books by Dr. Wheeler.
You can also visit our website where many of these SPC tools are described in our past free e-zines. Go
to www.spcforexcel.com.
6 ©2007 Business Process Improvement
Pareto Diagrams
A Pareto diagram is a special type of bar chart that is used to separate the "vital few" from the "trivial
many." It is based on the 80/20 rule; e.g., 20% of our customers buy 80% of our products. The
horizontal (x) axis most often represents problems or causes of problems (the “categories”). The vertical
(y) axis most often represents frequency or cost. The problem or cause that occurs most frequently (or
costs the most) is listed first on the x axis. The second most frequently occurring problem or cause is
listed second and so on. A bar is generated for each cause or problem. The height of the bar is the
frequency with which that problem or cause occurred. A cumulative percentage line is sometimes added
to the Pareto diagram.
An example of a Pareto
diagram is shown to the
right. In this Pareto
diagram, the number of
return goods by product is
analyzed. The x axis is
the different types of
products. The y axis is
how often each product
has been returned. The
bars are arranged so the
first bar (for Product B)
has the largest frequency.
The other bars are then
arranged in decreasing
frequency.
The above Pareto diagram
indicates that product B has been returned more times (25) than any other product. To reduce the number
of returned goods, one would probably want to investigate why product B is returned so often. The
highest bars represent the “vital few.” The smaller bars represent the “trivial many,” such as for products
C and D.
This program will construct Pareto diagrams with or without a cumulative percentage line. If selected,
the calculations for the cumulative percentage line are completed and added to the Pareto diagram. The
program will not alter your worksheet. The data are copied from your worksheet to a hidden sheet.
Data Entry
The data entry requirements for the Pareto diagram are shown below. In all cases, it is recommended you
select a range in the worksheet. This helps save time when the input dialog box appears. The data is in
columns in the examples below but can also be in rows.
Option 1: Basic Pareto Diagram
For this option, the frequencies have already been totaled by category. For
example, suppose you are tracking returns by product name for four products: A,
B, C, and D. You collect data for a two-month period. You then total the number
of returns and enter the data into an Excel spreadsheet. To start the Pareto
program, highlight the product names as shown to the right (shaded area) and
Products Number of Returns
A 15
B 25
C 8
D 2
Pareto Diagram
25
15
8
2
50%
80%
96%
100%
0
5
10
15
20
25
30
35
40
45
50
B A C D
Products
Nu
mb
er
of
Re
turn
s
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Pe
rcen
t
7 ©2007 Business Process Improvement
select the Pareto Diagram option from the toolbar. You could also highlight both the product and number
of returns information. The data does not have to in adjacent columns. In this case, you would select the
category range, then hold down the Control key and select the frequency range. Then select the Pareto
Diagram option on the SPC toolbar. You will get the Pareto Diagram dialog which is described below
(after the data entry requirements for option 3). Once you fill the information in the dialog box and select
OK, you will get the Pareto diagram shown above (with the cumulative line option selected).
Option 2: Basic Pareto Diagram but Program Calculates the Totals
For this option, the frequencies have been totaled over some time period
but not overall. For example, suppose you are tracking the returns and
total the returns for each product by week. In this case, you would enter
the following data into an Excel spreadsheet. You would select the
products (shaded area) and then select the Pareto diagram option from
the toolbar. The program will automatically calculate the overall totals.
Option 3: Pareto Diagram Based on Data in One
Column Only
For this option, none of the frequencies have been
totaled. For example, you might be tracking each
individual returned product to discover the reason for
returns. In this case, you would enter data similar to the
data shown below into an Excel spreadsheet. To make a
Pareto diagram based on data in one column only, select
the range in the column to include in the Pareto. Then
select the Pareto diagram option on the toolbar.
Pareto Dialog Box
When you select the Pareto Diagram option (PD) on the SPC toolbar, you will get the form below. This
example is for Option 1: Basic Pareto Diagram above with the product names selected prior to the
selecting the Pareto diagram option from the SPC toolbar. There are two pages on the form: Input
Ranges/Chart Name and Options. The Input Ranges/Chart Name always comes up first. The entries on
both pages are given below. Selecting OK at the bottom of each page will run the program. Selecting
Cancel will cancel the program. The Switch Tabs button can be used to switch between the two pages.
Week Product Number of Returns
1 A 4 1 B 2 1 C 12 1 D 3 2 A 0 2 B 3 2 C 1 2 D 4 3 A 4 3 B 2 3 C 5 3 D 1 4 A 8 4 B 1 4 C 10 4 D 1
Date Product Returned
Reason
2/1/03 A Customer Did Not Need
2/4/03 A Broken
2/6/03 B Wrong Quantity
2/9/03 C Wrong Quantity
2/11/03 A Salesman Ordered Wrong
2/14/03 A Wrong Quantity
2/14/03 D Wrong Quantity
1/2/00 B Broken
2/23/03 A Customer Did Not Need
2/24/03 D Salesman Ordered Wrong
3/1/03 A Wrong Quantity
3/2/03 A Wrong Quantity
8 ©2007 Business Process Improvement
Input Ranges/Chart Name Page
Enter Category Range: This is the range
containing the categories (used for Options 1
and 2 above). The default value is what is
selected prior to selecting the Pareto Diagram
option on the toolbar.
Enter Frequency Range: This is the range
containing the frequencies for Options 1 and 2
above. The default value is the range next to
the categories (but the categories and
frequencies do not have to be adjacent.
Name of Chart: This is very important. This
will be the name of the worksheet tab that
contains the chart in your workbook.
Include Cumulative Line Select “Yes” to
include a cumulative line. The default value is
“No.”
Categories On: Selecting X axis puts the
categories on the x (horizontal) axis. Select Y axis places the categories on the Y axis. This is
helpful if the categories have long names. You cannot use a cumulative line if the categories are
on the Y axis.
Enter Pareto Diagram Title: The default title is “Pareto Diagram.” Enter the title you want to
appear above the chart.
Enter X-Axis (Category) Label: If there is a title in the cell about the first frequency selected, this
is the default entry. Otherwise, the label is left blank. Enter the category label you want for the
x-axis.
Enter Y-Axis (Frequency) Label: If there is a title in the cell above the frequency range, this is the
default entry. Otherwise, the label is left blank. Enter the frequency label you want for the y-
axis.
Data in: Select columns or rows depending on
how the data is entered into the spreadsheet.
The program selects one or the other
depending on the range selected prior to
selecting PD on the SPC toolbar.
Dates of Data Collection: Add the starting
date and ending dates of data collection.
These dates are optional. If entered, they will
appear in a dialog box in the lower left-hand
corner of the chart.
Options Page
Calculation Options: This is Option 2: Basic
Pareto Diagram but Program Calculates the
Totals. Select “Yes” if you want the program
to total the frequency results for the various
categories. “No” is the default value. Once
you select “Yes”, you must select the option
you want. Most of the time it will be “Sum,”
9 ©2007 Business Process Improvement
but there are other options including count, average, and standard deviation.
Pareto on One Column? This is Option 3: Pareto Diagram Based on One Column. Select “Yes”
if the data are in one column. The “Data Range” contains the worksheet range containing the
data. The default value is the range that is selected prior to PD being selected on the toolbar.
“Include Frequencies >= to” is used to determine what frequencies you want to include in the
chart. For example, if you enter 3, only those items that occur three or more times will be
included in the chart.
Examples
Below are the results for Options 2 and 3 using the data given above.
Option 2: Summing the results for each week
Option 3: Reasons for return in one column
Pareto Diagram
28
16
98
46%
72%
87%
100%
0
10
20
30
40
50
60
C Total A Total D Total B Total
Product
Nu
mb
er
of
Re
turn
s
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Pe
rcen
t
Pareto Diagram
6
2 2 2
50.0%
66.7%
83.3%
100.0%
0
2
4
6
8
10
12
Wrong Quantity Broken Customer Did Not Need Salesman Ordered Wrong
Reason
0.0%
10.0%
20.0%
30.0%
40.0%
50.0%
60.0%
70.0%
80.0%
90.0%
100.0%
Pe
rcen
t
10 ©2007 Business Process Improvement
Histograms
A histogram is a bar chart that provides a snapshot in time of the variation in a process. It tells us how
often a value or range of values occurred in a given time frame. A histogram will tell us the most
frequently occurring value (the mode), the overall range, and the shape of the distribution (e.g., bell-
shaped, skewed, bimodal, etc.). It is best to have 50 to 100 data points to construct a histogram, if
possible. This program will construct a histogram from the raw data. It will automatically determine the
number of classes (bars) as well as the class width. You have the opportunity to change the number of
classes. An example of a histogram is shown below.
Data Entry
Enter the data you want to use in the histogram into a worksheet. The data
can be in any number of rows and columns. Select the cells containing the
data for the histogram as shown to the right. Then select the histogram
option (H) from the SPC toolbar.
Histogram Dialog Box
81 77 75 74 77 73 77 74 76 75 79 74 74 79 73 75 75 74 75 80 80 79 72 78 73 74 74 73 75 74 77 75 75 72 75 74 76 75 74 74 78 75 76 76 78 77 78 75 74 76 77 76 72 73 79 82 73 75 74 79 77 73 72 75 73 73 76 76 76 75 74 72 76 76 76 74 79 79 75 81 77 74 77 71 84 74 79 70 77 74 73 77 76 74 81 75
Histogram of Yields
1 (1.0%)
0 (0.0%)
1 (1.0%)
3 (3.1%)
2 (2.1%)
8 (8.3%)
4 (4.2%)
11 (11.5%)
13 (13.5%)
17 (17.7%)
19 (19.8%)
10 (10.4%)
5 (5.2%)
1 (1.0%)1 (1.0%)
0
2
4
6
8
10
12
14
16
18
20
69.5 to
70.5
70.5 to
71.5
71.5 to
72.5
72.5 to
73.5
73.5 to
74.5
74.5 to
75.5
75.5 to
76.5
76.5 to
77.5
77.5 to
78.5
78.5 to
79.5
79.5 to
80.5
80.5 to
81.5
81.5 to
82.5
82.5 to
83.5
83.5 to
84.5
Measurement
Fre
qu
en
cy
Descriptive Stats
Mean=75.625
Standard Error=0.26
Median=75
Standard Deviation=2.547
Variance=6.489
Sum=7260
Count=96
Maximum=84
Mininum=70
Range=14
Kurtosis=0.6157
Skewness=0.7079
11 ©2007 Business Process Improvement
When you select the histogram option (H) on the SPC toolbar, you will get the dialog box shown to the
left. Each entry is discussed below.
Enter location of Values: This is the range containing the values for the histogram. The default
range is the range selected on the worksheet before selecting the histogram option on the toolbar.
Enter Histogram Title: This is the title that goes on the histogram chart. The default value is
“Histogram.”
Enter Y-Axis (Vertical Label): This is the vertical axis label. The default is “Frequency.”
Enter X-Axis (Horizontal Label): This is the horizontal axis label. The default is “Measurement.”
Name of Chart: This is very important. This will be the name of the worksheet tab that contains
the chart in your workbook.
Enter Number of Integers to Right of Decimal: This is the rounding that is used in the data. For
example, if the data contains whole numbers, this value is 0 (the default value). If the data has
one decimal point to the right of the data (as shown in the data above), this value is 1. It is used
to set the class boundaries.
Dates of Data Collection: Add the starting date and ending dates of data collection. These dates
are optional. If entered, they will appear in a dialog box in the lower left-hand corner of the chart.
Include Descriptive Statistics?” If you want the descriptive statistics on the chart, select “Yes.”
The descriptive statistics include the average, standard deviation, count, etc. The default value is
“Yes.” There is also the option to “Select Which to Include.” This option allows you to
determine which of the descriptive statistics you want to include. If you select this option, you
will see the dialog box below. Select which statistics you want to include. The statistics you
select will remain the same if you update the histogram. You can “Check All” or “Uncheck All”
if desired.
12 ©2007 Business Process Improvement
The number of classes (bars) on the histogram is determined automatically
by the program. It is set as the square root of the number of data
points in the range. Once the histogram is made, you can change
the number of classes. There is a button in the upper left hand
corner of the histogram chart that is used for this (you will see it
when the histogram is first made).
When you select this button on the chart, you will get the dialog
box to the right. There are essentially two options:
Enter the number of classes you want and select OK.
The chart will then be displayed.
Enter the class width and enter the lower bound. This
lets you set the starting point for the histogram (the lower
bound) and the width of each class. The number of
classes is set by these two values.
You also have the option to view the frequency distribution for the
histogram. This is done by selecting the button with the caption
“View/Hide Frequency Distribution.” This button appears the first time the histogram is made. An
example of a histogram with the frequency distribution added is shown below. Selecting the button again
hides the frequency distribution.
Change Number of Classes
View/Hide Frequency Distribution
Histogram of Yields
1 (1.0%)
0 (0.0%)
1 (1.0%)
3 (3.1%)
2 (2.1%)
8 (8.3%)
4 (4.2%)
11 (11.5%)
13 (13.5%)
17 (17.7%)
19 (19.8%)
10 (10.4%)
5 (5.2%)
1 (1.0%)1 (1.0%)
0
2
4
6
8
10
12
14
16
18
20
69.5 to
70.5
70.5 to
71.5
71.5 to
72.5
72.5 to
73.5
73.5 to
74.5
74.5 to
75.5
75.5 to
76.5
76.5 to
77.5
77.5 to
78.5
78.5 to
79.5
79.5 to
80.5
80.5 to
81.5
81.5 to
82.5
82.5 to
83.5
83.5 to
84.5
Measurement
Fre
qu
en
cy
Descriptive Stats
Mean=75.625
Standard Error=0.26
Median=75
Standard Deviation=2.547
Variance=6.489
Sum=7260
Count=96
Maximum=84
Mininum=70
Range=14
Kurtosis=0.6157
Skewness=0.7079
Classes Freq. Rel. Freq.
69.5 to 70.5 1 1.0%
70.5 to 71.5 1 1.0%
71.5 to 72.5 5 5.2%
72.5 to 73.5 10 10.4%
73.5 to 74.5 19 19.8%
74.5 to 75.5 17 17.7%
75.5 to 76.5 13 13.5%
76.5 to 77.5 11 11.5%
77.5 to 78.5 4 4.2%
78.5 to 79.5 8 8.3%
79.5 to 80.5 2 2.1%
80.5 to 81.5 3 3.1%
81.5 to 82.5 1 1.0%
82.5 to 83.5 0 0.0%
83.5 to 84.5 1 1.0%
13 ©2007 Business Process Improvement
Attribute Control Charts
This program handles p, np; c and u attribute control charts. The data
entry depends on the type of chart you are using. You access this
feature by selecting the attribute control chart option (ATT) on the SPC
toolbar. You will see the dialog box to the right. Select the type of
chart you want to make.
p Charts
A p control chart is used to examine the variation in the proportion (or percentage) of defective items in a
group of items. An item is defective if it fails to conform to some preset specification (operational
definition). The p control chart is used with "yes/no" attributes data. This means that there are only two
possible outcomes: either the item is defective or it is not defective. For example: either the phone is
answered or it is not answered.
An example of a p chart generated by this program is given below. In this example, the percentage of
telemarketing calls that result in an order each day is being examined. "n" is the subgroup size (the
number of telemarketing calls made each day). "np" is the number of "defective" items -- in this case, the
number of calls that result in an order. "p" is the proportion defective and is determined by p = np/n. For
example, on the first day there were 40 telemarketing calls made (n = 40). Of these, 5 resulted in an order
(np = 5). Thus, p = np/n = 5/40 = 0.125 or 12.5%. In the chart below, 12.5% is the point plotted on
2/1/2003.
The values of p are plotted
over time. The average
( p ), the upper control limit
(UCL) and the lower control
limit (LCL) are calculated
using the equations below.
The average is plotted as a
green solid line and the
control limits are plotted as
red dashed lines. The
control limits in this
example vary because the
subgroup size varies. The
values for the average and
control limits (based on the
average subgroup size, n )
are also printed on the chart
or in the title depending on
the option selected.
n
npp
n
)p1(p3pUCL
n
)p1(p3pLCL
p Control Chart
Avg=19.47
UCL=36.16
LCL=2.780%
5%
10%
15%
20%
25%
30%
35%
40%
45%
2/1/
2003
2/2/
2003
2/3/
2003
2/4/
2003
2/5/
2003
2/6/
2003
2/7/
2003
2/8/
2003
2/9/
2003
2/10
/200
3
2/11
/200
3
2/12
/200
3
2/13
/200
3
2/14
/200
3
2/15
/200
3
Subgroup Number
% D
efe
cti
ve
14 ©2007 Business Process Improvement
The above control limits are not valid for the “small np case.” This occurs when n p < 5 or n(1- p )< 5.
In this case, the program automatically calculates the control limits using the binomial distribution.
Data Entry
The p chart monitors the fraction or percentage of defective
items in a group of items. Subgroup number (like the date
shown to the right), subgroup size (n) and number
nonconforming (np) are required as shown in the example
below. After entering the data, highlight the subgroup
numbers (in the example these are the dates). Then select the
attribute control chart option (Att) from the SPC toolbar and
select the p control chart option.
p Chart Dialog Box
Once you select the p control chart option, you will get the
dialog box shown to the right. There are two pages for this
dialog box. Each page is discussed below. Selecting OK
at the bottom of each page will run the program. Selecting
Cancel will cancel the program. The Switch Tabs button
can be used to switch between the two pages.
Input Ranges/Chart Name/Labels Page
Range containing the subgroup identifiers: This is
the range containing the subgroup numbers (dates
in the above example). The default value is the
range selected on the worksheet prior to selecting
the attribute control option on the toolbar.
Range containing the n values: This is the range
containing the subgroup size (n). The default
value is the range next to the subgroups unless you selected multiple ranges using the control key.
Range containing the np values: This is the range containing the number non-conforming (np).
The default value is the range next to the n values unless you selected multiple ranges using the
control key.
Name of Chart: This is very important. Decide what you want to call the chart. This will be the
name of the sheet that contains the chart in your workbook.
Control Chart Title: This is the title that goes on the control chart. The default value is “p
Control Chart.”
Y-Axis Label: This is the vertical axis label. The default value is “% Defective.”
X-Axis Label: This is the horizontal axis label. The default value is “Subgroup Number”
Date Number of Telemarketing Calls (n)
Number that Result in an Order (np)
2/1/2003 40 5 2/2/2003 63 10 2/3/2003 47 12 2/4/2003 52 7 2/5/2003 34 3 2/6/2003 59 21 2/7/2003 36 12 2/8/2003 71 7 2/9/2003 53 11 2/10/2003 50 3 2/11/2003 41 12 2/12/2003 48 10 2/13/2003 67 5 2/14/2003 45 12 2/15/2003 54 18
15 ©2007 Business Process Improvement
Data in: Select columns or rows depending on how the data is entered into the spreadsheet. The
program selects one or the other depending on the range selected prior to selecting Att on the SPC
toolbar.
Control Limits/Other Options Page
Test for Control: There are two options:
points beyond the limits and the rules of
seven (seven in a row above or below the
average, or seven in a row trending up or
trending down).
Automatic Update of Limits?: This
determines if the control limits are
automatically updated when you add
additional data to the chart. Select “Yes” if
you want the control limits to automatically
update; no if you don’t want the limits to
automatically update. The default is yes.
Based Limits on Average n? Select no to
change the limits each time the subgroup size
changes. Select Yes to base the limits on the
average subgroup size. The default value is
No.
Print Average/Limits: Selecting “On Avg. and Limits” will print these on the lines in the chart.
Selecting “In Chart Title” will print the values in the chart title.
Target for Average: This is the target value for the variable. It is not required.
Use Percent for Format?: Select yes to format the chart as percent; no to format the chart as a
general number.
Dates of Data Collection: Add the starting date and ending dates of data collection. These dates
are optional. If entered, they will appear in a dialog box in the lower left-hand corner of the chart.
Rounding to Use in Titles: This the rounding to use for the average and control limits printed in
the title. The default value is determined by the program.
16 ©2007 Business Process Improvement
np Control Charts
A np control chart is used to monitor the variation in the number of defective items in a group of items.
With this chart, the subgroup size (n), the number of items in the group, must be the same each time. An
item is defective if it fails to conform to some preset specification (operational definition). The np control
chart is used with "yes/no" attributes data. This means that there are only two possible outcomes: either
the item is defective or it is not defective. For example: either the phone is answered or it is not
answered.
An example of a np chart generated by this program is shown below. In this example, the number of
defective invoices each day is being tracked. The control chart is developed by taking a random sample
of 100 invoices each day and determining the number that are defective. In this case, the subgroup size is
constant (100). np is the number of defective items. For example, on day one, there were 22 defective
invoices.
The values of np are plotted
over time. The average
( pn ), the upper control
limit (UCL), and the lower
control limit (LCL) are
calculated using the
equations below. k is the
number of subgroups used
in the calculations (k = 15 in
this chart). The average is
plotted as a solid green line
and the control limits are
plotted as red dashed lines.
The values for the average
and control limits, along
with the subgroup size, are
printed on the chart or in the
chart title depending on the
option selected.
k
nppn
n
pnp )p1(pn3pnUCL )p1(pn3pnLCL
The above control limits are not valid for the “small np case.” This occurs when n p < 5 or n(1- p )< 5.
In this case, the program automatically calculates the control limits using the binomial distribution.
np Control Chart
Avg=24.87
UCL=37.83
LCL=11.9
0
5
10
15
20
25
30
35
40
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Subgroup Number
Nu
mb
er
De
fec
tiv
e
17 ©2007 Business Process Improvement
Data Entry
A np control chart monitors the number of defective items in a constant
subgroup size. The required data to enter into the spreadsheet are the
subgroup numbers and the number of defective items as shown to the right.
Select the subgroup numbers (shaded area). Then select the attribute control
chart option (Att) from the SPC toolbar and select the np control chart
option.
np Chart Dialog Box
After selecting the np chart option, you will get the two
page dialog box shown here. Only items not described
in the p chart dialog box are explained below. See page
14 for the p chart dialog box.
Input Ranges/Chart Name/Labels Page
Subgroup size for np chart: Enter the constant
subgroup size. It is required.
Control Limits/Other Options Page
All entries are explained in the p control chart
section. See page 14 for the p chart dialog box.
Day Number
Number of Defective Invoices (np)
1 22 2 33 3 24 4 20 5 18 6 24 7 24 8 29 9 18 10 27 11 31 12 26 13 31 14 24 15 22
18 ©2007 Business Process Improvement
c Control Charts
A c control chart is used to monitor the variation in the number of defects. A defect occurs when
something does not meet a preset specification (operational definition). A c control chart is used with
counting type attributes data (e.g., 0, 1, 2, 3). These are whole numbers. You cannot have 1/2 defect. In
addition, to use a c control chart, two other conditions must be true:
The opportunity for defects to occur must be large.
The actual number that occurs must be small.
With a c control chart, we are often looking at an area, not a group of items. For example, we may use a c
control chart to monitor injuries in a chemical plant. In this case, the subgroup is the plant. The
opportunities for injuries to occur is large; the actual number that occur is small relative to the
opportunity. With a c control chart, the area of opportunity for defects to occur must be constant.
An example of a c control
chart generated using this
program is given to the
right. In this example, the
number of returned goods
to a distributor is being
tracked. “c” is the
number of returned goods
each day. For the first
date, there were 20 goods
returned.
The values of c are plotted
over time. The average
( c ), the upper control
limit (UCL), and the
lower control limit (LCL)
are calculated using the
equations below. k is the
number of subgroups used in the calculations (k = 15 in the above chart). The average is plotted as a
solid green line and the control limits are plotted as red dashed lines. The values for the average and
control limits, along with the subgroup size, are printed on the chart or in the chart title depending on the
option selected.
k
cc
c3cUCL c3cLCL
These control limits are valid only if c > 3. The program will automatically use the Poisson Distribution
to determine the control limits if the average is less than 3.
c Control Chart
Avg=23.13
UCL=37.56
LCL=8.7
0
5
10
15
20
25
30
35
40
45
50
2/1/
2003
2/2/
2003
2/3/
2003
2/4/
2003
2/5/
2003
2/6/
2003
2/7/
2003
2/8/
2003
2/9/
2003
2/10
/200
3
2/11
/200
3
2/12
/200
3
2/13
/200
3
2/14
/200
3
2/15
/200
3
Subgroup Number
Nu
mb
er
of
De
fec
ts
19 ©2007 Business Process Improvement
Data Entry
The c control chart is used to monitor the variation in the number of defects in
a constant subgroup size. Require data include the subgroup number and the
number of defects. An example of a c chart data is given to the right. To
make a c chart, select the subgroup numbers in the worksheet (shaded area).
Then select the attribute control chart option (Att) from the SPC toolbar and
select the c control chart option.
c Chart Dialog Box
After selecting the c Chart option in the dialog box, you
will get a two page dialog box shown here. Only items
not described in the p chart dialog box are explained
below. See page 14 for the p chart dialog box.
Input Ranges/Chart Name/Labels Page
Range containing c values: The range
containing the number of defects. The default
value is the column next to the subgroup
identifiers unless you selected multiple ranges
using the control key.
Control Limits/Other Options Page
All entries are explained in the p control chart
section. See page 14 for the p chart dialog box.
Day Number of
Returned Goods (c)
2/1/2003 20 2/2/2003 24 2/3/2003 14 2/4/2003 32 2/5/2003 28 2/6/2003 16 2/7/2003 19 2/8/2003 32 2/9/2003 27
2/10/2003 25 2/11/2003 24 2/12/2003 12 2/13/2003 17 2/14/2003 44 2/15/2003 13
20 ©2007 Business Process Improvement
u Control Charts
A u control chart is used to monitor the variation in the number of defects. A defect occurs when
something does not meet a preset specification (operational definition). A u control chart is used with
counting type attributes data (e.g., 0, 1, 2, 3). These are whole numbers. You can not have 1/2 defect. In
addition, to use a u control chart, two other conditions must be true:
• The opportunity for defects to occur must be large.
• The actual number that occur must be small.
With a u control chart, we are often looking at an area of opportunity for defects to occur. A u control is
similar to a c control chart, except that the area of opportunity for defects to occur is not constant.
An example of a u chart generated by this program is given below. In this example, radiators are being
checked for leaks. Each day, the number of radiators assembled is counted. This is the area of
opportunity for leaks to occur (n). The number of leaks found when two portions of the radiator were
assembled for the first time is also counted (c). For example, on the first day, 39 radiators were hooked
up. There were 14 leaks detected. In this case, u = c/n = 14/39 = .359
The u values are plotted
over time. The average
( u ), the upper control
limit (UCL) and the lower
control limit (LCL) are
calculated using the
equations below. There is
no LCL in this example
(it is negative). The
average is plotted as a
green solid line and the
control limits are plotted
as red dashed lines. The
values for the average and
control limits (based on
the average subgroup size,
n ) are printed on the
chart or in the chart title
depending on the option
selected.
n
cu
n
u3uUCL
n
u3uLCL
The control limits will be based on the actual subgroup size for each point. If the subgroup size varies,
the control limits will also vary (as shown in the above example). These control limits are valid only if
c > 3. The program will automatically use the Poisson Distribution to determine the control limits if the
average is less than 3.
u Control Chart
Avg=0.15
UCL=0.32
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
2-Jun 3-Jun 4-Jun 5-Jun 6-Jun 7-Jun 8-Jun 9-Jun 10-Jun 11-Jun 12-Jun 13-Jun 14-Jun 15-Jun 16-Jun
Subgroup Number
De
fects
pe
r In
sp
ecti
on
Un
it
21 ©2007 Business Process Improvement
Data Entry
A u control chart is used to monitor the number of defects in
a changing subgroup size. The required data to be entered
into the spreadsheet are the subgroup numbers, the subgroup
size, and the number of defects. To make a u chart, select the
subgroup numbers (shaded area), select the attribute control
chart option (Att) from the SPC toolbar, and then select the u
control chart option.
u Chart Dialog Box
Once you select the u chart option on the dialog box, you
will get the two page dialog box shown here. Only items not
described in the p or c chart dialog box are explained below.
See page 14 for the p chart dialog box.
Input Ranges/Chart Name/Labels Page
Range containing n values: The range containing the
subgroup size. The default value is the column next
to the subgroup identifiers unless you selected
multiple ranges using the control key.
Range containing c values: The range containing the
number of defects. The default value is the column
next to n unless you selected multiple ranges using
the control key.
Inspection Unit: Enter the size of the inspection unit.
For example, you can have an inspection unit of 1
radiator, 10 radiators, 20 radiators, etc. This choice
impacts the scaling of the chart.
Control Limits/Other Options Page
All entries are explained in the p control chart
section. See page 14 for the p chart dialog box.
Date Number of Radiatiors
Assembled (n)
Number of Leaks (c)
2-Jun 39 14 3-Jun 45 4 4-Jun 46 5 5-Jun 48 13 6-Jun 40 6 7-Jun 58 2 8-Jun 50 4 9-Jun 50 11
10-Jun 50 8 11-Jun 50 10 12-Jun 32 3 13-Jun 50 11 14-Jun 33 1 15-Jun 50 3 16-Jun 50 6
22 ©2007 Business Process Improvement
Variable Control Charts
You access these control charts by selecting the variable control chart
option (Var) on the SPC toolbar. You will then get the dialog box
shown to the right. Select the option you want. The options are:
X -R control charts
X -s control charts
Moving average and moving range control charts
X-MR (individuals) control charts
Table X-MR (for making multiple individuals charts at once)
Run charts
There is also an option to make subgroups from data in a single
column. This option is described latter in this section.
The dialog boxes for all the options are very similar. The X -R control chart is used to show how the
program works.
X -R Control Chart
An X -R control chart is used to examine the variation in variables data. Variables data are
“measurements” (e.g., height, weight, time, dollars, density). This control chart is used when you have
lots of data and a method of rationally subgrouping the data. An example of an X -R chart is given on the
next page. In this example, sales per day are monitored. A subgroup is made up of the results for one
week. The subgroup size (n) in this case is 5.
The X -R chart is really two charts. The top chart is the X chart. This chart looks at the variation in
subgroup averages. The subgroup average is the average of the individual results in the subgroup. The
bottom chart is the range chart. The subgroup range is the largest result minus the smallest result in the
subgroup.
The values of X and the moving range are plotted over time. The average and control limits for both
charts are calculated using the equations below. The average is plotted as a green solid line and the
control limits are plotted as red dashed lines on both charts. For the equations below, k is the number of
subgroups. A2, D3, and D4, d2 are constants used in the calculations for charts. See the e-zines on our
website for more information about these constants.
X Chart Equations:
X
X
k UCL X A 2R LCL X A2R
Range Chart Equations:
R
R
k UCL D4R LCL D3R
ˆ R
d2
The values for the average and control limits are printed on the respective charts.
23 ©2007 Business Process Improvement
Xbar Chart
Avg=30.2
UCL=33.8
LCL=26.6
26
27
28
29
30
31
32
33
34
35
2/1/2003 2/8/2003 2/15/2003 2/22/2003 3/1/2003 3/8/2003 3/15/2003 3/22/2003 3/29/2003 4/5/2003 4/12/2003 4/19/2003 4/26/2003 5/3/2003 5/10/2003
Subgroup Number
Su
bg
rou
p A
vera
ge
R Chart
Avg=6.3
UCL=13.3
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
2/1/2003 2/8/2003 2/15/2003 2/22/2003 3/1/2003 3/8/2003 3/15/2003 3/22/2003 3/29/2003 4/5/2003 4/12/2003 4/19/2003 4/26/2003 5/3/2003 5/10/2003
Subgroup Number
Su
bg
rou
p R
an
ge
24 ©2007 Business Process Improvement
Data Entry
The data input for this type of chart is shown
to the right. The subgroup identifiers (week of
in this example) are in the first column. In
this example, data is collected once a day
every weekday. The results for one week are
used to form the subgroup (n = 5). Select the
subgroup identifiers and data (shaded). Then
select the variable control chart option (Var)
from the SPC toolbar. You will get the dialog
box above. Select the X -R chart option and
select OK.
X -R Chart Dialog Box
You will get the three-page dialog box shown
to the right. Each page is discussed below.
Selecting OK at the bottom of each page will
run the program. Selecting Cancel will cancel
the program. The Next Page and Previous
page buttons can be used to switch between the
three pages.
Input Ranges/Chart Name/Labels Page
Range Containing the Subgroup
Identifiers: This is the range that
contains the subgroup numbers. The
default value is the first column in the
range you selected prior to selecting
the variable control chart option in the
toolbar.
Range Containing the Data: This is
the range containing the data. The default range is the range you selected prior to selecting the
variable control chart option excluding the first column in the range.
Subgroup Size: This is the subgroup size. The default value is the number of columns minus one
in the range you selected prior to selecting the variable control chart option in the toolbar. THIS
VALUE DETERMINES WHAT DATA IS INCLUDED.
Name of Chart: This is very important. Decide what you want to call the chart. This will be the
name of the sheet that contains the chart in your workbook.
Xbar Chart Title and Labels
o Title: This is the title that goes on the control chart. The default title is Xbar Chart.
o Y-Axis Label: This is the vertical axis label. The default label is Subgroup Average.
o X-Axis Label: This is the horizontal axis label. The default label is Subgroup Number.
R Chart Title and Labels
o Title: This is the title that goes on the range chart. The default title is R Chart.
o Y-Axis Label: This is the vertical axis label. The default label is Subgroup Range.
Chart Options
Week of Monday Tuesday Wednesday Thursday Friday 2/1/2003 33.0 33.1 26.4 28.3 28.9 2/8/2003 30.0 30.1 29.2 31.5 28.4
2/15/2003 31.8 29.4 28.0 26.9 32.2 2/22/2003 28.5 34.0 33.6 29.7 33.4 3/1/2003 27.2 27.6 30.6 30.1 27.4 3/8/2003 30.5 30.5 28.1 37.7 28.7
3/15/2003 35.4 31.3 27.8 31.3 33.0 3/22/2003 33.6 33.3 26.4 32.4 34.1 3/29/2003 35.8 34.1 30.1 30.3 26.1 4/5/2003 30.4 32.6 32.5 25.2 32.1
4/12/2003 26.9 32.4 29.0 26.8 29.3 4/19/2003 28.0 28.2 25.5 31.1 34.4 4/26/2003 29.1 31.6 29.0 33.1 30.9 5/3/2003 26.4 30.8 34.0 27.0 31.7
5/10/2003 27.4 26.0 28.2 27.9 27.3
25 ©2007 Business Process Improvement
o Xbar Chart Only: only the X chart is constructed. This is the default option
o Xbar and R Charts – Different Worksheets: Both the X and range charts are constructed
but on different worksheets.
o Xbar and R Charts – Same Worksheet: Both the X and range charts are constructed on
the same worksheet.
Data in: Select columns or rows depending on how the data is entered into the spreadsheet. The
program selects one or the other depending on the range selected prior to selecting the variable
control chart option (Var) on the SPC toolbar.
Options Page
Tests for Control: There are three
options for interpreting the charts for
control: points beyond the limits, the
rules of seven (seven in a row above or
below the average or trending up or
down) and the zone tests (zones A, B, C,
stratification, mixtures). The zone tests
are not applied to range or standard
deviation charts. If an out of control
situation is detected, the points on the
chart will be in red.
Target for Average: This is the target
value for the variable. It is not required.
Print Average/Limits: There are two
options.
o On Avg. and Limits: This option
prints the average and control
limits values on the lines. This is the default option.
o In Chart Title: This option prints the values in the control chart title.
Allow values below 0?: Sometimes, it is not possible for the variable to have values below 0. If
that is the case, select “No” for this option. The default value is “Yes.”
Generate New/Update Existing Capability Chart? Select Yes to do a process capability analysis.
The default option is No. See the Process Capability section in this manual for more information.
Dates of Data Collection: Add the starting date and ending dates of data collection. These dates
are optional. If entered, they will appear in a dialog box in the lower left-hand corner of the chart.
Rounding to Use in Titles: This is the rounding to use for the average and control limits printed in
the title. If the first cell in the range has been formatted, this format is used. If not, the value
entered here is used for rounding. The program will estimate the rounding in the data.
26 ©2007 Business Process Improvement
Control Limit Option
Automatic Update of Limits?: This
determines if the control limits are
automatically updated when you add
additional data to the chart. Select
“Yes” if you want the control limits to
automatically update; No if you don’t
want the limits to automatically
update. The default value is Yes.
The rest of this dialog box is used only if you
want to change the default way the program
calculates the control limits. The program uses
the equations given in this manual for the +/-
three sigma limits. There are two other
options you have:
Base control limits on +/- “x” sigma:
You can select the sigma limits you want to use in the control chart. The default value is 3. DO
NOT CHANGE ANYTHING IF YOU WANT THE PROGRAM TO USE THE STANDARD
CONTROL LIMIT EQUATIONS. You can also add two additional lines to the charts (above
and below the average). Any values entered for these additional lines are ignored if the 3 sigma
limits are being used. If you use any other value than 3 sigma for the control limits, the zone tests
for out of control points will not be applied since it is no longer valid.
Enter your own limits: You may also enter your own values for the X chart control limits. An
additional two lines can also be added to the chart. The values entered here must be between the
average and the UCL entered. The program will add them automatically to the area between the
average and the LCL.
27 ©2007 Business Process Improvement
X -s Control Charts
A X -s chart is very similar to the X -R chart. Instead of using the subgroup range, the X -s chart uses
the subgroup standard deviation to determine process variability. It is usually used when your subgroup
is greater than or equal to 10.
For the equations below, k is the number of subgroups. A3, B3, and B4, C4 are constants used in the
calculations for the charts.
X Chart Equations:
X
X
k UCL X A3s LCL X A3s
s Chart Equation:
s
s
k UCL B4s LCL B3s
ˆ s
c4
The data entry requirements and the dialog boxes for these two charts are the same as the X -R control
chart. Please refer to the instructions above for the X -R control charts (page 22). The X -s charts for the
same data as used above for the X -R charts are shown below.
Xbar Chart
Avg=30.2
UCL=33.9
LCL=26.5
26
27
28
29
30
31
32
33
34
35
2/1/2003 2/8/2003 2/15/2003 2/22/2003 3/1/2003 3/8/2003 3/15/2003 3/22/2003 3/29/2003 4/5/2003 4/12/2003 4/19/2003 4/26/2003 5/3/2003 5/10/2003
Subgroup Number
Su
bg
rou
p A
vera
ge
s Chart
Avg=2.6
UCL=5.4
0.0
1.0
2.0
3.0
4.0
5.0
6.0
2/1/2003 2/8/2003 2/15/2003 2/22/2003 3/1/2003 3/8/2003 3/15/2003 3/22/2003 3/29/2003 4/5/2003 4/12/2003 4/19/2003 4/26/2003 5/3/2003 5/10/2003
Subgroup Number
Su
bg
rou
p S
tan
dard
Devia
tio
n
28 ©2007 Business Process Improvement
X-MR (Individuals) Control Charts
An individuals control chart (with a moving range of two) is used to examine the variation in variables
data. Variables data are “measurements” (e.g., height, weight, time, dollars, density). This chart is used
when you have limited data (for example, one data point per day or per week). It is also useful when data
are difficult to obtain. To use this chart, the individual measurements should be normally distributed, i.e.,
a histogram of the individual measurements is bell-shaped.
An example of an individuals control chart is given below. In this example, the dollar value of accounts
receivable past due 90 days is being monitored. An individuals control chart is really two charts. The top
chart is the X chart where the individual result (accounts receivable past due 90 days for a week) is
plotted. For example, the first point corresponds to $110,000 in past due receivables for the first week
(2/6). The second point corresponds to $104,000 for the second week (2/13).
Individuals Chart
Avg=103.6
UCL=124.3
LCL=82.9
79
84
89
94
99
104
109
114
119
124
129
2/5/
2003
2/12
/200
3
2/19
/200
3
2/26
/200
3
3/5/
2003
3/12
/200
3
3/19
/200
3
3/26
/200
3
4/2/
2003
4/9/
2003
4/16
/200
3
4/23
/200
3
4/30
/200
3
5/7/
2003
5/14
/200
3
5/21
/200
3
5/28
/200
3
6/4/
2003
6/11
/200
3
6/18
/200
3
Sample Number
Resu
lt
Moving Range Chart
Avg=7.8
UCL=25.5
0
5
10
15
20
25
30
2/5/
2003
2/12
/200
3
2/19
/200
3
2/26
/200
3
3/5/
2003
3/12
/200
3
3/19
/200
3
3/26
/200
3
4/2/
2003
4/9/
2003
4/16
/200
3
4/23
/200
3
4/30
/200
3
5/7/
2003
5/14
/200
3
5/21
/200
3
5/28
/200
3
6/4/
2003
6/11
/200
3
6/18
/200
3
Sample Number
Mo
vin
g R
an
ge
The bottom chart is the moving range chart. The moving range between consecutive points is plotted on
this chart. For example, the range between accounts receivable past due for 90 days between the week of
2/6 and 2/13 is $110,000 - $104,000 = $6,000. There is no range corresponding to the first data point on
the X chart.
The values of X and the moving range are plotted over time. The average and control limits for both
charts are calculated using the equations below. The average is plotted as a green solid line and the
control limits are plotted as red dashed lines on both charts. For the equations below, k is the number of
samples (individual X values).
29 ©2007 Business Process Improvement
X Chart Equations:
k
XX
R66.2XUCL R66.2XLCL
Moving Range Chart Equations:
1
k
RR R27.3UCL NoneLCL
128.1
Rˆ
The values for the average and control limits are printed on the respective charts
Data Entry
The only data required for an individuals control chart are the sample number
and the result as shown to the right. Select the sample numbers (shaded area).
Then select the variable control chart option (Var) on the SPC toolbar and
select the X-MR (Individuals) Chart option. Select OK and you will get the
two-page dialog box for the individuals control chart. This dialog box is the
same as for the X -R control chart. Please refer to the instructions above for
the X -R control charts.
Week of Accounts
Receivable 2/5/2003 110
2/12/2003 104 2/19/2003 98 2/26/2003 112 3/5/2003 113
3/12/2003 100 3/19/2003 89 3/26/2003 113 4/2/2003 109 4/9/2003 105
4/16/2003 108 4/23/2003 95 4/30/2003 101 5/7/2003 98
5/14/2003 100 5/21/2003 105 5/28/2003 103 6/4/2003 99
6/11/2003 112 6/18/2003 98
30 ©2007 Business Process Improvement
Moving Average/Moving Range (MA/MR) Charts
A moving average/moving range (MA/MR) chart is very similar to the X -R chart. The data entry
requirements are the same. Please refer to the X -R chart directions (page 22). The only major difference
in constructing a MA/MR chart is in how the subgroups are formed. The MA/MR chart reuses data. For
example, the data for the X-MR chart above could be regrouped into subgroup sizes of three using a
MA/MR chart. The first subgroup for the MA/MR chart is formed using the first three results (for the
weeks of 2/5, 2/12 and 2/19. The second subgroup for the MA/MR chart uses the weeks of 2/12 and 2/19
and then adds in the week of 2/26. This continues for each of the remaining samples. You use a MA/MR
chart when you have infrequent data that is not normally distributed. For MA/MR Chart
For the X-MR Chart
Subgroup Number
1 2 3
Week of Accounts
Receivable 1 110 104 98 2/5/2003 110 2 104 98 112 2/12/2003 104 3 98 112 113 2/19/2003 98 4 112 113 100 2/26/2003 112 5 113 100 89 3/5/2003 113 6 100 89 113 3/12/2003 100 7 89 113 109 3/19/2003 89 8 113 109 105 3/26/2003 113 9 109 105 108 4/2/2003 109
10 105 108 95 4/9/2003 105 11 108 95 101 4/16/2003 108 12 95 101 98 4/23/2003 95 13 101 98 100 4/30/2003 101 14 98 100 105 5/7/2003 98 15 100 105 103 5/14/2003 100 16 105 103 99 5/21/2003 105 17 103 99 112 5/28/2003 103 18 99 112 98 6/4/2003 99
6/11/2003 112 6/18/2003 98
The charts below are the output from the MA/MR chart for this data.
Moving Averge Chart
Avg=103.4
UCL=115.8
LCL=91
89
94
99
104
109
114
119
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Subgroup Number
Mo
vin
g A
vera
ge
Moving Range Chart
Avg=12.1
UCL=31.2
0
5
10
15
20
25
30
35
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Subgroup Number
Mo
vin
g R
an
ge
31 ©2007 Business Process Improvement
Table X-MR (Individuals) Chart
This option is used to generate multiple individual control charts at the same time. You can either
generate the charts one at a time (loops through the dialog box each time) or all at once using chart names
and labels that already are entered on the worksheet.
Generate Charts One at a Time
The data is entered as shown to the right. The sample numbers are in one
column. The results are in the adjacent columns. Select the sample numbers
(shaded area). Then select the variable control chart option (Var) on the SPC
toolbar and select the Table X-MR (Individuals) Chart option. Select OK and
you will get the two-page dialog box for the individuals control chart. Enter the
required information into the dialog box and select OK. The first individuals
chart will be constructed. The program then moves to the adjacent column and
shows the dialog box again. The program runs until it finds a blank cell for
sample 1.
Generate Charts All at Once
The data entry requirements are shown to the right. To use this option, the
unique name of the charts as well as the Y labels and X labels must be
entered into the worksheet as shown to the right. Select the sample numbers
(shaded area). Then select the variable control chart option (Var) on the SPC
toolbar and select the Table X-MR (Individuals) Chart option. Select OK
and you will get the two-page dialog box for the individuals control chart.
Select the second page. In the lower right hand side of the dialog box is
“Base Labels on Cell Locations and Run Automatically.” Select Yes. You
will then get the dialog box below.
Select the row containing the title (name of chart),
the Y labels, and the X labels. Then select OK.
This returns you to the individuals control chart
form. Select OK. This will generate all the charts
automatically.
Sample Result 1 Result 2
1 98.5 93.61
2 101.22 106.38
3 105.99 108.67
4 89.08 98.83
5 105.48 94.57
6 96.55 91.55
7 90.77 95.11
8 96.13 89.41
9 97.16 97.98
10 100.67 98.17
Name Chart 1 Chart 2
Y Label Y Y
X Label X X
Sample Result 1 Result 2
1 98.5 93.61
2 101.22 106.38
3 105.99 108.67
4 89.08 98.83
5 105.48 94.57
6 96.55 91.55
7 90.77 95.11
8 96.13 89.41
9 97.16 97.98
10 100.67 98.17
32 ©2007 Business Process Improvement
Run Charts
The data entry requirements and the dialog box for the run chart are essentially the same as the X-MR
chart. Please review to the information above on the X-MR chart (page 28).
Subgroup Maker: Make Subgroups from Column of Numbers
The program has the option to make subgroups from a single column of numbers. The data
must be in a single column as shown to the right.
Select the data you want to make into subgroups (the data only, not any sample
identifier).
Select the variable control chart option on the SPC toolbar
Select the “Make Subgroups from Single Column” option. You will get the dialog
box shown below.
The range listed is the range you selected
on the worksheet. You may change it here
if it is not correct.
Enter the subgroup size, not to exceed 25.
Select the Output Option you desire:
o First cell of output range on a
worksheet: enter the cell location
on the worksheet where you want
the subgroups formed.
o New worksheet: select this option
to put the subgroups on a new worksheet.
Select OK: The subgroups will be generated and
place based on your output option. You will then get
the Variables Chart dialog box to select the type of
chart you want to make and follow the instructions
for that chart.
Data
97.00
87.22
102.44
112.76
111.98
117.33
78.16
97.66
110.95
89.13
93.10
83.10
81.53
90.22
92.26
78.82
94.32
95.96
101.35
96.35
96.73
96.30
113.43
99.15
98.14
94.87
119.72
108.66
123.76
93.45
33 ©2007 Business Process Improvement
Process Capability
Process capability answers the question: Is the process capable of meeting specifications? Specifications
can be set by customers. Specifications could also be standards set by management for a process. For
example, the standard for days sales outstanding might be set by leadership to be less than 46 days. One
measure of process capability is the Cpk index. Another is Ppk. To determine the process capability, the
individual sample results should be normally distributed (the histogram is a bell shaped curve) and the
process should be in statistical control.
The value of Cpk is the minimum of two process capability indices. One process capability is Cpu, which
is the process capability based on the upper specification limit. The other is Cpl, which is the process
capability based on the lower specification limit. Algebraically, Cpk is defined as:
Cpk = Minimum (Cpu, Cpl)
'ˆ3
XUSLCpu
'ˆ3
LSLXCpl
where USL = upper specification limit and LSL = lower specification limit. Both Cpu and Cpl take into
account where the process is centered. The value of Cpk is the difference between the process average
( X ) and the nearest specification limit divided by three times the standard deviation ( '̂ ). This standard
deviation is the standard deviation estimated from a range or s chart. In determining Ppk, the standard
deviation is the actual standard deviation of the measurements.
Cpk values above 1.0 are desired. This means that essentially no product or service is being produced
above USL or below LSL. The figure below shows how the Cpk values are developed. If Cpk is less
than 1.0, this means that there is some product being produced out of specification.
X=
+3̂'X=
+2̂'X=
+1̂'X=
X=
-1̂'X=
-2̂'X=
-3̂'
LSL USL
X=
- LSL USL - X=
3̂' 3̂'
The process capability feature of this program includes Cpk and Ppk. The data used in the analysis can
either be data entered into a spreadsheet for this analysis alone or data that has been used for a control
chart previously.
34 ©2007 Business Process Improvement
An example of the process capability analysis performed by the program is shown below. The histogram
of the data is given along with a normal curve. The specification limits are added. The statistics are
given to the right. The percentages in parentheses give the % out of specification for that metric.
Capability Analysis
LSL=60 USL=80Nominal=70
0
5
10
15
20
25
30
35
57 62 67 72 77 82 87
Measurement
Fre
qu
en
cy
Statistics
Cp=1.34
Cpk= 0.59
Cpu= 0.59 (3.84%)
Cpl= 2.09 (0%)
Est. Sigma= 2.5
Pp=1.31
Ppk= 0.57
Ppu= 0.57 (4.36%)
Ppl= 2.04 (0%)
Sigma= 2.6
Average=75.6
Min=70
Max=84
Count=96
No. Out of Spec=5 (5.21%)
Kurtosis=0.62
Skewness=0.71
Sigma Level=1.77
DPMO=394117.9
The statistics include the following:
Cp: = (USL-LSL)/6 '̂ where '̂ is the estimated standard deviation from a range or s chart
Cpk: the minium of Cpu or Cpl
Cpu: the capability based on the USL = (USL- X )/3 '̂ where X is the overall average (the
number in parentheses is the theoretical % greater than the USL)
Cpl: the capability based on the LSL = ( X -LSL)/3 '̂ (the number in parentheses is the
theoretical % less than the LSL)
Est. Sigma = '̂
Pp: = (USL-LSL)/6s where s is the standard deviation of the measurements
Ppk: the minium of Ppu or Ppl
Ppu: the capability based on the USL = (USL- X )/3s where X is the overall average (the number
in parentheses is the theoretical % greater than the USL)
Ppl: the capability based on the LSL = ( X -LSL)/3s (the number in parentheses is the theoretical
% less than the LSL)
Sigma: = s
Average: = X
Count: = number of data points in the analysis
No. Out of Spec: = actual number out of specification (number in parentheses is the % out)
35 ©2007 Business Process Improvement
Kurtosis: a measure of the shape of the distribution. A positive value means that the distribution
has longer tails than a normal distribution; a negative value means that the distribution has shorter
tails. The normal distribution has kurtosis of 0.
Skewness: a measure of asymmetry. If skewness is 0, there is perfect symmetry (like the normal
distribution). A positive value means that the tail of the distribution is stretched on the side above
the mean. The negative values means it is stretch on the side below the mean.
Sigma Level: A statistical term that measures how much a process varies from perfection, based
on the number of defects per million units.
o One Sigma = 690,000 per million units
o Two Sigma = 308,000 per million units
o Three Sigma = 66,800 per million units
o Four Sigma = 6,210 per million units
o Five Sigma = 230 per million units
o Six Sigma = 3.4 per million units
DPMO: Defects per million opportunities
Data Entry
If you are just using data to determine process capability without using a
control chart, enter the data into the spreadsheet. An example is shown to
the right. Select the data to be used in the analysis and then select the
process capability option (Cpk) on the SPC toolbar. If you want to do a
process capability analysis for an existing chart, you do not have to select
anything on a worksheet prior to selecting the process capability option on
the SPC toolbar.
81 77 75 74 77 73 77 74 76 75 79 74 74 79 73 75 75 74 75 80 80 79 72 78 73 74 74 73 75 74 77 75 75 72 75 74 76 75 74 74 78 75 76 76 78 77 78 75 74 76 77 76 72 73 79 82 73 75 74 79 77 73 72 75 73 73 76 76 76 75 74 72 76 76 76 74 79 79 75 81 77 74 77 71 84 74 79 70 77 74 73 77 76 74 81 75
36 ©2007 Business Process Improvement
Process Capability Dialog Box
Once you select the process capability option,
you will get the two page dialog box shown.
Each page is discussed below. Selecting OK at
the bottom of the page will run the program.
Selecting Cancel will end the program. The
Switch Tabs button can be used to switch
between the two pages.
Input Ranges/Chart Name Page
Data or Existing chart?: Select the
option you want. “Data Only” is the
default option. When “Data Only” is
selected, the “Range Containing Values”
is enabled.
o Range Containing Values: This
is the range containing the values on which to do the process capability analysis. The
default value is the range selected on the spreadsheet before selecting the process
capability option.
If “Existing Chart” is selected, the “Select Existing Chart” list box is enabled and a list of
available charts is given in the list box. Select the chart you want to do the process capability
analysis on.
Name of Chart: This is very important. Decide what you want to call the chart. This will be the
name of the sheet that contains the chart in your workbook. If you select the “Existing Chart”
option, the chart automatically will be the name of the existing chart worksheet with Cpk added.
Data in: Select columns or rows depending on how the data is entered into the spreadsheet. The
program selects one or the other depending on the range selected prior to selecting the process
capability option on the SPC toolbar.
Specifications: Enter the upper specification limit (USL), the lower specification limit (LSL) and
the nominal, the target (if desired). Only one specification limit is required.
Add +/- 3 Sigma Limits: In addition to the specifications, you can add the +/- three sigma limits to
the chart. The default is No. If you select Yes, you can chose sigma to the estimated sigma from
the range chart or the calculated standard deviation of all the data.
Titles/Labels/Dates of Data Collection/Multiple Charts/Outliers Page
Capability Chart Title: This is the title
that goes on the chart. The default value
is “Capability Analysis.”
Y-Axis Label: This is the vertical axis
label. The default value is “Frequency.”
X-Axis Label: This is the horizontal axis
label. The default value is
“Measurement.”
Number of Decimal Places for Rounding:
This is the rounding to use for the values
in the titles on the chart.
37 ©2007 Business Process Improvement
Dates of Data Collection: Add the starting date and ending dates of data collection. These dates
are optional. If entered, they will appear in a dialog box in the lower left-hand corner of the chart.
More Than One Chart? Select “Yes” if you want to make multiple process capability charts by
looping through the dialog box. The program assumes that the next set of data for the process
capability analysis is adjacent to the current set. Use one row or one column of data if you are
selecting this option. “No” is the default value.
Remove Outliers? Select “Yes” if you want to remove outliers from the calculations. Enter the
number of standard deviations you want to remove outliers beyond (e.g., beyond +/- 6 sigma).
The default option is “No.”
38 ©2007 Business Process Improvement
Advanced Process Capability
This option is used to automatically generate multiple process capability analysis, to remove outliers,
adjust specification limits, and generate a summary process capability table.
Data Entry
The data entry requirements for this option are shown to
the right. There must be a row containing the unique
“Name of Chart.” This becomes the worksheet tab name.
In addition, there must be a row containing the LSL and/or
USL. The row containing the nominal value is optional.
Select the data in the column containing the data for the
first process capability chart (shaded). Then select the
advanced process capability (ACpk) from the SPC toolbar.
Advanced Process Capability Dialog Box
One you select the Advanced Process
Capability option from the toolbar, you get
the two page dialog box shown to the right.
Each page is discussed below. Selecting
OK at the bottom of the page will run the
program. Selecting Cancel will end the
program. The Switch Tabs button can be
used to switch between the two pages.
Input Page
Capability Results Table: If “Yes”
is selected, a table summarizing the
process capability for all charts will
be generated. An example is shown
at the end of this section.
Range Containing Values: This is the range of the data for the first process capability chart. The
default value is the selected area on the spreadsheet. The data must be in columns for this feature.
Select Row Containing Name: Select a cell in the row or the row itself that contains the unique
name of the chart. This name will be on the worksheet tab containing the process capability
chart.
Select Row Containing USL: Select a cell in the row or the row that contains the USL values.
Select Row Containing Nominal: Select a cell in the row or the row that contains the nominal
values.
Select Row Containing LSL: Select a cell in the row or the row that contains the LSL values.
Name of Chart Chart 1 Chart 2 Chart 3 Chart 4 Chart 5
LSL 70 68 75 60 65
Nominal 100 100 97.5 100 95
USL 130 132 120 140 125
90 92 96 109 111
92 112 101 102 99
109 82 117 103 90
89 91 91 116 117
92 109 105 83 95
97 107 112 76 105
112 85 97 108 75
95 99 101 115 94
95 108 105 108 94
102 99 85 112 101
108 97 89 99 107
101 93 111 83 106
116 89 104 105 102
110 118 102 98 99
81 87 117 114 107
94 101 97 116 95
91 103 106 100 99
108 97 106 108 87
95 87 84 116 105
100 96 113 114 112
39 ©2007 Business Process Improvement
Remove Outliers? Select “Yes” if you want to remove outliers from the calculations. Enter the
number of standard deviations you want to remove outliers beyond (e.g., beyond +/- 6 sigma).
The default option is “No.”
Reset Specifications Limits? Select “Yes” if you want the program to replace the existing
specification limits with new limits set at the value of +/- sigma you enter. This is useful if you
are trying to set specification limits, e.g., for prototype data.
Add +/- 3 Sigma Limits: In addition to the specifications, you can add the +/- three sigma limits to
the chart. The default is No. If you select Yes, you can chose sigma to the estimated sigma from
the range chart or the calculated standard deviation of all the data.
Labels and Date Page
Y-Axis Label: This is the vertical
axis label. The default value is
“Frequency.”
X-Axis Label: This is the horizontal
axis label. The default value is
“Measurement.”
Dates of Data Collection: Add the
starting date and ending dates of
data collection. These dates are
optional. If entered, they will
appear in a dialog box in the lower
left-hand corner of the chart.
Example of Process Capability Table Output
An example of the process capability table output is shown below. This is from the data in the example
workbook.
Name Cp Cpk Cpu Cpl Est. Sigma Pp Ppk Ppu Ppl Sigma Average Count Minimum Maximum Kurtosis Skewness LSL USL
Chart 1 1.07 1.03 1.11 1.03 9.33 1.09 1.05 1.13 1.05 9.17 98.85 20 81 116 -0.65 0.19 70 130
Chart 2 0.94 0.87 1.01 0.87 11.38 1.1 1.02 1.18 1.02 9.72 97.6 20 82 118 -0.53 0.37 68 132
Chart 3 0.67 0.54 0.54 0.8 11.24 0.77 0.62 0.62 0.92 9.73 101.95 20 84 117 -0.58 -0.28 75 120
Chart 4 1.29 1.16 1.16 1.43 10.31 1.13 1.01 1.01 1.25 11.78 104.25 20 76 116 0.74 -1.2 60 140
Chart 5 1.02 0.85 0.85 1.19 9.85 1.04 0.87 0.87 1.21 9.63 100 20 75 117 1.16 -0.68 65 125
40 ©2007 Business Process Improvement
Scatter Diagram
A scatter diagram is used to show the relationship between two kinds of data. It could be the relationship
between a cause and an effect, between one cause and another, or even between one cause and two others.
In the example file, there is data that relates steam usage in a plant to the atmospheric temperature. The
question being answered here is “Does the atmospheric temperature have an effect on steam usage in the
plant.” For 25 days, data were collected on steam usage and temperature. There are 25 sets of data point.
Each set of data points is charted on a scatter. The scatter diagram is shown below.
As can be seen in the
figure, there is a negative
correlation in the data.
This means that as
temperature decreases, the
steam usage in the plant
tends to increase. There
can be a positive
correlation, a negative
correlation, or no
correlation.
The program determines if
the relationship between
the two variables is
statistically significant at a
probability of 0.05. If
there is a significant
relationship, the resulting probability is given in the title (in this case, the round goes to p =0). The
equation is of the form:
y = b1x + b0
where y is the variable on the y axis, x is the variable on the x axis, b1 is the slope of the line and b0 is
where the line crosses the y axis. In the example above, the slope is -0.0871. This means that for each
unit increase in x (one degree of temperature in this case), the y value (steam usage in this case) decreases
by -0.0871.
The value of R2 in the chart is the % of variation in y that is explained by x. In this example, 75% of the
variation in steam usage is explained by the variation in temperature.
Scatter Diagram (Significant, p = 0)
y = -0.0871x + 14.098
R2 = 0.7525
6.3
7.3
8.3
9.3
10.3
11.3
12.3
13.3
28 38 48 58 68 78 88
Temperature (X)
Ste
am
Us
ag
e (
Y)
41 ©2007 Business Process Improvement
Data Entry
Enter the X values and the Y Value into a spreadsheet as shown to
the right. Select the X values and the Y values. If the X value
and Y values are adjacent, you can just select the X values. Then
select the scatter diagram option (SD) from the SPC toolbar. The
sample number entries can be used for point labels (see below).
Scatter Diagram Dialog Box
Once you select the scatter diagram option
from the SPC toolbar, you will see the two
page dialog box shown to the right. Each page
is discussed below. Selecting OK at the
bottom of the page will run the program.
Selecting Cancel will end the program. The
Switch Tabs button can be used to switch
between the two pages.
Input Data/Titles Page
X Values Range: This is the range
containing the X values. The default
value is the range you selected prior to
selecting the scatter diagram option in
the toolbar.
Y Values Range: This is the range containing the Y values. The default value is the range next to
the X values or the second range selected on the worksheet.
Name of Chart: This is very important. Decide what you want to call the chart. This will be the
name of the sheet that contains the chart in your workbook.
Scatter Diagram Title: This is the title that goes on the scatter diagram. The default value is
“Scatter Diagram.”
Y-Axis Label: This is the vertical axis label. The default value is the cell contents above the X
values range.
X-Axis Label: This is the horizontal axis label. The default value is the cell contents above the Y
values range.
Trend/Regression Options: Select the regression you want. The options are:
o Linear
o Logarithmic
o Polynomial (activates order or period option)
o Power
o Exponential
Dates of Data Collection: Add the starting date and ending dates of data collection. These dates
are optional. If entered, they will appear in a dialog box in the lower left-hand corner of the chart.
Sample
No.
Temperature
(X)
Steam
Usage (Y)
1 35.3 10.98
2 29.7 11.13
3 30.8 12.51
4 58.8 8.4
5 61.4 9.27
6 71.3 8.73
7 74.4 6.36
8 76.7 8.5
9 70.7 7.82
10 57.5 9.14
11 46.4 8.24
12 28.9 12.19
13 28.1 11.88
14 39.1 9.57
15 46.8 10.94
42 ©2007 Business Process Improvement
Data in: Select columns or rows depending on how the data is entered into the spreadsheet. The
program selects one or the other depending on the range selected prior to selecting the scatter
diagram option on the SPC toolbar.
Rounding/Forecasting/Point Labels
Rounding to Use in Titles: This the
rounding to use for the probablity
printed in the title. The default value
is 4.
Options: There are three options to
consider:
o Intercept: check this box if
you want to force the y-
intercept through 0 or another
value
o Display equation on chart:
select this option to display
the equation on the chart.
o Display R-Square: select this
option to display R2 on the
chart.
Forecasting: You can forecast forward or backward by changing the 0 values in the appropriate
boxes.
Add Labels to Point: Select “Yes” if you want to add labels to the points.
o Point Range Label: This is the range containing the point label ranges and should be
equal to the number of points on the chart.
o Label Position: This determines where to put the labels (above, below, left, center, right)
relative to the point.
43 ©2007 Business Process Improvement
Updating Charts
All charts can be updated easily after new data has been entered into the spreadsheet. There is no need to
select anything on the worksheet. The program automatically checks to see what new data has been
entered. Once you have entered the new data, select the
update option from the SPC toolbar. You will get the
dialog shown to the right.
The dialog box lists all the available charts for updating
in the workbook. You may select multiple charts at
once. You can also check the “Update All Charts”
option to update all the charts in the workbook.
Caution on Updating Charts:
If you change the name on the worksheet tab containing your chart, you will not be able to update the
chart because the program can’t find the new name. There is a manual method that allows you to change
the name on the worksheet tab. See the section on “Frequently Asked Questions” in the manual.
Changing Chart Options
You make changes to the chart using the options button on the SPC
toolbar. When you select this button, you get the dialog box to the
right. Select the chart whose options you want to change. The
dialog box for that chart then is shown. You can change anything
except the name of the chart.
Note on chart title, y-axis label and x-axis label: To make
permanent changes to the chart title or the labels on either axis, you
must go through the options shown here. Making changes directly on the chart will not permanently
change the title and labels. If you make the changes on the chart and then update the chart, the program
will use the stored values.
Caution on Updating Charts:
If you change the name on the worksheet tab containing your chart, you will not be able to update the
chart because the program can’t find the new name. There is a manual method that allows you to change
the name on the worksheet tab. See the section on “Frequently Asked Questions” in the manual.
44 ©2007 Business Process Improvement
Single Point Actions
This option is used for action on a single point on a chart including:
Splitting control limits at a point
Removing the split at the point
Starting the chart at the point
Undo starting the chart at the point
Removing a point from the calculations
Adding a point back to the calculations
Adding or replacing a comment to the point
Deleting the existing comment for the point
You must select a point on the chart prior to selecting the single point
option from the menu. To select a single point:
Select the series by pointing the mouse at the series and
clicking
Select the point you want using the mouse.
Below is an example of a chart with one point selected (this is the c chart data from the example
workbook).
After selecting the point, select the single point action option (SP) from the SPC toolbar. The dialog box
above will appear. Select the option you want and then select OK. The average and limits are
recalculated based on your option and the chart is re-made. See the notes on the following page for more
information.
45 ©2007 Business Process Improvement
Notes on Single Point Actions
Some of the actions on this option will produce minor changes in your workbook. These changes along
with other issues on single point actions are described below.
Control limits can be split multiple times within a chart.
o This will produce a change to your worksheet. The cell containing the point will be in
italics. This will occur in the first column or row of data.
Starting the chart at a new point will produce a change on your worksheet. The cell containing
that point will be in bold. This will occur for in the first column or row of data.
If a point is removed from the calculations, it is still plotted. Its appearance will change - it will
just be outlined as shown to the right.
o This will also produce a change to your worksheet. The cell containing the point will be
shaded a light tan. The shading will occur in
the first column or row of data. The shading
used is shown to the right.
Comments added to or deleted from the points must
be added through this option. Adding or deleting
them manually to the chart will not store the result.
o This will also produce a change to your
worksheet. The comments will be added to
the cell containing that point as an Excel
comment.
c Control Chart
Avg=21.64
UCL=35.6
LCL=7.69
0
5
10
15
20
25
30
35
40
45
50
2/1/2003 2/2/2003 2/3/2003 2/4/2003 2/5/2003 2/6/2003 2/7/2003 2/8/2003 2/9/2003 2/10/2003 2/11/2003 2/12/2003 2/13/2003 2/14/2003 2/15/2003
Subgroup Number
Nu
mb
er
of
Defe
cts
c Control Chart
Avg=23.13
UCL=37.56
LCL=8.7
0
5
10
15
20
25
30
35
40
45
50
2/1/2003 2/2/2003 2/3/2003 2/4/2003 2/5/2003 2/6/2003 2/7/2003 2/8/2003 2/9/2003 2/10/2003 2/11/2003 2/12/2003 2/13/2003 2/14/2003 2/15/2003
Subgroup Number
Nu
mb
er
of
De
fec
ts
Point included in
calculations
Point not included in
calculations
46 ©2007 Business Process Improvement
All Points Action
When you select the All Points Action from the SPC toolbar, you will
see the dialog box to the right. With this option, you can:
remove or add back to the calculations all points beyond the
control limits.
Select the range to base control limits on.
A chart must be selected before this option can be used. If you have
the two charts on the same worksheet (e.g., X -R chart), you must
select the X chart. You cannot delete points by selecting the range
chart.
Once you have selected the chart, select the all points option (All) on the SPC toolbar. You will get the
dialog box to the right. Select the option you want.
If you select the option “Select Range to Base Control Limits On,” you will
see a box like the one to the right. This box will contain the subgroup
identifiers from your chart. Select the subgroup you want to include in the
calculation of averages and control limits. Selecting this option will set the
option to automatic update the averages and limits to No.
Note: When removing all points beyond the limits, the average and limits are
recalculated. It is possible that additional points will now be beyond the
limits. You may have to run this several times to remove all points beyond
the limits.
47 ©2007 Business Process Improvement
Cause and Effect Diagram
This program contains a cause and effect (fishbone) diagram. To use this feature, select the cause and
effect option (CE) on the SPC toolbar. A blank cause and effect diagram will be inserted into your
workbook.
Date:
Machines Methods Materials
Product out of
specifications
Measurement People
Cause and Effect Diagram DiagramPrepared by:
Environment
You can change the main category headings (measurement, people, etc). You can enter the problem or
goal at the head of the fishbone (see above). You will see a button that says “Add Item.” Select this
button and you will get the dialog box below.
Enter an item to add to the cause and effect diagram. For example, you might enter “Not calibrated.”
Then select OK. This item is then shown on the chart and you may move it to any location you want.
Date:
Machines Methods Materials
Product out of
specifications
Measurement People
Cause and Effect Diagram DiagramPrepared by:
Environment
Not calibrated
48 ©2007 Business Process Improvement
Measurement Systems Analysis
This Measurement Systems Analysis used by the program is based on the following two sources:
1. Measurement Systems Analysis, Third Edition, AIAG, May 2003 (www.aiag.org)
2. Evaluating the Measurement System by Donald Wheeler and Richard Lyday, SPC Press,
Knoxville, TN, 1989 (www.spcpress.com)
Both are excellent references for developing a better understanding of the measurement system. The
program has the following components:
1. Average and Range Method to generate the classical Gage R&R report with the following chart
options:
a. Averages charts – stacked and unstacked
b. Range charts – stacked and unstacked
c. Run chart by part
d. Scatter plots
e. Whiskers charts
f. Error charts
g. Normalized histograms
h. X-Y Plots
i. Range charts for each operator
j. Operator bias chart
k. Operator consistency chart
2. ANOVA Method that includes:
a. ANOVA table
b. Residuals plot
c. ANOVA Gage R&R report
3. Range Method for Gage R&R
4. Bias Method – Independent Sample Method
5. Bias Method – Control Chart Method (checks Stability also)
6. Linearity Method
7. Attribute Gage R&R that includes:
a. Effectiveness table (attribute Gage R&R report)
b. Crosstabulations
c. Kappa values
These are explained in detail on the following pages.
49 ©2007 Business Process Improvement
Average and Range Method
Set-up Data Entry
The example below uses the data from page 101 of Measurement System Analysis, Third Edition.
Suppose you have completed a Gage R&R with 3 appraisers, 10 parts, and 3 trials. The first step in using
the Gage R&R program is to setup the data entry page. Select the MSA icon on the SPC toolbar. You
will get the form shown below.
Select the first option to setup the data entry sheet based on the number of operators, parts, and trials and
then select OK. You will see the form below which has been filled in with the numbers for this example.
You must enter all the information. The number of decimal places in the measurement is VERY
IMPORTANT. It controls how the data is rounded and shown. Entering zero when you have two or
three decimal places in the data may lead to inaccurate results. After entering all the information, select
OK. This will generate the data entry sheet shown below. The number of trials and parts can range from
2 to 20; the number of appraisers can range from 1 to 25 (with one appraiser you will only get a Gage
R&R report based on the average and range method).
Enter the operator names in the upper right hand corner. The names will automatically appear in the first
column. NOTE: The program uses Microsoft Excel’s naming function to run. You cannot have
spaces or certain characters (e.g. /). Instead of using John Smith, use John_Smith. Enter the rest of
the information for Date, Gage Name, Gage Number, Gage Type, Product, Characteristic, Upper
Specification Limit, Lower Specification Limit, and Performed By. None of this information is required
to run the program with the possible exception of the specification limits. These are required if you are
basing the acceptability of the measurement system on the tolerances. You then enter the data from the
appraisers for each trial and each part. A completed data entry screen is shown on the next page.
50 ©2007 Business Process Improvement
Blank Data Entry Form: Gage R&R Study 2
Date: Operator 1: Enter Operator 1 Name Here
Gage Name: Operator 2: Enter Operator 2 Name Here
Gage Number: Operator 3: Enter Operator 3 Name Here
Gage Type:
Product:
Characteristic:
Upper Specification Limit:
Lower Specification Limit:
Performed By:
Operator Trial/Part 1 2 3 4 5 6 7 8 9 10
Enter Operator 1 Name Here 1
Enter Operator 1 Name Here 2
Enter Operator 1 Name Here 3
Enter Operator 2 Name Here 1
Enter Operator 2 Name Here 2
Enter Operator 2 Name Here 3
Enter Operator 3 Name Here 1
Enter Operator 3 Name Here 2
Enter Operator 3 Name Here 3
Completed Data Entry Form: Gage R&R Study 2
Date: 10/31/2005 Operator 1: Hal
Gage Name: Thickness Gage Operator 2: Beth
Gage Number: T-101 Operator 3: Loa
Gage Type: Thickness
Product: Widget
Characteristic: Thickness
Upper Specification Limit: 3
Lower Specification Limit: -3
Performed By: Bill
Operator Trial/Part 1 2 3 4 5 6 7 8 9 10
Hal 1 0.29 -0.56 1.34 0.47 -0.8 0.02 0.59 -0.31 2.26 -1.36
Hal 2 0.41 -0.68 1.17 0.5 -0.92 -0.11 0.75 -0.2 1.99 -1.25
Hal 3 0.64 -0.58 1.27 0.64 -0.84 -0.21 0.66 -0.17 2.01 -1.31
Beth 1 0.08 -0.47 1.19 0.01 -0.56 -0.2 0.47 -0.63 1.8 -1.68
Beth 2 0.25 -1.22 0.94 1.03 -1.2 0.22 0.55 0.08 2.12 -1.62
Beth 3 0.07 -0.68 1.34 0.2 -1.28 0.06 0.83 -0.34 2.19 -1.5
Loa 1 0.04 -1.38 0.88 0.14 -1.46 -0.29 0.02 -0.46 1.77 -1.49
Loa 2 -0.11 -1.13 1.09 0.2 -1.07 -0.67 0.01 -0.56 1.45 -1.77
Loa 3 -0.15 -0.96 0.67 0.11 -1.45 -0.49 0.21 -0.49 1.87 -2.16
Generating the Results
You are now ready to run the program to generate the results. To run the program, select the icon on the
SPC toolbar. You will get the form shown above when you have selected the “Run the analysis (have
entered data into the data entry sheet)” under the Average/Range Method.
You have two things to decide at this point. First, on the
left-hand side of the form is what to base acceptability of the
measurement on. You have the following three options:
1. Tolerances: Use this option if your parts have very
little variation or not representative of the total
variation in your production process.
2. Total Variation Based on Parts: Use this option if
your parts are representative of the total variation in
your process
3. Process Standard Deviation: Use this if your parts
are not representative of the total variation in your
process and if you have a good estimate of the
process standard deviation (e.g., from a control chart
kept on the process).
51 ©2007 Business Process Improvement
On the right-hand side, you have three options for additional charts that can be generated along with the
Gage R&R report. The options are:
1. All Charts: this will generate all the charts associated with the study (see the first page of this
instructional manual for the list or the figure below)
2. No Charts: only the Gage R&R report will be generated
3. Select Charts: only the charts you select will be generated
If you select “Select Charts”, you will get the dialog box below. You select the charts you want to
include in the output and then select OK. This returns you to the form above.
Once you have selected your options, select OK and the program will generate the Gage R&R report as
well as the charts you have selected (if any).
When finished, the program will display the Gage R&R report. The one generated from this data (using
the Total Variation Based on Parts Option) is shown below. The report contains all the information in a
classical Gage R&R study and bases the conclusion if the measurement system is acceptable based on one
of the three options selected below. Any charts that were selected are generated on separate worksheets
in the workbook. You can download a completed workbook with all the charts from our website
(www.spcforexcel.com). A summary of each chart is given below.
Stacked Averages Chart – the average of each appraiser on each part is plotted by appraiser
using the part number as the index. There is one line for each appraiser. This helps
determine how consistent the operators are. The overall average and control limits are also
plotted. If the parts represent the total (true) variation in the process, at least half of theses
points should be out of control. If this not the case, the measurement system does not have
the ability to distinguish between samples (poor resolution) or the parts do not reflect the total
variation in the process.
Unstacked Averages Chart – same as the stacked chart but the appraisers are plotted together,
not separately.
Stacked Range Chart – used to show the range of each operator’s trials on a part and includes
the average range and control limits. There is one line for each appraiser. The chart is used
to determine if the process is in control. If there are out of control points, the special causes
need to be found and eliminated. Care should be taken with interpreting the Gage R&R
results if there are special causes present. Special causes occur if there are points beyond the
control limits.
Unstacked Range Chart – same as the stacked range chart but the appraisers are plotted as
one line.
Run Chart by Part – plots the individual readings by part for all appraisers to help see if there
are any outliers and to see the variation in the individual parts.
52 ©2007 Business Process Improvement
Scatter Plot – plots the individual readings by part-by-appraiser to examine how consistent
the appraisers are, to look for part-appraiser interactions, and to look for outliers.
Whiskers Charts – plots the high, average, and low value by part for each appraiser to
examine how consistent the appraisers are, to look for part-appraiser interactions, and to look
for outliers (same items as for the scatter plot).
Error Charts – plots the error (observed value – average measurement of the part) by part-
appraiser to determine which operator may have bias and which operator has the most
variability.
Normalized Histograms – plots the normalized value (observed value – average measurement
of part) as a histogram to determine how the error is distributed by appraiser.
X-Y Plot – plots the average of the readings by each appraiser against the overall part
averages to examine consistency in linearity between appraisers.
Appraiser Charts – consists of three charts:
o Range charts for each appraiser to determine if each is in control
o Bias chart for all appraisers to determine if different appraisers display detectably
different average values for the parts.
o Consistency chart for all appraisers to determine if different appraisers display detectably
different standard deviations for the parts.
Gage Repeatability and Reproducibility Report
Gage Name: Thickness Gage Product: Widget Date: 10/31/05
Gage No. T-101 Characteristic: Thickness Performed by: Bill
Gage Type: Thickness USL: 3
LSL: -3
Rbar= 0.341667 XbarDiff= 0.444667 Rp= 3.511111
K1= 0.5908 K2= 0.5231 K3= 0.3146
Measurement Unit Analysis % Total Variation (TV) % Tolerance
Repeatability - Equipment Variation (EV)
EV = Rbar * K1 % EV = 100(EV/TV) % EV = 100(EV/(USL-LSL)/6)
= 0.20186 = 17.61% = 20.19%
Reproducibility - Appraiser Variation (AV)
AV= Sqrt((XbarDiff * K2)2 - (EV
2)/nr)) % AV = 100(AV/TV) % AV = 100(AV/(USL-LSL)/6)
= 0.22967 = 20.04% = 22.97%
Repeatability & Reproducibility (R & R)
R&R= sqrt(EV2 + AV
2) % R&R = 100(R&R/TV) % R&R = 100(R&R/(USL-LSL)/6)
= 0.30577 = 26.68% = 30.58%
Part Variation (PV)
PV= Rp * K3 % PV = 100(PV/TV) % PV = 100(PV/(USL-LSL)/6)
= 1.1046 = 96.38% = 110.46%
Total Variation (TV)
TV= sqrt(R&R2 + PV
2) ndc= 1.41(PV/R&R)
= 1.14614 = 5.093652
Conclusion
% R&R under 10% of Total Variation: Measurement system is acceptable
**** % R&R from 10% to 30% of Total Variation: Measurement system may be acceptable based the application
% R&R over 30% of Total Variation: Measurement system needs improvement
53 ©2007 Business Process Improvement
ANOVA Method
Set-up Data Entry
The set-up is the same as for the Average and Range Method. Please follow the instructions for set-up
data entry as well as data entry for the Average and Range Method.
Generating the Results
After the data has been entered into the worksheet, select the MSA icon on the SPC toolbar. You will get
the form below. Select the ANOVA Method option as shown in the form and then select OK.
The program generates two new worksheets. One (ANOVA Report) contains the Gage Repeatability and
Reproducibility ANOVA Method Report as shown below. The acceptability of the measurement system
is based on percent contribution, not on % Total Variation.
Gage Name: Thickness Gage Product: Widget Date: 10/31/05
Gage No. T-101 Characteristic: Thickness Performed by: Bill
Gage Type: Thickness USL: 3
LSL: -3
% TOTAL PERCENT
STD DEV. VARIATION CONTRIBUTION
Repeatability (EV) 0.199933 18.42% 3.39%
Reproducibility (AV) 0.226838 20.90% 4.37%
Appraiser by Part (INT) 0 0.00% 0.00%
GRR 0.302372 27.86% 7.76%
Part (PV) 1.042327 96.04% 92.24%
Number of distinct data categories (ndc)= 4
Total Variation (TV) = 1.0853
Gage Repeatability and Reproducibility ANOVA Method Report
% R&R under 10%: Measurement system is acceptable
The other worksheet (GRR ANOVA) contains the ANOVA table and the residuals plot as shown below.
The residuals chart plots the residual versus the average for each appraiser for each part. The residual is
the result minus that average. The points should be randomly scattered above and below zero.
54 ©2007 Business Process Improvement
ANOVA Results
Source df SS MS F Sig
Appraiser 2 3.16726222 1.58363111 34.44 0.0000
Part 9 88.3619344 9.81799272 213.517 0.0000
Appraiser by Part 18 0.35898222 0.01994346 0.434 0.9740
Equipment 60 2.75893333 0.04598222
Total 89 94.6471122
F values in italics are significant at alpha = 0.05 level
Source of
Variation
Estimate of
Variance Std. Dev.
% Total
Variation
%
Contribution
Equipment 0.03997328 0.19993318 EV = 1.02965588 18.42% 3.39%
Appraiser 0.05145526 0.22683752 AV = 1.16821324 20.90% 4.37%
Interaction 0 0 INT = 0 0.00% 0.00%
GRR 0.09142854 0.30237152 GRR = 1.55721334 27.86% 7.76%
Part 1.0864466 1.04232749 PV = 5.36798659 96.04% 92.24%
Total Variation 1.17787514 1.08529956 TV = 5.58929275 100.00%
ndc = 4.86051648 or 4
5.15 Std Dev.
Residuals versus Average Values
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Average Values
Resid
uals
55 ©2007 Business Process Improvement
Range Method for Gage R&R
This method provides a quick look at measurement variability and requires that you have an estimate of
the process standard deviation. This method typically uses two appraisers and five parts. Each appraiser
measures the part one time only. An example of the data input required is shown in the figure below and
is based on the data from page 98 of Measurement Systems Analysis, Third Edition. The data can be
anywhere on the worksheet.
Select the data as highlighted above. Do not select the column headings. To run the program, select the
icon on the SPC toolbar. You will see the first page of the form as usual. Select the second page tab
labeled “Range/Bias/Linearity/Attribute Gage R&R.”
Select the Range Gage R&R Method and select OK. The dialog below will appear.
The range that appears in the “Range containing part numbers and appraiser results’ is the range that is
selected on the worksheet. You can save some time by selecting the data before selecting the icon on the
56 ©2007 Business Process Improvement
toolbar. Enter the process standard deviation. For the example, this standard deviation is 0.0777. Then
select OK. A new worksheet will be added to the workbook with the following output.
Range Method for Gage R&R
Average Range (Rbar) = 0.07
Upper Control Limit = 0.22869
Lower Control Limits = None
In Control? Yes
GRR = Rbar/d2* = 0.058772
Process Standard Deviation = 0.0777
%GRR = 100(GRR/Process Standard Deviation = 75.6%
Conclusion: The measurement system needs improvement.
Range Chart
0
0.05
0.1
0.15
0.2
0.25
1 2 3 4 5
Part Number
Ran
ge
The results give the average range and control limits. The range chart is shown to check for special
causes of variation. The % GRR is calculated and the conclusion given based on the % GRR.
57 ©2007 Business Process Improvement
Bias – Independent Sample Method
This method determines if the measurement system is biased. It is done by using one
sample and determining its reference value. The one appraiser measures the sample ten
or more times. The data used in this example is from page 87 in Measurement Systems
Analysis, Third Edition. An example of how the data is entered in the spreadsheet is
given to the right. The data can be anywhere in the spreadsheet.
Select the data as highlighted to the right. Do not select the column heading or the trial
numbers – just the results of running the sample multiple times. To run the program,
select the icon on the SPC toolbar. You will see the first page of the form as usual.
Select the second page tab labeled “Range/Bias/Linearity/Attribute Gage R&R.” Select
the Bias (Independent Sample Method) option and select OK. You will then see the
dialog below.
The range that appears in the dialog box is the range selected on the
worksheet. You can change it here if it is not correct. Enter the
reference value (which is 6.00 in this example); enter the number of
decimal places (1), and alpha. The default value is 0.05 which gives
95% confidence limits.
The second page of the dialog box is output options. It is shown to
the left. These options are available for both bias reports. There are
two options for plotting the histogram – by midpoint or by class
width. By midpoint is the default value. The histogram can be
plotted on the same sheet as the analysis (recommended) or as a new
sheet in the workbook. There are two output options for the analysis
of bias study. You can place it in the worksheet where the data is or
as a new sheet (recommended). You do not have to go to this page if
you are satisfied with the default options.
Select OK and the results are generated. A new worksheet is added
with the results as shown on the next page. A histogram of the
results is included along with the numerical calculation results. The
numerical values include:
n = number of readings
Mean = average of the readings
Reference Value = reference value of the sample
Standard Deviation (s) = standard deviation of the readings
t statistic = the t value based on the degrees of freedom
df = degrees of freedom
t value (2 tailed) = t value from the t tables
Bias = average – reference value
Lower = lower confidence interval (based on alpha)
Upper = upper confidence interval (based on alpha)
A conclusion is also presented that states if you can assume the bias is zero.
58 ©2007 Business Process Improvement
n Mean
Reference
Value
Standard
Deviation
() t statistic df
t value (2
tailed) Bias Lower Upper
Measured Value 15 6.006667 6 0.21202 0.121781 14 2.144787 0.006667 5.889254 6.124079
There is no evidence that the average is significantly different than reference value. You may assume the bias is zero.
Alpha=0.05 Confidence Interval
Bias - Independent Sample Method
0
1
2
3
4
5
5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4
Measured Value
Fre
qu
en
cy
59 ©2007 Business Process Improvement
Bias – Control Chart Method
This method uses the control charts to determine if the measurement system is biased. It
can also be used to check the stability of the measurement system. You must have a
reference value for the sample. The control chart can be an individuals chart (X-MR),
X -R chart, or X -s chart. The example below uses the X-MR chart. An example of the
data entry requirements are shown to the right.
Select the data as highlighted to the right. Do not select the column heading but do select
the sample numbers. To run the program, select the icon on the SPC toolbar. You will
see the first page of the form as usual. Select the second page tab labeled
“Range/Bias/Linearity/Attribute Gage R&R.” Select the Bias (Control Chart Method)
option and select OK. You will then see the dialog below.
You have an option of selecting the type of chart
you are using. The program selects what it thinks you have based
on the selected area on the worksheet. You can change it if it is not
correct. The dialog box also shows the range containing the
subgroup identifiers (sample numbers) and the range containing the
measurements. The subgroup identifiers are always assumed to be
in the first column, followed by the data.
Enter the reference value, the number of decimal places in the data,
and alpha (default is 0.05). In this example, the reference value is
100.3.
The second page in the dialog box contains the Output Options.
These are the same as those given in the Bias – Independent Sample
Method above. Please refer to that section for instructions.
The third page of the dialog box contains the chart title and labels as shown below. You can use the
default ones or change them. You can also change the titles and labels after the results are generated.
Once you have entered the information into the dialog box, select OK. A new worksheet is added to the
workbook with the results as shown on the next page for this example.
60 ©2007 Business Process Improvement
The output contains the same information as given in the Bias – Independent Sample Method. It also
includes the control charts for the sample to help determine stability.
n Mean
Reference
Value
Standard
Deviation
() t statistic df
t value (2
tailed) Bias Lower Upper
Measured Value 0 101.045 100.3 0.566127 5.885146 19 2.093024 0.745 100.78 101.31
There is evidence that the average is significantly different than the reference value. The bias is not zero.
Alpha=0.05 Confidence Interval
Bias - Independent Sample Method
0
0.5
1
1.5
2
2.5
100.
1
100.
2
100.
3
100.
4
100.
5
100.
6
100.
7
100.
8
100.
9
101.
0
101.
1
101.
2
101.
3
101.
4
101.
5
101.
6
101.
7
101.
8
101.
9
102.
0
Measured Value
Fre
qu
en
cy
X Chart
Avg=101.05
UCL=102.98
UCL=99.11
97
98
99
100
101
102
103
104
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Sample Number
Sa
mp
le R
es
ult
Moving Range Chart
Avg=0.73
UCL=2.38
0
0.5
1
1.5
2
2.5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Sample Number
Mo
vin
g R
an
ge
61 ©2007 Business Process Improvement
Linearity
Linearity is the difference of bias throughout the
measurement range. To determine linearity, the
samples you select must cover the expected operating
range of the measurement system. You should use at
least five samples that cover this range. One
appraiser should measure each of the parts at least ten
times. An example of the required data input is
shown to the right (page 95, Measurement Systems
Analysis, Third Edition). The data must be in
columns. The first row of data contains the part
number; the second row contains the reference values
for each part; and the remaining rows contain the
measurements.
Select the data as highlighted above. Do not select the first column. To
run the program, select the icon on the SPC toolbar. You will see the
first page of the form as usual. Select the second page tab labeled
“Range/Bias/Linearity/Attribute Gage R&R.” Select the Linearity
option and select OK. You will then see the dialog box to the left.
The range is the range selected on the worksheet before starting the
program. Enter the number of decimal places and alpha (default is
0.05). The “Rounding in Equations” determines how the best fit equation is displayed. The default value
is 3. Once you have entered the information, select OK and the program will generate a chart like the one
below.
Linearity
y = -0.132x + 0.737, R Sqr = 71.4%
-1
-0.5
0
0.5
1
1.5
2 3 4 5 6 7 8 9 10
Reference Values
Bia
s
Bias
Regression
Upper 95% CI
Lower 95% CI
Bias Average
Bias=0
The linearity is NOT acceptable. Ta=12.043, Tcritical=2.002
The bias is NOT the same for all reference values. Tb=10.158, Tcritical=2.002
In the upper left-hand side of the chart, the conclusion is given for linearity. In this example, there is a
prl0bem with linearity. The bias = 0 line (green on the chart) should be contained by the upper and lower
95% confidence intervals. The equation is the title is the best fit equation for the individual readings.
The R squared value gives the % of variation in the bias that is explained by the variation in reference
values.
62 ©2007 Business Process Improvement
Attribute Gage R&R
Set-up Data Entry
The attribute gage R&R component will generate the effectiveness table, crosstabulations and kappa
scores. The example below uses the data from page 127 of Measurement System Analysis, Third Edition.
To set-up the data entry, select the icon on the SPC toolbar and then:
Select the second page tab labeled “Range/Bias/Linearity/Attribute Gage R&R.”
Select the Attribute Gage R&R option.
Select the first option to setup the data entry sheet based on the number of operators, parts and
trials
Select OK.
You will then see the dialog box to the right. Enter the number of
appraisers, parts, and trials. Enter the pass value and fail value (e.g, 1
and 0, pass and fail, etc.). Then enter the name of the Gage R&R
study. The values in the dialog box to the right are for this example.
Then select OK. A new worksheet will be added containing the data
entry sheet as shown below for this example (first 13 parts shown).
Attribute Gage R&R Study
Date: Operator 1: Enter Operator 1 Name Here
Gage Name: Operator 2: Enter Operator 2 Name Here
Gage Number: Operator 3: Enter Operator 3 Name Here
Gage Type:
Product:
Characteristic:
Pass Value 1
Fail Value 0
Performed By:
Reference
Operator Trial/Part 1 2 3 4 5 6 7 8 9 10 11 12 13
Enter Operator 1 Name Here 1
Enter Operator 1 Name Here 2
Enter Operator 1 Name Here 3
Enter Operator 2 Name Here 1
Enter Operator 2 Name Here 2
Enter Operator 2 Name Here 3
Enter Operator 3 Name Here 1
Enter Operator 3 Name Here 2
Enter Operator 3 Name Here 3
Enter the operator names in the upper right hand corner. The names will automatically appear in the first
column. NOTE: The program uses Microsoft Excel’s naming function to run. You cannot have
spaces or certain characters (e.g. /). Instead of using John Smith, use John_Smith. Enter the rest of
the information for Date, Gage Name, Gage Number, Gage Type, Product, Characteristic, Pass Value,
Fail Value, and Performed By. None of this information is required to run the program except the Pass
Value and Fail Value. Then fill in the data as shown below.
Attribute Gage R&R Study
Date: Operator 1: A
Gage Name: Operator 2: B
Gage Number: Operator 3: C
Gage Type:
Product:
Characteristic:
Pass Value 1
Fail Value 0
Performed By:
Reference 1 1 0 0 0 1 1 1 0 1 1 0 1
Operator Trial/Part 1 2 3 4 5 6 7 8 9 10 11 12 13
A 1 1 1 0 0 0 1 1 1 0 1 1 0 1
A 2 1 1 0 0 0 1 1 1 0 1 1 0 1
A 3 1 1 0 0 0 0 1 1 0 1 1 0 1
B 1 1 1 0 0 0 1 1 1 0 1 1 0 1
B 2 1 1 0 0 0 1 1 1 0 1 1 0 1
B 3 1 1 0 0 0 0 1 1 0 1 1 0 1
C 1 1 1 0 0 0 1 1 1 0 1 1 0 1
C 2 1 1 0 0 0 0 0 1 0 1 1 1 1
C 3 1 1 0 0 0 0 1 1 0 1 1 0 1
63 ©2007 Business Process Improvement
To generate the results, select the icon on the SPC toolbar. You will see the first page of the form as
usual. Select the second page tab labeled “Range/Bias/Linearity/Attribute Gage R&R.” You will see the
form below. Select the Attribute Gage R&R option, followed by the Run the Attribute Gage R&R
analysis.
There are three options: crosstabulations, kappa values, and the effectiveness table. Select the options
you want and select OK. The program will generate the following results depending on options selected.
Crosstabulations
You will get a table like this one for each of the
combinations of appraisers. The kappa value is
given. If kappa is above 0.75 there is good
agreement between the appraisers. If it is less
than 0.40, there is poor agreement. The count
information is as follows:
A and B both rate as fail
A rates as fail and B rates as pass
A rates as pass and B rates as fail
A and B both rate as pass
These tables will help you determine how well
the appraisers agree with one another.
Kappa Values
The output for Kappa values is shown on the next page. It includes the kappa values for the appraisers as
well as the kappa value compared to the reference values (if there are any).
Effectiveness Table
The effectiveness table is shown on the next page. This table determines how effective each appraiser is.
Fail Pass Total Kappa
A Fail Count 44 6 50 0.86
Expected Count 15.7 34.3 50.0
Pass Count 3 97 100
Expected Count 31.3 68.7 100
Total Count 47 103 150
Expected Count 47.0 103.0
A * B Crosstabulation
B
64 ©2007 Business Process Improvement
Kappa Measures Output
Kappa Measures for the Appraisers
Kappa A B C
A - 0.86 0.78
B 0.86 - 0.79
C 0.78 0.79 -
There is good to excellent agreement since all kappa values are greater than 0.75
Kappa Values For Each Appraiser to Reference
A B C
Kappa 0.88 0.92 0.77
There is good to excellent agreement since all kappa values are greater than 0.75
Effectiveness Table
Attribute Gage R&R Effectiveness
Gage Name: Product: Date:
Gage No. Characteristic: Performed by:
Gage Type:
Source A B C A B C
Total Inspected 50 50 50 50 50 50
# Matched 42 45 40 42 45 40
False Negative (Appraiser biased toward rejection) 0 0 0
False Positive (Apprasier biased toward acceptance) 0 0 0
Mixed (Appraiser accepts and rejects the same part) 8 5 10
95% UCI 92.8% 96.7% 90.0% 92.8% 96.7% 90.0%
Calculated Score 84.0% 90.0% 80.0% 84.0% 90.0% 80.0%
95% LCI 70.9% 78.2% 66.3% 70.9% 78.2% 66.3%
Total Inspected 50 50
# in Agreement 39 39
95% UCI 88.5% 88.5%
Calculated Score 78.0% 78.0%
95% LCI 64.0% 64.0%
Notes:
(1) Appraiser agrees with him/herself on all trials
(2) Appraiser agrees on all trails with the known reference
(3) All appraisers agreed within and between themselves
(4) All appraisers agreed with and between themselves and agreed with the reference
(5) UCI and LCLI are the upper and lower confidence interval bounds respectively
System % Effectiveness Score3
System % Effectiveness Score vs Reference4
% Appraiser1
% Score vs Attribute2
If the calculated score for each appraiser falls within the confidence interval of the other appraisers, the
effectiveness of the appraisers is the same.
65 ©2007 Business Process Improvement
Transfer Charts to PowerPoint or Word
You can transfer one or more charts to PowerPoint by selecting “PP” on the SPC toolbar or to Word by
selecting “W.”
PowerPoint
To transfer to PowerPoint, a presentation must be opened. The program adds a slide to the presentation
and copies the chart over. You can transfer multiple charts at once by selecting multiple worksheets in
Excel before running this option.
Word
A Word document must be opened to transfer a chart. The chart is placed in the open document wherever
the cursor is. You can transfer multiple charts at once by selecting multiple worksheets in Excel before
running this option.
66 ©2007 Business Process Improvement
Regression
The program contains a multiple regression component under the miscellaneous button on the SPC
toolbar. This is used to determine which independent variables (the X’s) have a significant impact on the
dependent variable Y. An example of the data entry is shown below. In this example, we want to find
out if attendance (Y) at major league baseball games is impacted by the team batting average, the number
of home runs hit by the team, the team’s earned run average, winning percentage of total payroll. Data
for the 2005 baseball season is given below.
Team Average Home Runs
Earned Run Avg.
Winning % Total Payroll Attendance
Arizona Diamondbacks 0.256 191 4.84 0.475 $62,329,166 2,059,331
Atlanta Braves 0.265 184 3.98 0.556 $86,457,302 2,521,534
Baltimore Orioles 0.269 189 4.56 0.457 $73,914,333 2,624,804
Boston Red Sox 0.281 199 4.74 0.586 $123,505,125 2,813,354
Chicago Cubs 0.27 194 4.19 0.488 $87,032,933 3,100,262
Chicago White Sox 0.262 200 3.61 0.611 $75,178,000 2,342,834
Cincinnati Reds 0.261 222 5.15 0.451 $61,892,583 1,943,157
Cleveland Indians 0.271 207 3.61 0.574 $41,502,500 1,973,185
Colorado Rockies 0.267 150 5.13 0.414 $48,155,000 1,915,586
Detroit Tigers 0.272 168 4.51 0.438 $69,092,000 2,024,505
Florida Marlins 0.272 128 4.16 0.512 $60,408,834 1,823,388
Houston Astros 0.256 161 3.51 0.549 $76,779,000 2,762,472
Kansas City Royals 0.263 126 5.49 0.346 $36,881,000 1,371,181
Los Angeles Angels 0.27 147 3.68 0.586 $97,725,322 3,404,686
Los Angeles Dodgers 0.253 149 4.38 0.438 $83,039,000 3,603,680
Milwaukee Brewers 0.259 175 3.97 0.5 $39,934,833 2,211,023
Minnesota Twins 0.259 134 3.71 0.512 $56,186,000 2,013,453
New York Mets 0.258 175 3.76 0.512 $101,305,821 2,782,212
New York Yankees 0.276 229 4.52 0.586 $208,306,817 4,090,440
Oakland Athletics 0.262 155 3.69 0.543 $55,425,762 2,109,298
Philadelphia Phillies 0.27 167 4.21 0.543 $95,522,000 2,665,301
Pittsburgh Pirates 0.259 139 4.42 0.414 $38,133,000 1,794,237
San Diego Padres 0.257 130 4.13 0.506 $63,290,833 2,832,039
San Francisco Giants 0.261 128 4.33 0.463 $90,199,500 3,140,781
Seattle Mariners 0.256 130 4.49 0.426 $87,754,334 2,689,529
St. Louis Cardinals 0.27 170 3.49 0.617 $92,106,833 3,491,837
Tampa Bay Devil Rays 0.274 157 5.39 0.414 $29,679,067 1,124,189
Toronto Blue Jays 0.267 260 4.96 0.488 $55,849,000 2,486,925
Washington Nationals 0.265 136 4.06 0.494 $45,719,500 1,977,949
Texas Rangers 0.252 117 3.87 0.5 $48,581,500 2,692,123
To run the regression program, select the shaded area as shown. You MUST select the column labels
(data can be rows also). Then select the regression option under the MISC icon on the SPC toolbar. You
will get the dialog box shown below.
67 ©2007 Business Process Improvement
This two-page dialog box is used to enter the
information for the regression. The first page
contains the following:
Enter unique name for regression: This
is the name that is used on the
worksheet tab containing the results
and for updating regression results.
Enter range containing the Y values:
This is assumed to be the last
column/row in the selected range on the
worksheet.
Enter range containing X values: This
is assumed to be all except the Y values
above. You can select just one cell in
the data field and the program will
expand that range as the input range.
Data in: Select columns if the data is I columns; the default depends on the number of columns
and rows selected on the worksheet prior to selecting the SPC toolbar.
Set b0 = Zero: Select Yes is you want to force the best line through the origin. The default value
is No.
All Residual Data and Charts?: This option allows you to select all the options on the second
page of the dialog box (see below). The default value is No.
The second page of the dialog box is shown to
the right. Select the options you want for the
charts and data. These include:
Time sequence plot of residuals: the
difference between the actual and
predicted y over time.
Residuals versus the predicted Y
Residuals versus the X variables
Normal probability plot
Line fit plots for each X variables.
You can also print out the residuals and
standardized residuals on a worksheet.
The output from the regression program
(excluding the charts and data options shown on
the second page of the dialog box) is given
below.
68 ©2007 Business Process Improvement
Regression Output
ANOVA Table
df SS MS F Signif. F
Regression 5 9.79271E+12 1.95854E+12 14.54672883 1.33582E-06
Residual 24 3.23131E+12 1.34638E+11
Total 29 1.3024E+13
Coefficients
Coefficient Standard Error t Stat p Value 95% Lower 95% Upper
Intercept 8099237.433 2667080.801 3.03674243 0.005686025 2594653.242 13603821.62
AVG -18922620.41 12537980.63 -1.509223931 0.144295197 -44799740.41 6954499.592
HR 689.429779 2600.899626 0.265073582 0.793216208 -4678.56318 6057.422738
ERA -355703.5027 270091.4996 -1.316974074 0.200284332 -913144.9564 201737.9511
Winning % -863435.1508 2564965.184 -0.33662646 0.739324292 -6157263.068 4430392.766
Totalpayroll 0.016759643 0.00246773 6.791523367 5.03538E-07 0.0116665 0.021852787
Regression Statistics
Multiple R 0.867119393
R Square 0.751896042
Adjusted R Square 0.700207717
Standard Error 366930.4105
Observations 30
Durbin-Waston Statistic 1.655584043
Regression Summary for Attendance
Actual verus Predicted
790,000
1,290,000
1,790,000
2,290,000
2,790,000
3,290,000
3,790,000
4,290,000
4,790,000
790,000 1,290,000 1,790,000 2,290,000 2,790,000 3,290,000 3,790,000 4,290,000 4,790,000
Actual
Pre
dic
ted
69 ©2007 Business Process Improvement
Changing the Variables in the Regression
You have the option to change the variables included in the regression after you have run the initial
regression. There are often variables that are not significant and you may want to remove them from the
regression. You start this routine from the sheet with the regression summary (as shown above). Select
the Update icon on the SPC toolbar. You will get the dialog box below.
You have the following options:
Select variables from the listbox to
include
Remove any variable with a p value
>0.05
Remove any variable with a p value >
0.20
Remove the variable with the highest p
value
Remove the variable with a p value
greater than a value you enter
You also have the option here to change the
chart options. The default value is No. If you
select Yes, you get the dialog box to the right.
Select the option you want or check the “Select
All” box for all options.
You will not lose any previous regression data.
The new worksheets will be named the same as
the previous regression with a “1” after the
previous name.
70 ©2007 Business Process Improvement
Miscellaneous
Selecting the miscellaneous option (Misc) on
the SPC toolbar generates the dialog box
shown to the right. Select the option you
want. The various options are described
below.
Descriptive Statistics
This option displays certain statistics on a number of samples. For example,
suppose you have measured the moisture content of a powder over time and
have fifteen sample results. The data is entered into the spreadsheet as shown
to the right. Select the data only (shaded area), then select the miscellaneous
option (Misc) on the SPC toolbar and then the descriptive statistics option.
You will get the dialog below.
The input range is the range selected on the
spreadsheet. You can change this if it is
not correct. You have two output options:
on the current worksheet (select the cell
location) or a new worksheet. Select OK
and the program will generate the descriptive statistics. A check is
made to ensure that there is no data in the area selected for the output.
The output for the data in this example is shown below.
Descriptive Statistics
Mean 0.131333
Standard Error 0.006537
Median 0.13
Mode 0.14
Standard Deviation 0.025317
Sample Variance 0.000641
Kurtosis -0.0048
Skewness -0.29422
Range 0.09
Minimum 0.08
Maximum 0.17
Sum 1.97
Count 15
Observation % Moisture
1 0.08
2 0.13
3 0.12
4 0.17
5 0.1
6 0.16
7 0.14
8 0.14
9 0.13
10 0.14
11 0.10
12 0.17
13 0.14
14 0.12
15 0.13
71 ©2007 Business Process Improvement
Confidence Interval Around a Mean
This option constructs a confidence interval around a mean based on a number of observations (samples)
There are two cases: one with a known standard deviation and one without a known standard deviation.
The procedure is essentially the same for both. With the know standard deviation, you enter the value and
the program uses the normal distribution to set the confidence interval. When the standard deviation is
not known, the program calculates the standard deviation of the samples and uses the t distribution to set
the confidence interval.
Known Standard Deviation
As an example, consider a process that produces a powdered product whose moisture content is critical to
downstream applications. Too much moisture causes clumping problems in downstream equipment.
Control charts have been kept on moisture content for a long time, and the process is in statistical control.
The average has been estimated to be 0.15% moisture (from the center line on the X chart); the standard
deviation has been estimated to be 0.02 (from the R chart).
An engineer has made a process change that she believes will decrease the
average moisture content. After making the process change, fifteen samples
were collected from the process and measured for moisture content. The
results are given to the right. The question we want to answer is "Has the
process change significantly decreased the moisture content of the product?"
Select the shaded data as shown. Select the confidence interval around a mean
option after selecting the miscellaneous option (Misc) from the SPC toolbar.
You will get the dialog box below.
Enter data range (no headings): The default range is the range
selected on the spreadsheet. You can change this if necessary.
Alpha: The default value for alpha is 0.05. This represents the chance
of what we find out in this sample is not representative of the population. It is typically 0.05.
Enter the known standard deviation (if known): In
this example, it is known and is 0.02.
Output Options: You have two output options: on
the current worksheet (select the cell location) or a
new worksheet. Select OK and the program
generates the output shown below.
Confidence Interval Around a Mean
Mean 0.131333
Standard Deviation 0.02
Count 15
Degrees of Freedom 14
Alpha 0.05
t Value 1.959964
Upper Confidence Level 0.141455
Lower Confidence Level 0.121212
Since the range of the lower to upper confidence levels (0.121 to 0.141) does not include 0.15, you
conclude that the change has made a significant difference.
Observation % Moisture
1 0.08
2 0.13
3 0.12
4 0.17
5 0.1
6 0.16
7 0.14
8 0.14
9 0.13
10 0.14
11 0.10
12 0.17
13 0.14
14 0.12
15 0.13
72 ©2007 Business Process Improvement
Unknown Standard Deviation
The procedure for the unknown standard deviation is identical to the one for the known standard
deviation. When you get the dialog box, leave the box for the known standard deviation empty. For the
example data above, the resulting output is shown below.
Confidence Interval Around a Mean
Mean 0.131333
Standard Deviation 0.025317
Count 15
Degrees of Freedom 14
Alpha 0.05
t Value 2.144787
Upper Confidence Level 0.145353
Lower Confidence Level 0.117313
The confidence interval for the average is between 0.117 and 0.145.
73 ©2007 Business Process Improvement
Confidence Interval Around a Variance
This option places a confidence interval around the variance (the square of the standard deviation) based
on a number of observations (samples). The chi-squared distribution is used.
For example, suppose you are interested in determining a 95% confidence interval
for the variance in bulk density of a powdered product. Ten observations are
pulled from the process and measured for bulk density in grams/cc. The results are
given to the right.
Select the confidence interval around a variance option after selecting the
miscellaneous option (Misc) from the SPC toolbar. You will get the dialog box
shown to the right below. This is the same used for the variance around a mean
(with the standard deviation box not used). See above for the description of each
item. Select the output option and OK to generate the output shown below.
The confidence level for the variance is 0.000165 to 0.001166.
Sample Number
Bulk Density
1 0.697
2 0.698
3 0.673
4 0.657
5 0.710
6 0.702
7 0.680
8 0.709
9 0.670
10 0.671
Confidence Interval Around a Variance
Mean 0.6867
Standard Deviation 0.018703
Variance 0.00035
Count 10
Degrees of Freedom 9
Alpha 0.05
Upper Confidence Level 0.001166
Lower Confidence Level 0.000165
74 ©2007 Business Process Improvement
Confidence Interval for the Difference in Two Means
This option is used to determine the confidence interval for the difference in two means – that is, are two
processes operating at difference averages.
To compare the averages and variances of two processes, we take observations from each process.
Suppose we take n1 observations from process 1 and n
2 observations from process 2. We can then
calculate the sample statistics listed below.
Process 1 Process 2
Sample size n1 n2
Sample average Y–
1 Y
– 2
Sample standard deviation s1 s
2
Sample variance s1
2
s2
2
These sample statistics will be used to compare the variances and averages of the two processes. The
variances will be compared by taking the ratio of the two variances and using the F distribution to
determine if there is a significant difference between the two. The averages will be compared by
constructing a confidence interval around the difference in two averages. If the confidence interval
contains zero (i.e., the difference could be zero), we will conclude that there is no evidence that the two
processes are operating at different averages. If the confidence interval does not include zero, we will
conclude that there is evidence that the processes are operating at different averages.
For example, consider two batch reactors that make the "same" product.
Questions have arisen about whether the reactors really do make the same
product. One indication of the completeness of reaction is the residual
catalyst remaining after reaction. Ten observations were taken from each
reactor. The results are given to the right.
Select the cells in the shaded area for the two processes (do not have to be
adjacent on spreadsheet) and then select the confidence interval for the
difference in two means option after selecting the miscellaneous option
(Misc) from the SPC toolbar. You will get the dialog box shown below.
Enter range for variable 1: The default range is the first range
selected on the spreadsheet. You can change this if necessary.
Enter range for variable 2: The default range is the second range selected on the spreadsheet.
You can change this if necessary.
Alpha: The default value for alpha is 0.05. This
represents the chance of what we find out in this
sample is not representative of the population. It is
typically 0.05.
Enter the known standard deviation (if known): In
this example, it is known and is 0.02.
Reactor 1 Reactor
2
450 482
423 422
443 463
476 492
490 445
436 483
457 476
421 462
485 479
491 495
75 ©2007 Business Process Improvement
Output Options: You have two output options: on the current worksheet (select the cell location)
or a new worksheet. Select OK and the program generates the output shown below.
Difference Betwen Two Means Confidence Interval
Variable 1 Variable 2
Mean 457.2 469.9
Standard Deviation 26.93119 22.56078
Variance 725.2889 508.9889
Observations 10 10
Pooled Variance 617.1389
Variance Same? Yes
t Statistic 1.143134
Degrees of Freedom 18
Alpha 0.05
Critical t value 2.100922
Upper Confidence Level 10.64084
Lower Confidence Level -36.0408
P(T<t) 0.26796
Conclusion No statistical difference in the means.
The program will provide the conclusion for you. In this case, there is no statistical difference in the
means. Note that the program also tells you if the variances in the two processes are the same. In this
case, the variances are the same also.
76 ©2007 Business Process Improvement
Confidence Interval for Multiple Processes
This option is used to determine if the averages and variation in multiple processes are the same or not.
You start with n samples from each process. You can have up to 25 samples per process.
For example, suppose you have four furnaces producing ethylene. You measure the % ethylene from
each furnace. You want to know if there a difference in the average results from each furnace. To
determine this you take seven samples from each furnace. The results are given below.
Furnace
1
Furnace
2
Furnace
3
Furnace
4
67 64 68 69
67 64 65 72
64 64 67 70
65 64 64 68
64 64.1 67 67
65 64 65 68
67 64 65 70
To run the program, select the data including the headings. Then select the Confidence Interval for
Multiple Processes. You will see the dialog box below.
Alpha: The default value for alpha is 0.05. This represents the chance of what we find out in this sample
is not representative of the population. It is typically 0.05. Select OK. The program will insert a new
worksheet with the output. The output from the data above is shown on the next page. The following are
calculated:
Mean: average for each process
Sigma: standard deviation of each process
Variance: variance of each process
Observations: number of observations per process
Average Sigma: average standard deviation
UCLs: Upper control limit for the s control chart
LCLs: Lower control limit for the s control chart
Pooled Variance: the estimated variance
Interval Alpha: the interval alpha (which is the alpha entered above divided by the number of
confidence intervals)
t value: the value of the t distribution
77 ©2007 Business Process Improvement
Furnace 1 Furnace 2
Furnace 3
Furnace 4
67 64 68 69
67 65 65 72
64 67 67 70
65 64 64 68
64 65 67 67
65 68 65 68
67 64 65 70
Mean 65.57143 65.28571 65.85714 69.14286
Sigma 1.397276 1.603567 1.46385 1.676163
Variance 1.952381 2.571429 2.142857 2.809524
Observations 7 7 7 7 Average Sigma 1.535214
UCLs 2.889273
LCLs 0.181155 Pooled Variance 2.369048
Interval Alpha 0.008
T Value 2.892495
Process Lower Confidence Upper Confidence
Furnace 1 -2.094 2.665432 No statistical difference in the means.
Furnace 2
Furnace 1 -2.66543 2.094004 No statistical difference in the means.
Furnace 3
Furnace 1 -5.95115 -1.19171 Means are different
Furnace 4
Furnace 2 -2.95115 1.808289 No statistical difference in the means.
Furnace 3
Furnace 2 -6.23686 -1.47743 Means are different
Furnace 4
Furnace 3 -5.66543 -0.906 Means are different
Furnace 4
Each possible pair of averages is checked. The program tells you if the means are different (see italics
above).
78 ©2007 Business Process Improvement
Paired Sample Comparison
There are occasions when the same samples may be used in two different processes. For example, you
might be interested in comparing two test methods. To do this, you would mix a sample thoroughly and
then split it in two. Half of the sample would be run in one test, and the other half would be run in the
other test. The samples used are not independent. In this case, the method for comparing two processes
given above can not be used. The paired sample comparison method option must be used.
For example, suppose you are interested in comparing two test
methods for analyzing particle size in microns. One test method
involves the use of sieves. The other test method is a particle
analyzer that measures particle size in slurry. Ten samples are split
in half and run in each test method. The results are shown to the
right. The program is examining the difference between each
process for the same sample to see if the mean difference is
significantly different than 0.
Select the shaded areas (the data for the two tests; do not have to be
adjacent) and then select the paired sample comparison option after
selecting the miscellaneous option (Misc) from the SPC toolbar.
You will get the dialog box shown below. This is identical to the
dialog box for the confidence interval between two means. Please
see the above section for the description of the dialog box
entries.
Fill in the dialog box and select OK. The program will
generate the output below.
The program will provide the conclusion for you. In this
case, there is a difference between the two processes. The
confidence interval defined by the lower and upper
confidence limits do not contain zero.
Paired Sample Comparison
Mean Difference 5.2
Standard Deviation 5.266245
Variance 27.73333
Observations 10
Degrees of Freedom 9
Alpha 0.05
t value 2.262157
Upper Confidence Level 8.967245
Lower Confidence Level 1.432755
Conclusion Means are different
Observation Number
Sieve Test
Particle Size Analyzer
1 245 242
2 196 190
3 205 208
4 226 215
5 213 203
6 234 235
7 229 220
8 192 193
9 233 224
10 204 195
79 ©2007 Business Process Improvement
Analysis of Means
Analysis of means is a graphical and statistical way of comparing k treatments means with the overall
mean. The method used in this program is described in the book Advanced Topics in Statistical Control
by Dr. Donald J. Wheeler (www.spcpress.com). The example is from the book.
The maximum number of treatments is 25. The maximum subgroup size for each treatment is also 25.
Suppose you are studying five different methods
(treatments) of applying a coating and are
measuring the weight of the coating. The data
entry requirement for this option is shown to the
right. The treatments are A – E. The weight for
each treatment is given in the column under the treatment letter.
To run the Analysis of Means, select the treatment headings and the data
(the shaded area above). Then select the Analysis of Means option after
selecting the miscellaneous option (Misc) from the SPC toolbar. The
dialog box to the right appears.
Select the range containing the treatments with the headings:
Select both the data and the treatment names.
Treatment Data in Columns/Row: The data can either be in
columns or rows.
Output Options: You have two output options: on the current
worksheet (select the cell location) or a new worksheet.
Title: The title of the averages chart. Default is “ANOM.”
Y-Axis Label: Default value is “Treatment Average”
X-Axis Label: Default value is “Treatment Number.”
Rounding to Use in Titles: This is the rounding that is used in the
chart titles for the averages and control limits.
Select OK and the output and charts on the next page are generated. The UDL and LDL are the upper
decision limit and the lower decision limits. Any points beyond these limits on the top chart represent
significant differences from the overall treatment average. The range chart is a classical range chart and
compares the variation within treatments to see if they are the same.
A B C D E
250 310 250 340 250
260 330 230 270 240
230 280 220 300 270
270 360 260 320 290
80 ©2007 Business Process Improvement
Treatment A B C D E
250 310 250 340 250
260 330 230 270 240
230 280 220 300 270
270 360 260 320 290
Average 252.5 320 240 307.5 262.5
Maximum 270 360 260 340 290
Minimum 230 280 220 270 240
Range 40 80 40 70 50
Treatment Variance 291.6666667 1133.333333 333.3333333 891.6666667 491.6666667
Treatment DF 3 3 3 3 3
Overall Average 276.5
Average Range 56
Est. V(X) N/A
d2* 2.096
Est SD(X) 26.71755725
Est SD(Xbar) 13.35877863
Degrees of Freedom 14
H 2.266666667
ANOM Upper Limit 306.7798982
ANOM Lower Limit 246.2201018
ANOM (Avg=277, UDL=307, LDL=246)
Avg
UDL
LDL
216
236
256
276
296
316
336
A B C D E
Treatment Number
Tre
atm
en
t A
vera
ge
Range Chart (Avg=56, UCL=128, LCL=None)
Avg
UCL
LCL0
20
40
60
80
100
120
140
A B C D E
Treatment Number
Tre
atm
en
t R
an
ge
81 ©2007 Business Process Improvement
Correlation Coefficients
The linear correlation coefficient, R, is a measure of the association between two
variables. The data to the right shows the lines picked per hour in a warehouse and
the overtime hours. The value of R will measure the degree of association
between these two variables. The maximum value for R is + 1. The minimum
value for R is - 1. In both these cases, all sample points fall on a straight line.
As R approaches +1 or -1, the stronger the correlation between x and y. The
square of this coefficient (R2) indicates the fraction of variation in y that is
associated with x.
To determine the correlation coefficient, select the data including the headings
(shaded area to the right) and then select the Correlation Coefficients options after
selecting the miscellaneous option (Misc) from the SPC toolbar. The dialog box
below appears.
Input Range: The input
range is the range selected
on the worksheet. If it is not
correct, you can change it.
Output Options: You have
two output options: on the current worksheet
(select the cell location) or a new worksheet.
Select OK and the output below is generated.
Lines Picked Hours Overtime
Lines Picked 1.00 0.92
Hours Overtime 0.92 1.00
The value of R is 0.92 indicating a strong relationship between lines picked and overtime hours.
In most cases, you will have more than two variables that you are examining. The program works the
same for multi-variables and will generate a correlation matrix as shown below (for an example using 6
variables, A – F.
A B C D E F
A 1.00 0.14 0.37 -0.03 -0.15 -0.04
B 0.14 1.00 0.30 0.08 -0.34 0.19
C 0.37 0.30 1.00 -0.17 -0.35 -0.05
D -0.03 0.08 -0.17 1.00 0.09 0.12
E -0.15 -0.34 -0.35 0.09 1.00 0.13
F -0.04 0.19 -0.05 0.12 0.13 1.00
Lines Picked
Hours Overtime
599 23.5
658 28.5
699 29
738 30.5
791 31.5
685 28
656 28
570 24.5
614 26
684 29.5
749 30
608 24.5
653 25.5
650 27
671 29
606 24
648 25.5
758 31
712 30
611 25.5
671 26
651 27
82 ©2007 Business Process Improvement
Failure Mode and Effect Analysis
A Failure Mode and Effects Analysis (FMEA) template is included in the program. To access the
template, select the FMEA option from the toolbar. The template below will be added to the workbook.
Date Prepared:
What is the
Potential Failure
Mode?
What are the Potential Effects of
the Failure Mode
Severi
ty
What are the Possible Causes of
the Failure?
Occu
rren
ce
How Do We Currently Prevent
Each Listed Cause of Failure from
Happening?
Dete
cti
on
S O D RPN
No. ResponsibilityO D
Improved
RPNWhat Needs to Be Done Status
What is the
Process?
Recommended Action Steps and Status Due
DateS
Failure Effects and Mode AnalysisPrepared by:
Add the text as you would in an Excel spreadsheet.
83 ©2007 Business Process Improvement
Box and Whisker Plots
A Box and Whisker plot is used to present a visual
representation of how data is spread out and how much
variation there is in the data. It focuses attention on the
median, the quartiles, and the minimum and maximum
values. For example, the data to the right shows how the
average monthly temperature for three cities varies. The Box
and Whisker plot can show this variation.
Select the data including the headings (the shaded area to the
right) and then select the Box and Whisker plots option after
selecting the miscellaneous option (Misc) from the SPC
toolbar. You will see the dialog box below.
Select the range: The default range is the range that
is selected on the worksheet.
Treatment Data in Columns/Rows: The data can be in
columns or rows.
Box and Whisker Title and Labels
o Title: The title that will appear on the chart
o Y and Axis Label: The label that will appear on the
y axis.
Selecting OK will generate the Box and Whisker plot shown on the
next page. The graph below shows the values for each part of the
plot. The maximum value is presented by the top line (whisker).
The top part of the box is the 75% quartile; the bottom part is the
25% quartile. The minimum is represented by the bottom line
(whisker).
Seattle, WA
San Antonio TX
New York, NY
Jan 46 61 38
Feb 51 66 40
Mar 54 74 50
Apr 58 80 61
May 64 85 72
June 70 92 80
July 74 95 85
Aug 74 95 84
Sept 69 89 76
Oct 60 82 65
Nov 52 72 54
Dec 46 64 43
Box and Whisker Chart
Ne
w Y
ork
, N
Y
San
An
ton
io T
X
Sea
ttle
, W
A
0
10
20
30
40
50
60
70
80
90
100
Su
bg
rou
p A
ve
rag
eMedian
75% quartile
Maximum
25% quartile
Minimum
84 ©2007 Business Process Improvement
Box and Whisker Chart
Ne
w Y
ork
, N
Y
Sa
n A
nto
nio
TX
Se
att
le, W
A
0
10
20
30
40
50
60
70
80
90
100
Su
bg
rou
p A
vera
ge
85 ©2007 Business Process Improvement
Sample Size Calculator
The sample size calculator is available under the MISC option on the
SPC toolbar. When you select this option, you will see the dialog
boxes to the right. The first page is for variables data. The second
page is for attributes data.
For variables data, enter the following:
Confidence interval
Standard deviation
Measurement error
Then select “Calculate Sample Size,” and the sample size needed
will appear in the bottom box.
For attributes data, enter the following:
Confidence interval
Estimated percentage of successes
Measurement error
Population size (if known)
Then select “Calculate Sample Size,” and the sample size needed
will appear in the bottom box.
86 ©2007 Business Process Improvement
Side by Side Histogram
You can develop side by side histograms to compare results. For example, you may have done a survey
that separates the male and female responses. A side by side histogram is shown below.
Histogram of Male/Female Responses
1
3
1
0
2
4
3 3 3
4
1
6
0
1
5
4
2 2
3
00
1
2
3
4
5
6
7
0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
Rating
Fre
qu
en
cy
Female
Male
There are two options you have. The first option
is that you have already totaled the data by
groups. In this case, your data entry will look
the data to the right. The classes are in the first
column, followed by the data that you have
already totaled.
The second option is to let the program total the
data. In this case, you simply enter in the results
as shown to the left.
Class Female Male
0-10 1 1
11-20 3 6
21-30 1 0
31-40 0 1
41-50 2 5
51-60 4 4
61-70 3 2
71-80 3 2
81-90 3 3
91-100 4 0
Female Male
41 18
99 89
78 56
96 78
99 88
58 45
69 51
85 65
54 45
79 60
65 47
7 4
52 36
23 14
15 12
63 45
41 15
78 55
12 11
87 76
96 87
13 12
55 45
85 64
87 ©2007 Business Process Improvement
When you select the “Side by Side Histogram” option
under the Misc icon on the SPC toolbar, you will get the
form shown to the right. Each dialog box entry is
described below.
Enter range containing data including labels;
data must be in columns: Enter the worksheet
range containing the data including the column
headings (see examples above). The data must be
in columns. The default value is the range
selected on the worksheet before selecting the
Side by Side Histogram option.
Data: There are the two options explained above.
o Totaled by Class Already: The data has
already be summed by class.
o Not Totaled: The data has not been
totaled. The program will perform this
function based on the following two
values:
Lower Bound >: This value gives the starting point for the histogram. For
example, if you enter 0 here, the first class will involve values greater than 0 to
the class width
Class Width =: This is the width of one class.
Enter Histogram Title: Enter the title that will appear on the chart. The default title is
“Histogram.”
Enter Y-Axis (Vertical Label): Enter the label for the y axis. The default value is “Frequency.”
Enter X-Axis (Horizontal Label): Enter the label for the x axis. The default value is
“Measurement.”
Date of Data Collection: You can enter the dates of data collection. This is optional.
88 ©2007 Business Process Improvement
Plot Multiple Y Variables Against One X Variable
The program will plot multiple Y variables against one X variable. An example of this type of chart is
shown below.
Amps versus Time
-6
-4
-2
0
2
4
6
8
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2
time (sec)
Y
Experimental Intensity (amps)
Theoretical Intensity (amps)
The data for this chart must be in columns with the X variable in
the first column. The Y variables must be in adjacent columns.
The data used to generate the above chart is shown to the right.
When you select the “Plot Multiple Y Variables Against One X
Variable” from the “Misc” icon on the SPC toolbar, you will get
the form shown below. Each entry is discussed below.
The first entry is for the range containing the data (including the
headings as shown to the right). The default value is the range
selected on the worksheet. Enter the title for the chart as well as
the axis labels. You can enter the dates of data collection
(optional).
time (sec)
Experimental Intensity (amps)
Theoretical Intensity (amps)
0 6 6
0.2 5.8 5.967131372
0.4 5.8 5.868885604
0.6 5.6 5.706339098
0.8 5.5 5.481272746
1 5 5.196152423
1.2 4.7 4.854101966
1.4 4.5 4.458868953
1.6 4 4.014783638
1.8 3.4 3.526711514
2 2.9 3
2.2 2.3 2.440419858
2.4 1.7 1.854101966
2.6 1 1.247470145
2.8 0.5 0.62717078
3 0 -9.64723E-16
3.2 -0.05 -0.62717078
3.4 -1.25 -1.247470145
3.6 -1.75 -1.854101966
3.8 -2.25 -2.440419858
4 -3 -3
4.2 -3.5 -3.526711514
89 ©2007 Business Process Improvement
Select Cells
You can save some time with some of the tools in this program by selecting the appropriate cells prior to
selecting the icon on the SPC toolbar. For example, if you are making a p control chart, it is beneficial to
select the subgroup identifiers before selecting the attribute control chart icon from the SPC toolbar. This
can be a little cumbersome if you have lots of subgroups. The Select Cells (SC) on the SPC toolbar helps
make this easier.
Selecting One Cell Only
If you have the cursor in one cell only (as shown by the
shaded cell in the table to the right) and you select the SC
icon on the SPC toolbar, the program will select the cells
directly below the shaded cell (including the shaded cell)
as shown the table below.
Date Number of
Telemarketing Calls (n)
Number that Result in an Order (np)
2/1/2003 40 5
2/2/2003 63 10
2/3/2003 47 12
2/4/2003 52 7
2/5/2003 34 3
2/6/2003 59 21
Selecting More Than One Cell
If you select more than one cell (as shown to the right), all
adjacent cells (beginning with the first row and first
column) will be selected.
Date Number of
Telemarketing Calls (n)
Number that Result in an Order (np)
2/1/2003 40 5
2/2/2003 63 10
2/3/2003 47 12
2/4/2003 52 7
2/5/2003 34 3
2/6/2003 59 21
Date Number of
Telemarketing Calls (n)
Number that Result in an Order (np)
2/1/2003 40 5
2/2/2003 63 10
2/3/2003 47 12
2/4/2003 52 7
2/5/2003 34 3
2/6/2003 59 21
Date Number of
Telemarketing Calls (n)
Number that Result in an Order (np)
2/1/2003 40 5
2/2/2003 63 10
2/3/2003 47 12
2/4/2003 52 7
2/5/2003 34 3
2/6/2003 59 21
90 ©2007 Business Process Improvement
Frequently Asked Questions
What out of control tests does the program use?
The program uses the following tests to check if a control chart is out of control:
Points beyond the limits
Rule of seven tests
o Seven in a row above or below the average
o Seven in a row trending up or trending down
Zone Tests
o Zone A: 2 out of 3 consecutive points in zone A or beyond
o Zone B: 4 out of 5 consecutive points in zone B or beyond
o Zone C: 7 or more consecutive points in zone C or beyond
o Mixtures: 8 or more consecutive points fall outside of zone C on both sides the average
o Stratification: 15 or more consecutive points fall in zone C on either side of the average
Do all out of control tests apply to all the charts?
No. You will have the option to select which out of control charts you want to apply to your chart when
the dialog box for the control chart is shown. The out of control tests listed in the dialog box are the ones
that apply for your chart.
How do I know if the chart has any out of control points?
Out of control points are shown in red on the chart. The in-control points are in blue.
Can I remove the out of control points from the calculations?
Yes. You can remove the out of control point from the calculations by selecting the point and then
selecting “SP” from the SPC toolbar. This brings up a dialog box that allows you to remove the point
from calculations (or to add it back in). The point remains plotted on the graph but is outlined in color
only.
You can also remove all points beyond the control limits at once by selecting “All” from the SPC toolbar.
This brings up a dialog box that allows you to remove all the points beyond the limits at once (or add
them back in). This option does not remove the out of control points for the rule of seven tests or the
zone tests.
Can I change the name of the worksheet tab containing the chart?
If you do this, the program will not be able to find the chart if you want to update it or to make changes.
There is a manual method of doing this, but it is better if you just make a new chart.
How come I can’t see the name of one of my charts in the list of charts to be updated?
The most common cause of this problem is that the name on the worksheet tab containing the chart has
been changed. The program can no longer find the chart. The easiest solution is to make a new chart.
91 ©2007 Business Process Improvement
How can I change the title or the x and y labels on an existing chart?
To change the chart title or labels on an existing chart, you must go select the Options icon on the SPC
toolbar and change the title or labels there. If you make the changes directly on the chart, they will not be
saved if the chart is updated.
.
Any other questions?
Please feel free to e-mail us with your questions or suggestions for improvement ([email protected])
or visit our website (www.spcforexcel.com) for all the SPC information we have in our e-zines and
articles.
Enjoy the program!