MGS8020 Measure.ppt/Mar 26, 2015/Page 1 Georgia State University - Confidential MGS 8020 Business Intelligence Measure Mar 26, 2015

MGS8020 Measure.ppt/Mar 26, 2015/Page 1Georgia State University - Confidential

MGS 8020

Business Intelligence

Measure

Mar 26, 2015


Measure - SMART

“Voice of the Process” (The “Voice of the Data”)

Based on natural (common cause) variation

Tolerance limits (The “Voice of the Customer”) Customer requirements/Specs

Process Capability A measure of how “capable” the process is to meet customer requirements

Compares process limits to tolerance limits


Agenda

1. Analysis Tools

2. Control Charts

3. Process Capability


Data Analysis Tools

02468

1012

0 10 20 30Hours of Training

De

fects

Scatter Diagram

0.46

0.5

0.54

0.58

1 2 3 4 5 6 7 8 9 10 11 12

Time

Dia

met

er

Run Chart

Can be used to identify when equipment or processes means are drifting away from specs

Can be used to illustrate the relationships between factors such us quality and training

Fre

quency

Data Ranges

Histogram

Use to identify if the process is predictable (in control)

Can be used to display the shape of variation in a set of data

400

420

440

460

480

500

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

LCL

UCL

400

420

440

460

480

500

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

LCL

UCL

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

LCLLCL

UCLUCL

Control Chart


Cause and Effect Diagram

MaterialMethod

Environmental

ManMachine

Effect


Pareto ChartsRoot Cause Analysis

Design Assy.Instruct.

Purch. Training Other

80% of theproblems may beattributed to 20%

of the causes


Agenda

1. Analysis Tools

2. Control Charts



A Processis not in control when one or more points is/are outside the control limits

Special Causes

UCL

LCL

Process in Statistical Control

Process not in Statistical Control

Process not in Statistical ControlUCL

LCL

UCL

LCL

A Processis in control when all points are inside the control limits

Statistical process control is the use of statistics to measure the quality of an ongoing process

Statistical Process Control (SPC): Used to determine if process is within process control limits during the process and to take corrective action when out of control


When to Investigate

Even if in control the process should be investigated if any non random patterns are observed OVER TIME

UCL

LCL

1 2 3 4 5 6

In Control

UCL

LCL 1 2 3 4 5

Close to Control Limit

UCL

LCL

1 2 3 4 5 6

Consecutive Points Below/Above Mean UCL

LCL

5 10 15 20

Cycles

1 2 3 4 5 6

UCL

LCL

Trend - Constant Increase/Decrease


Types of Variation

Caused by factors that can be clearly identified and possibly managed; assignable causes evident, not in statistical control

Short-term objective - to eliminate unexpected variation Inherent in the process

Normal variation only, stable, predictable, in statistical control

Long-term objective - to

reduce expected variation

Prediction

Time

Special cause (unexpected) variation

Time

Prediction

Common cause (expected) variation


Control Chart Development Steps

INPUTSOUTPUT

X’s Y’s

Identify Measurement1Sample

Sample Size Defective p

1 100 4 0.042 100 3 0.033 100 5 0.054 100 6 0.065 100 2 0.026 100 1 0.017 100 6 0.068 100 7 0.079 100 3 0.03

10 100 8 0.0811 100 1 0.0112 100 2 0.0213 100 1 0.0114 100 9 0.0915 100 1 0.01

Total 1500 59

Collect Data2

0

0.02

0.04

0.06

0.08

0.1

0 2 4 6 8 10 12 14 16 18

Determine Control Limits3Improve Process4

A B C D

Defects

Start

Eliminate Special Causes

Reduce Common Cause Variation Improve

Average


Quality Measures – Attributes & Variables

• An attribute is a product characteristics such as color, surface texture, cleanliness, or perhaps smell or taste. Attributes can be evaluated quickly with a discrete response such as good or bad, acceptable or not, yes or no. An attribute measure evaluation is sometimes referred to as a qualitative classification, since the response is not measured.

• A variable measure is a product characteristics that is measured on a continuous scale such as length, weight, temperature, or time. For example, the amount of liquid detergent in a plastic container can be measured to see if it conforms to the company’s product specifications.


Control Charts

• Control Charts have historically been used to monitor the quality of manufacturing process. SPC is just as useful for monitoring quality in services. The difference is the nature of the “defect” being measured and monitored. Using Motorola’s definition – a failure to meet customer requirements in any product or service.

• Control Charts are graphs that visually show if a sample is within statistical control limits. The control limits are the upper and lower bands of a control chart. They have two basic purposes, to establish the control limits for a process and then to monitor the process to indicate when it is out of control. All control charts look alike, with a line through the center of a graph that indicates the process average and lines above and below the center line that represent the upper and lower limits of the process.


Control Charts for Attributes

• The quality measures used in attribute control charts are discrete values reflecting a simple decision criterion such as good or bad. A p-chart uses the proportion of defective (defectives) items in a sample as the sample statistics; a c-chart uses the actual number of defects per item in a sample.

p-charts• Although a p-chart employs a discrete attribute measure (i.e. number of

defective items) and thus is not continuous, it is assumed that as the sample size gets larger, the normal distribution can be used to approximate the distribution of the proportion defective.

Source: Selected Chapters on Business Analysis – Ch15 Statistical Process Control

Z


Control Charts for Attributes~ p-chart

• The p-formula – the sample proportion defective; an estimate of the process average

• The standard deviation of the sample proportion

• To calculate control limits for the p-chart:

• z = the number of standard deviations from the process average. In the control limit formulas for p-charts (and other control charts), z is occasionally equal to 2.00 but most frequently is 3.00. A z value of 2.00 corresponds to an overall normal probability of 95 percent and z = 3.00 corresponds to a normal probability of 99.74 percent.

Z

δp =

Z

Total defectives Total sample observations

n

n

k = the number of samples

n = the sample size

-2 -1 0 1 2 3-3

Z- VALUE is the number of Standard Deviations from the mean of the Normal Curve

Normal Distribution: Z-Value

Z


Control Charts for Attributes~ p-chart (Example)

• The Western Jeans company produces denim jeans. The company wants to establishes p-chart to monitor the production process and maintain high quality. Western believes that approx. 99.74 percent of the variability in the production process (z = 3.00) is random and thus should be within control limits, whereas 0.26 percent of the process variability is not random and suggests that the process is out of control.

• The company has taken 20 samples (one per day for 20-days), each containing 100 pairs of jeans (n=100), and inspected them for defects. The total number of defectives are 200.

• Find the control limits.

Z


Control Charts for Attributes~ c-chart

• A c-chart is used when it is not possible to compute a production defective and the actual number of defects must be used. For example, when automobiles are inspected, the number of blemishes (i.e. defects) in the paint job can be counted for each car, but a proportion cannot be computed, since the total number of possible blemishes is not known.

•

• The standard deviation

• To calculate control limits for the p-chart:

Z

Z

δc =

f = the total number of defects / total number of samples


Control Charts for Attributes~ c-chart (Example)

• The Ritz Hotel believes that approximately 99% of the defects (corresponding to 3-sigma limits) are caused by natural, random variations in the housekeeping and room maintenance service, with 1% caused by nonrandom variability. They want to construct a c-chart to monitor the housekeeping service.

• 15 inspections samples are selected by the hotel. An inspection sample includes 12 rooms and the total number of defects is 190.

• Find the control limits.

Z


Control Charts for Variables~ R-chart

• Variable control charts are for continuous variables that can be measured, such as weight or volume. Two commonly used variable control charts are the range chart (R-chart) and the mean chart (x-bar chart).

R-chart• In an R-chart, the range is the difference between the smallest and largest

values in a sample. This range reflects the process variability instead of the tendency toward a mean value.

• R is the range of each samplek is the number of samples.

Source: Selected Chapters on Business Analysis – Ch15 Statistical Process Control

Z

Upper control limit

Lower control limit


Control Charts for Variables~ R-chart (Example)

• In the production process for a particular slip-ring bearing the employees have taken 10 samples (during 10-day period) of 5 slip-ring bearings (n=5). Please define the control limits for R-chart. The individual observations from each sample are shown as follows:

Z

Sample k 1 2 3 4 5 R

1 5.02 5.01 4.94 4.99 4.96 4.98 0.08

2 5.01 5.03 5.07 4.95 4.96 5.00 0.12

3 4.99 5.00 4.93 4.92 4.99 4.97 0.08

4 5.03 4.91 5.01 4.98 4.89 4.96 0.14

5 4.95 4.92 5.03 5.05 5.01 4.99 0.13

6 4.97 5.06 5.06 4.96 5.03 5.02 0.10

7 5.05 5.01 5.10 4.96 4.99 5.02 0.14

8 5.09 5.10 5.00 4.99 5.08 5.05 0.11

9 5.14 5.10 4.99 5.08 5.09 5.08 0.15

10 5.01 4.98 5.08 5.07 4.99 5.03 0.10

sum 50.11 1.15

average 0.115

R


Control Charts for Variables~ x-bar chart

• For an x-bar chart, the mean of each sample is computed and plotted on the chart; the points are sample means. The samples tend to be small, usually around 4 or 5.

n is the sample size (or number of observations)

k is the number of samples

Z

Upper control limit

Lower control limit


Control Charts for Variables~ x-bar chart (Example)

• Use the data from R-Chart and define the control limits for x-bar chart.

Z


Control Charts for Variables~ Tabular values for X-bar and R charts (Given)

Sample Size n A2 D3 D4

2 1.880 0 3.268

3 1.023 0 2.574

4 0.729 0 2.282

5 0.577 0 2.114

6 0.483 0 2.004

7 0.419 0.076 1.924

8 0.373 0.136 1.864

9 0.337 0.184 1.816

10 0.308 0.223 1.777

11 0.285 0.256 1.744

12 0.266 0.283 1.717

13 0.249 0.307 1.693

14 0.235 0.328 1.672

15 0.223 0.347 1.653


Control Charts for Variables~ Tabular values for X-bar and R charts (Given)

Sample Size n A2 D3 D4

16 0.212 0.363 1.637

17 0.203 0.378 1.622

18 0.194 0.391 1.608

19 0.187 0.403 1.597

20 0.180 0.415 1.585

21 0.173 0.425 1.575

22 0.167 0.434 1.566

23 0.162 0.443 1.557

24 0.157 0.451 1.548

25 0.153 0.459 1.541


Process Capability

Process Capability – A measure of how “capable” the process is to meet customer requirements; compares process limits to tolerance limits. There are three main elements associated with process capability – process variability (the natural range of variation of the process), the process center (mean), and the design specifications.

Process limits (The “Voice of the Process” or The “Voice of the Data”) - based on natural (common cause) variation

Tolerance limits (The “Voice of the Customer”) – customer requirements


Agenda

1. Analysis Tools

2. Control Charts



Process Capability

• Variation that is inherent in a production process itself is called common variation.

common variation

specification

(1)

specification

common variation

(3)

specification

common variation

(2)

specification

common variation

(4)


Process Capability Ratio

• One measure of the capability of a process to meet design specifications is the process capability ratio (Cp). It is defined as the ratio of the range of the design specifications (the tolerance range) to the range of process variation, which for most firms is typically ±3δ or 6δ

• If Cp is less than 1.0, the process range is greater than the tolerance range, and the process is not capable of producing within the design specifications all the time. If Cp equals 1.0, the tolerance range and the process range are virtually the same. If Cp is greater than 1.0, the tolerance range is greater than the process range.

• Companies would logically desire a Cp equal to 1.0 or greater, since this would indicate that the process is capable of meeting specifications.


Process Capability Ratio (Example)

• The XYZ Snack Food Company packages potato chips in bags. The net weight of the chips in each bag is designed to be 9.0 oz, with a tolerance of +/- 0.5 oz. The packaging process results in bags with an average net weight of 8.80 oz and a standard deviation of 0.12 oz. The company wants to determine if the process is capable of meeting design specifications.


Process Capability Index

• The Process Capability Index (Cpk) differs from the Cp in that it indicates if the process mean has shifted away from the design target, and in which direction it has shifted – that is, if it is off center.

• If the Cpk index is greater than 1.00 then the process is capable of meeting design specifications. If Cpk is less than 1.00 then the process mean has moved closer to one of the upper or lower design specifications, and it will generate defects. When Cpk equals Cp, this indicates that the process mean is centered on the design (nominal) target.

• Please read Example 7 on page 354.

where• x-bar is the mean of the process

• sigma is the standard deviation of the process

• UTL is the customer’s upper tolerance limit (specification)

• and LTL is the customer’s lower tolerance limit

3

X-UTLor

3

LTLXmin=Cpk


Interpreting the Process Capability Index

Cpk < 1 Not Capable

Cpk > 1 Capable at 3

Cpk > 1.33 Capable at 4

Cpk > 1.67 Capable at 5

Cpk > 2 Capable at 6


Process Capability Index (Example)

• A process has a mean of 45.5 and a standard deviation of 0.9. The product has a specification of 45.0 ± 3.0. Find the Cpk .


Process Capability Index (Example)

= min { (45.5 – 42.0)/3(0.9) or (48.0-45.5)/3(0.9) }

= min { (3.5/2.7) or (2.5/2.7) }

= min { 1.30 or 0.93 } = 0.93 (Not capable!)

However, by adjusting the mean, the process can become capable.

3

X-UTLor

3

LTLXmin=Cpk

Documents

MGS8020 Measure.ppt/Mar 26, 2015/Page 1 Georgia State University - Confidential MGS 8020 Business Intelligence Measure Mar 26, 2015