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Variables Control ChartsVariables Control Chartsfor Subgroupsfor Subgroups
(X-R & X-(X-R & X-ss Charts) Charts)
2
Basic SPC
What is “SPC”?What is “SPC”?
You Think You Know ... You Think You Know ...But Do You Really?But Do You Really?
3
Basic SPC
Enough of Teasing ..Enough of Teasing ..
Let’s start to undo the Let’s start to undo the confusion.confusion.
X =X
n
Distribution of Sampling Averages
XX
4
Basic SPC
VariabilityVariability The Devil is in the Deviations. No two things
can ever be made exactly alike, just like no two things are alike in nature.
Variation cannot be avoided in life! Every process has variation. Every measurement. Every sample!
LSL USLT
Time 1
Time 2
Time 3
Time 4
5
Basic SPC
Sources of VariationSources of Variation Variability can come about due to changes in:
Material quality
Machine settings or conditions
Manpower standards
Methods of processing
Measurement
Environment
6
Basic SPC
Types of VariationTypes of Variation
One way of classifying variation is:
within unit (positional variation)
between units (unit-unit variation)
between lots (lot-lot variation)
between lines (line-line variation)
across time (time-time variation)
measurement (gage repeatability & reproducibility)
7
Basic SPC
Quality and VariabilityQuality and Variability
yVariabilit
1Quality
Quality is fitness for use
What is “Quality”?
8
Basic SPC
Product ControlProduct Control Model for Model for Quality ControlQuality Control
Raw Material, Components & Sub-Assemblies
Process
Product
InspectionPass
Ship
Fail
Rework Scrap
ShipRecycle Disposal
9
Basic SPC
Process ControlProcess Control Model for Model for Quality ControlQuality Control
Raw Material, Components & Sub-Assemblies
Process
Product
Observation: Data Collection
Evaluation: Data Analysis
Diagnosis: Fault Discovery
Decision: Formulate Action
Implementation: Take Action
Uncontrollable Inputs
Controllable Inputs
10
Basic SPC
Statistical Process ControlStatistical Process Control The process control model shifts focus to the
home front, i.e. the manufacturing process, taking a preventive instead of reactive mode.
It also has something which the old concept of product control lacked - statistics. This allows use of samples to understand the entire process.
The new emphasis had to have a name - Statistical Process Control (SPC).
We owe the application of statistics as a tool for manufacturing to Dr Walter A. Shewhart.
11
Basic SPC
Dr Walter A. ShewhartDr Walter A. ShewhartFather of Control ChartsFather of Control Charts
Physicist at Bell Telephone Labs., specializing in the Brownian movement.
Asked to help in the war effort to design standard radio headset for army troops.
Developed important descriptive statisticsto aid in manufacturing, the most important of which was the X-R chart (invented in 1924).
Presented to the outside world in a series of lectures at Stevens Institute of Technology. The lecture material became his well-known book, Economic Control of Quality of Manufactured Product (1931).
12
Basic SPC
Success in ManufacturingSuccess in Manufacturing
The key to success in manufacturing is an effective SPC program that continuously finds and eliminates problems.
Central to an SPC program are the following:
Understand the causes of variability: Shewhart found two basic causes of variability:
Chance causes of variabilityAssignable causes of variability
Develop methods of recognizing these causes: SPC charts
13
Basic SPC
Introduction to SPC ChartsIntroduction to SPC Charts
Concepts and Principles of Control Charts
Let’s dive into them now ...
14
Basic SPC
Two Basic Causes of Two Basic Causes of VariabilityVariability
Chance Causes of Variation
Due to the cumulative effect of many small unavoidable sources of variation.
Also known as: common variation random variation inherent variation natural variation
A process operating with only chance causes of variation present is said to be “in statistical control”.
15
Basic SPC
Two Basic Causes of Two Basic Causes of VariabilityVariability
Assignable (or Special) Causes of Variation
Variation in a process that is different from from chance variation; disturbs a process so that what it produces seems unnatural.
Examples of such causes of variation are: improperly adjusted machine excessive tool wear defective raw material
A process operating in the presenceof assignable causes of variation issaid to be “out-of-control”.
16
Basic SPC
Objectives of SPC ChartsObjectives of SPC Charts All control charts have one primary purpose!
To detect assignable causes of variationthat cause significant process shift, so that:
investigation and corrective action may be undertaken to rid the process of the assignable causes of variation before too many non-conforming units are produced.
in other words, to keep the process in statistical control.
17
Basic SPC
Objectives of SPC ChartsObjectives of SPC Charts The following are secondary objectives or
direct benefits of the primary objective:
To reduce variability in a process.
To help estimate the parameters of a process and establish its process capability.
18
Basic SPC
Graphical comparison of a quality characteristic against computed control limits.
Usually, its sample statistic is plotted over time. Sometimes, the actual value of the quality characteristic is plotted.
Lower Control Limit
Upper Control Limit
Center Line
Sample Number or TimeSam
ple
Qua
lity
Cha
ract
eris
tic
Each point is usually a sample statistic (such as subgroup average) of the
quality characteristic
General Form of SPC ChartsGeneral Form of SPC Charts
19
Basic SPC
Control charts plot variation over time.
Control limits, Upper Control Limit (UCL) and Lower Control Limit (LCL), help us distinguish between the two basic causes of variability.
Lower Control Limit
Upper Control Limit
Center Line
Sample Number or Time
Sam
ple
Qua
lity
Cha
ract
eris
tic
General Form of SPC ChartsGeneral Form of SPC Charts
Center Line represents mean operating level of
process
UCL & LCL are vital guidelines for deciding when
action should be taken in a process
20
Basic SPC
A point outside of UCL or LCL is evidence that process is out of control: Investigation and corrective action are required to
eliminate the assignable cause(s). Assignable cause(s) may be measuring error, plotting
error, special variation from some process input, etc.
Lower Control Limit
Upper Control Limit
Center Line
Sample Number or Time
Sam
ple
Qua
lity
Cha
ract
eris
tic
General Form of SPC ChartsGeneral Form of SPC Charts
Out-of-control signal: Investigate assignable cause(s).
21
Basic SPC
Process Control vs Process Control vs Process Capability Process Capability
At this juncture, let’s distinguish between process control and
process capability ...
22
Basic SPC
Process ControlProcess Control
Means that chance causes are the only source of variation present.
Refers to “voice of the process”, i.e. we only need data from the process to determine if a process is in control.
Quality characteristic is monitored to verify if it forms a stable distribution over time, with control limits computed from the process data only.
Just because a process is in control does not necessarily mean it is a capable process.
23
Basic SPC
The “goodness” of a process is measured by its process capability.
Compares “voice of the process” with “voice of the customer”, which is given in terms of customer specs. or requirements.
Measures how well a stable distribution (process in control) meets customer requirements by the proportion of products within or out of customer specs.
Process CapabilityProcess Capability
Usl-lsl
24
Basic SPC
Control Limits vs Spec. LimitsControl Limits vs Spec. Limits
Specification Limits (USL , LSL) determined by design considerations represent the tolerable limits of individual
values of a product usually external to variability of the process
Control Limits (UCL , LCL) base on data derived based on variability of the process usually apply to sample statistics such as
subgroup average or range, rather than individual values
25
Basic SPC
Shewhart Control Charts - OverviewShewhart Control Charts - Overview
26
Basic SPC
Shewhart control charts are characterized by having control limits set at k distance from process mean. A usual value of k is 3, giving:
Upper Control Limit = w + 3w
Center Line = w
Lower Control Limit = w – 3w
Whether the data is variable or attribute, Shewhart control charts plot the sample statistic of the quality characteristic of interest.
Shewhart Control Charts - OverviewShewhart Control Charts - Overview
27
Basic SPC
Shewhart Variables Control Shewhart Variables Control Charts for SubgroupsCharts for Subgroups
28
Basic SPC
Introduction to Introduction to X-R ChartsX-R Charts
29
Basic SPC
Central Limit Theorem and Normal Central Limit Theorem and Normal DistributionDistribution
Shewhart variables control charts for subgroups work because of two important principles:
Central Limit Theorem Normal Distribution
Shewhart found that when the averages of subgroups from a constant-cause system are plotted in the form of a histogram, the normal distribution appears.
30
Basic SPC
Central Limit Theorem and Normal Central Limit Theorem and Normal DistributionDistribution
The constant-cause system does not itself have to be normally distributed. It can be skewed, rectangular or even inverted pyramid.
As long as the sample size is adequately large, the averages of the subgroups will show a central tendency and variation that tend to follow the normal curve.
This is called the Central Limit Theorem.
31
Basic SPC
Central Limit Theorem and Normal Central Limit Theorem and Normal DistributionDistribution
This discovery means that a process can be monitored over time by measuring the averages of a subgroup of parts (basis for X-chart).
If the process is a constant-cause system, these averages would fall within a normal curve. The variability is entirely due to common causes.
When assignable causes appear, they will affect the averages to the point where these averages will probably not fit within the normal curve.
32
Basic SPC
Central Limit Theorem and Normal Central Limit Theorem and Normal DistributionDistribution
Important Information from Central Limit Theorem:
If k observations of sample size n are taken, the distribution of x1, x2, … , xk will approximate a normal distribution N(x,x) distribution, with
n
k
x
xx
x
k
1ii
x
33
Basic SPC
Construction of X-R ChartsConstruction of X-R Charts
The X-R chart is the most versatile of control charts, and is used in most applications.
Charting of averages and charting of ranges are used to check if a constant-cause system exists.
2010Subgroup 0
74.015
74.005
73.995
73.985
Sam
ple
Mea
n
X=74.00
3.0SL=74.01
-3.0SL=73.99
0.05
0.04
0.03
0.02
0.01
0.00
Sam
ple
Ran
ge
R=0.02235
3.0SL=0.04726
-3.0SL=0.000
X-bar-R Charts X-chart measures variability between
samples
R-chart measures variability within
samples
R Always screw
34
Basic SPC
The control limits are the estimated +/-3 sigma limits for the process.
Tables of constants were developed to make the sigma calculations simple and to reduce error.
2010Subgroup 0
74.015
74.005
73.995
73.985
Sam
ple
Mea
n
X=74.00
3.0SL=74.01
-3.0SL=73.99
0.05
0.04
0.03
0.02
0.01
0.00
Sam
ple
Ran
ge
R=0.02235
3.0SL=0.04726
-3.0SL=0.000
X-bar-R Charts
Construction of X-R ChartsConstruction of X-R Charts
35
Basic SPC
The Center Line and Control Limits of a X-chart:
The Center Line and Control Limits of a R-chart:
XX2
X
XX2
3RAXLCL
XLineCenter
3RAXUCL
R3
R4
3RRDLCL
RLineCenter
3RRDUCL
Construction of X-R ChartsConstruction of X-R Charts
36
Basic SPC
n A2 A3 d2 c4 B3 B4 D3 D4
2 1.880 2.659 1.128 0.7979 0 3.267 0 3.267
3 1.023 1.954 1.693 0.8862 0 2.568 0 2.575
4 0.729 1.628 2.059 0.9213 0 2.266 0 2.282
5 0.577 1.427 2.326 0.9400 0 2.089 0 2.115
6 0.483 1.287 2.534 0.9515 0.030 1.970 0 2.004
7 0.419 1.182 2.704 0.9594 0.118 1.882 0.076 1.924
8 0.373 1.099 2.847 0.9650 0.185 1.815 0.136 1.864
9 0.337 1.032 2.970 0.9693 0.239 1.761 0.184 1.816
10 0.308 0.975 3.078 0.9727 0.284 1.716 0.223 1.777
11 0.285 0.927 3.173 0.9754 0.321 1.679 0.256 1.744
12 0.266 0.886 3.258 0.9776 0.354 1.646 0.283 1.717
13 0.249 0.850 3.336 0.9794 0.382 1.618 0.307 1.693
14 0.235 0.817 3.407 0.9810 0.406 1.594 0.328 1.672
15 0.223 0.789 3.472 0.9823 0.428 1.572 0.347 1.653
16 0.212 0.763 3.532 0.9835 0.448 1.552 0.363 1.637
17 0.203 0.739 3.588 0.9845 0.466 1.534 0.378 1.622
18 0.194 0.718 3.640 0.9854 0.482 1.518 0.391 1.608
19 0.187 0.698 3.689 0.9862 0.497 1.503 0.403 1.597
20 0.180 0.680 3.735 0.0969 0.510 1.490 0.415 1.585
21 0.173 0.663 3.778 0.9876 0.523 1.477 0.425 1.575
22 0.167 0.647 3.819 0.9882 0.534 1.466 0.434 1.566
23 0.162 0.633 3.858 0.9887 0.545 1.455 0.443 1.557
24 0.157 0.619 3.895 0.9892 0.555 1.445 0.451 1.548
25 0.153 0.606 3.931 0.9896 0.565 1.435 0.459 1.541
For sample size n > 10, R loses its efficiency in
estimating process sigma and R-chart may not be
appropriate.
Construction of X-R ChartsConstruction of X-R Charts
Shewhart Constants
37
Basic SPC
Control Charts – Sampling RisksControl Charts – Sampling Risks
Since the control limits are the +/-3 sigma limits for the process, the interval between the limits cover 99.73% of the normal distribution.
Output43210-1-2-3-4
0.4
0.3
0.2
0.1
0.0
Normal Curve and Probability Areas
68%
95%
99.73%
38
Basic SPC
Control Charts – Sampling RisksControl Charts – Sampling Risks
If there is no change in the process, there is still a chance of getting a point out of the 3 control limits. What is the implication?
3
3
99.73%
Lower Control Limit
Center Line
Upper Control Limit
What does each area of 0.135%
mean?
0.135%
0.135%
39
Basic SPC
Control Charts – Sampling RisksControl Charts – Sampling RisksType I Error = reject good lot = over reject Concluding that the process is out of control when it is
really in control
= probability of making Type I error = commonly known as the producer’s risk = total of 0.27% for control limits of +/- 3
Lower Control Limit
Upper Control Limit
Center Line
Sample Number or Time
0.135%
0.135%
Is process really out of control? Or is the
point outside due to random variation?
40
Basic SPC
Control Charts – Sampling RisksControl Charts – Sampling Risks
Type I Error and Tampering
If the process is really in control, and process adjustment is made because of Type I error, it is called tampering with the process.
Tampering has been shown to actually increase the variability of the process!
41
Basic SPC
Control Charts – Sampling RisksControl Charts – Sampling RisksType II Error = accept fail lot Concluding that the process is in control when it is really
out of control
= probability of making Type II error = commonly known as the consumer’s risk
Lower Control Limit
Upper Control Limit
Center Line
Sample Number or Time
0.135%
0.135%
Is process really in control? Or is the point inside due to
random variation of the shifted process?
Shifted Process
42
Basic SPC
Control Charts – Sampling RisksControl Charts – Sampling Risks
The control chart is a test of the hypothesis that the process is in statistical control.
Lower Control Limit
Upper Control Limit
Center Line
Sample Number or Time
Sam
ple
Qua
lity
Cha
ract
eris
tic Out-of-control signal Reject H0:- Process has shifted- Assignable causes present
In-control signalAccept H0:- Process remains unchanged- No assignable causes present
43
Basic SPC
Control Limits & Sampling RisksControl Limits & Sampling Risks
By moving the control limits further from the center line, the risk of a Type I error is reduced.
However, widening the control limits will increase the risk of a Type II error.
For a given Type I error (control limits interval), the risk of a Type II error canbe reduced by increasing the sample size.
44
Basic SPC
Let’s try an example of
X-R chart
45
Basic SPC
Example 1: X-R ChartExample 1: X-R ChartS/N X1 X2 X3 X4 X5 1 74.030 74.002 74.019 73.992 74.008 2 73.995 73.992 74.001 74.011 74.004 3 73.988 74.024 74.021 74.005 74.002 4 74.002 73.996 73.993 74.015 74.009 5 73.992 74.007 74.015 73.989 74.014 6 74.009 73.994 73.997 73.985 73.993 7 73.995 74.006 73.994 74.000 74.005 8 73.985 74.003 73.993 74.015 73.998 9 74.008 73.995 74.009 74.005 74.00410 73.998 74.000 73.990 74.007 73.99511 73.994 73.998 73.994 73.995 73.99012 74.004 74.000 74.007 74.000 73.99613 73.983 74.002 73.998 73.997 74.01214 74.006 73.967 73.994 74.000 73.98415 74.012 74.014 73.998 73.999 74.00716 74.000 73.984 74.005 73.998 73.99617 73.994 74.012 73.986 74.005 74.00718 74.006 74.010 74.018 74.003 74.00019 73.984 74.002 74.003 74.005 73.99720 74.000 74.010 74.013 74.020 74.003
Piston rings for an automotive engine are forged. 20 preliminary samples, each of size 5, were obtained. The inside diameter of these rings are shown here.
Verify if the forging process is in statistical control.
The data are found inSPC Charts.MTW.
46
Basic SPC
MiniTab:Stat Control Charts Xbar-R
Example 1: X-R ChartExample 1: X-R Chart
47
Basic SPC
Example 1: X-R ChartExample 1: X-R Chart
2010Subgroup 0
74.015
74.005
73.995
73.985
Sa
mp
le M
ea
n
Mean=74.00
UCL=74.01
LCL=73.99
0.05
0.04
0.03
0.02
0.01
0.00
Sa
mp
le R
ang
e
R=0.02235
UCL=0.04726
LCL=0
Xbar/R Chart for Inside Diameter of Piston Ring Is process in control?
Why are the 2 distances different in
value?
48
Basic SPC
The X-R chart must be interpreted together as well as separately.
Read the R-chart first to determine if it is in control, i.e. no points out of the control limits or non-random pattern (to be discussed later).
The R-chart is more sensitive to changes in uniformity or consistency. Anything that introduces changes to the process variability, such as poor material or lack of maintenance, will affect the R-chart.
Interpreting X-R Chart Together Interpreting X-R Chart Together
49
Basic SPC
Some assignable causes show up on both the X and R charts. Work on the R-chart first.
Never attempt to interpret the X-chart when the R-chart indicates an out-of-control condition, i.e. when the within-subgroup variability is not stable.
Interpreting X-R Chart Together Interpreting X-R Chart Together
Why?
50
Basic SPC
BREAK
51
Basic SPC
The initial trial control limits should be treated as subject to possible subsequent revision. The control chart should always reflect accurately the present conditions of the process.
A sustained change in the level of either chart, usually for at least 20 points, may call for revision of the control limits to recognize the permanent change.
Some practitioners establish regular periods for review of the control limits, such as every week, month, or every 50 samples, etc.
Revising Control Limits and Revising Control Limits and Center Lines Center Lines
52
Basic SPC
Some users will replace the center line of the X-chart with a target value, such as nominal spec.: If the process mean can be easily adjusted by
manipulating some process inputs, it may be helpful to shift the process mean to the desired value.
If the mean is not easily influenced by a simple process adjustment, such as flatness of a machined part, forcing a target value can result in many points out of the control limits.
Revising Control Limits and Revising Control Limits and Center Lines Center Lines
What about changing the sample size? revise control limit
53
Basic SPC
Indicators of InstabilityIndicators of Instability
Primary Indicators any point outside of a control limit
Secondary Indicators any non-random pattern of points on a control chart
– shift or run– trend– stratification– mixture– periodicity
54
Basic SPC
Primary Indicators of InstabilityPrimary Indicators of Instability
Any point outside a control limit 1 point beyond ±3 limits
Lower Control Limit
Upper Control Limit
Center Line
Sample Number or TimeSam
ple
Qua
lity
Cha
ract
eris
tic
55
Basic SPC
Common Causes
new workers, methods, raw materials or machines
change in inspection methods or standards
change in skill and/or motivation of operators
Primary Indicators of InstabilityPrimary Indicators of Instability
56
Basic SPC
Secondary Indicators of InstabilitySecondary Indicators of InstabilityShift or Run k consecutive points (usually 7, 8 or 9) on the same
side of the center line
4 out of 5 consecutive points beyond 1 (same side)
2 out of 3 consecutive points beyond 2 (same side)
Upper Control Limit
Center Line
Sample Number or TimeSam
ple
Qua
lity
Cha
ract
eris
tic
Lower Control Limit
+ 2+ 1
- 2- 1
57
Basic SPC
Common Causes of “Shift” or “Run”
new workers, methods, raw materials or machines
change in inspection methods or standards
change in skill and/or motivation of operators
Secondary Indicators of InstabilitySecondary Indicators of Instability
58
Basic SPC
Trend k consecutive points (usually 5, 6 or 7) moving
in the same direction
Upper Control Limit
Center Line
Sample Number or TimeSam
ple
Qua
lity
Cha
ract
eris
tic
Lower Control Limit
+ 2+ 1
- 2- 1
Secondary Indicators of InstabilitySecondary Indicators of Instability
59
Basic SPC
Common Causes of “Trend”
new workers, methods, raw materials or machines
change in inspection methods or standards
change in skill and/or motivation of operators
Secondary Indicators of InstabilitySecondary Indicators of Instability
60
Basic SPC
Stratification points “hugging” the center line, usually within
±1 limits
Upper Control Limit
Center Line
Sample Number or TimeSam
ple
Qua
lity
Cha
ract
eris
tic
Lower Control Limit
+ 2+ 1
- 2- 1
Secondary Indicators of InstabilitySecondary Indicators of Instability
61
Basic SPC
Common Causes of “Stratification”
incorrect calculation of control limits
sampling process collects one or more units from different underlying distributions within each subgroup
Secondary Indicators of InstabilitySecondary Indicators of Instability
Can irrational subgrouping be a cause
of stratification?
62
Basic SPC
Mixture points “hugging” the control limits
Upper Control Limit
Center Line
Sample Number or Time
Sam
ple
Qua
lity
Cha
ract
eris
tic
Lower Control Limit
+ 2+ 1
- 2- 1
Secondary Indicators of InstabilitySecondary Indicators of Instability
63
Basic SPC
Common Causes of “Mixture”
two (or more) overlapping distributions
over-control by operators
Secondary Indicators of InstabilitySecondary Indicators of Instability
64
Basic SPC
Cycle or Periodicity any ongoing, repeating pattern
Upper Control Limit
Center Line
Sample Number or Time
Sam
ple
Qua
lity
Cha
ract
eris
tic
Lower Control Limit
+ 2+ 1
- 2- 1
Secondary Indicators of InstabilitySecondary Indicators of Instability
65
Basic SPC
Common Causes of “Cycle” or “Periodicity”
systematic environmental changes– temperature– operator fatigue– rotation of operators– fluctuation in machine settings
maintenance schedules
tool wear
Secondary Indicators of InstabilitySecondary Indicators of Instability
66
Basic SPC
MiniTab’s Tests for InstabilityMiniTab’s Tests for Instability
Secondary Indicators
Primary Indicator
67
Basic SPC
Shift / Run
Shift / RunShift / Run
Trend
Stratification
Cycle
Mixture
MiniTab’s Tests for InstabilityMiniTab’s Tests for Instability
68
Basic SPC
Tests for InstabilityTests for Instability
CAUTION :CAUTION : Do not apply “tests” blindly
Not every “test” is relevant for all charts
Excessive number of “tests” Increased -error
Nature of application
69
Basic SPC
Relevance of Shut-Down RulesRelevance of Shut-Down Rules
Suitable for all charts
Suitable only for X-Chart
_
70
Basic SPC
X-S ChartsX-S Charts
The Center Line and Control Limits of a X Chart are
The Center Line and Control Limits of a S Chart are
S3
S4
3SSBLCL
SLineCenter
3SSBUCL
_
XX3
X
XX3
σ3μSAXLCL
μXLineCenter
σ3μSAXUCL
_
71
Basic SPC
Shewhart ConstantsShewhart Constantsn A2 A3 d2 c4 B3 B4 D3 D4
2 1.880 2.659 1.128 0.7979 0 3.267 0 3.267
3 1.023 1.954 1.693 0.8862 0 2.568 0 2.575
4 0.729 1.628 2.059 0.9213 0 2.266 0 2.282
5 0.577 1.427 2.326 0.9400 0 2.089 0 2.115
6 0.483 1.287 2.534 0.9515 0.030 1.970 0 2.004
7 0.419 1.182 2.704 0.9594 0.118 1.882 0.076 1.924
8 0.373 1.099 2.847 0.9650 0.185 1.815 0.136 1.864
9 0.337 1.032 2.970 0.9693 0.239 1.761 0.184 1.816
10 0.308 0.975 3.078 0.9727 0.284 1.716 0.223 1.777
11 0.285 0.927 3.173 0.9754 0.321 1.679 0.256 1.744
12 0.266 0.886 3.258 0.9776 0.354 1.646 0.283 1.717
13 0.249 0.850 3.336 0.9794 0.382 1.618 0.307 1.693
14 0.235 0.817 3.407 0.9810 0.406 1.594 0.328 1.672
15 0.223 0.789 3.472 0.9823 0.428 1.572 0.347 1.653
16 0.212 0.763 3.532 0.9835 0.448 1.552 0.363 1.637
17 0.203 0.739 3.588 0.9845 0.466 1.534 0.378 1.622
18 0.194 0.718 3.640 0.9854 0.482 1.518 0.391 1.608
19 0.187 0.698 3.689 0.9862 0.497 1.503 0.403 1.597
20 0.180 0.680 3.735 0.0969 0.510 1.490 0.415 1.585
21 0.173 0.663 3.778 0.9876 0.523 1.477 0.425 1.575
22 0.167 0.647 3.819 0.9882 0.534 1.466 0.434 1.566
23 0.162 0.633 3.858 0.9887 0.545 1.455 0.443 1.557
24 0.157 0.619 3.895 0.9892 0.555 1.445 0.451 1.548
25 0.153 0.606 3.931 0.9896 0.565 1.435 0.459 1.541
1n2c
31B
1n2c
31B
3n4
1n4c
nc
3A
4
4
4
3
4
4
3
For n > 25
72
Basic SPC
Example 2Example 2MiniTab’s Stat Control Charts Xbar-S
73
Basic SPC
R Chart vs S ChartR Chart vs S ChartFor ease of computation, the R Chart is preferred
The S Chart may be used when n is not constant
For large sample size (n 10), the range loses its efficiency as an estimator of
Larger sample size is required when– lower sampling risks are required– greater drift sensitivity is required– quality characteristic is non-normal
Historical Note: When Shewhart developed thest charts in the 1920’s, there was no easy way to calculate the standard deviation. Thus, the range approach became ingrained in SPC application.
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Using SPCUsing SPC Place charts only where necessary based on
project scope
Remove charts that are not value-added
Initially, the process outputs may need to be monitored
Goal: Monitor and control process inputs and, over time, eliminate the need for SPC charts
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Where to Use SPC ChartsWhere to Use SPC Charts When a mistake-proofing device is not feasible
Identify processes with high RPNs from FMEA
Evaluate the “Current Controls” column to determine “gaps” in the control plan. Does SPC make sense?
Identify critical variables based on DOE
Customer requirements
Management commitments
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Updating Control LimitsUpdating Control Limits
Control Limits should be updated when: Change in supplier for a critical material Change in process machinery Engineering change orders that affect process
flow Introduction of new operators Change in sample size
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Implementing the Control ChartImplementing the Control Chart
1) Preparation of Sampling
2) Data Collection
3) Construct the Control Chart
4) Analysis & Interpretation
5) Use the Control Chart as a Process Monitoring Tool
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Preparation of Sampling Choose the quality characteristic to be
measured– measurements taken on the final product– measurements taken on the in-process
product– measurements taken on the process
variables Determine the basis, size and frequency
Implementing the Control ChartImplementing the Control Chart
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Data Collection Record the data Calculate the relevant statistics: mean, range,
proportion, etc
Implementing the Control ChartImplementing the Control Chart
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Construct the Control Chart Calculate the trial center line and the trial control
limits Plot the trial center line and the trial control limits Plot the data collected on the chart
Implementing the Control ChartImplementing the Control Chart
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Analysis & Interpretation: Investigate the chart for lack of control Eliminate out-of-control points if required Recompute control limits if necessary Determine process capability
Implementing the Control ChartImplementing the Control Chart
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Use the Control Chart as a Process Monitoring Tool
Continue data collection and plotting
Identify out-of-control situations and take
correction action
If a permanent process shift has occurred,
recalculate the new center line and control limits
Implementing the Control ChartImplementing the Control Chart
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Review Data
Compute Trial Limits
Review Control Charts
Out-Of-ControlPoints?
Compute Production Limits
Real-Time Process Monitoring
ReviseControl Limits?
Yes
No
AssignableCause?
Censor Data?
No
No
Compute Trial LimitsYes
Yes
No
Yes
Implementing the Control ChartImplementing the Control Chart
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Adequate Discrimination
Inadequate Discrimination
Implementing the Control ChartImplementing the Control Chart
Measurement Variation Affects the Control Chart!
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Statistical Process ControlStatistical Process Control
A state of statistical control is not a natural state for a manufacturing process. It is an achievement, arrived at by elimination one by one, by determined effort, of special causes of excessive variation.
There is no process capability and no meaningful
specifications, except in statistical control.
- William Edwards Deming
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End of TopicEnd of TopicWhat question do you have?
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Reading ReferenceReading Reference
Introduction to Statistical Quality Control,
Douglas C. Montgomery, John Wiley & Sons,
ISBN 0-471-30353-4