Assessing Capability
Joel Smith
Commercial Sales
Minitab, Inc.
Schedule
Learn about the tools
Two “continuous” examples
• Assessment of cookout locations
• In class example
One “binomial” example
One “count” example (if time permits)
Brain Warmer
The Monty Hall Show
Brain Warmer
Pick
Shown Should
Pick
Shown Should
Pick
Shown Should
1
2/3
Stay
1
3
Move
1
2
Move
2
3
Move
2
1/3
Stay
2
1
Move
3
2
Move
3
2
Move
3
1/2
Stay
⅔
⅔
⅔
What is “Capability”?
Assess quality
Quantify ability to meet specifications
Distinguish short- and long-term
Data Types
Continuous
• Length
• Time
• Temperature
Binary
• Yes/No, Pass/Fail
• How many heads in X coin flips
Count
• Defects/part
• Orders in a day
Assessing Capability
Determine specifications
Verify Measurement System
• Gage R&R, Attribute Gage R&R
Collect data
Look at the data
• Histogram, Boxplot
Determine distribution of data
• Probability Plot
Evaluate stability
• Control Charts
Capability
• Capability Analysis
Assessing Capability
Determine specifications
• Avoid this topic here…
Verify Measurement System
• Error types
• Ability to measure accurately
Collect data
• Short-term and long-term
• Subgrouping
• Randomize collection of data
Assessing Capability
Look at the data
• Always!
Determine distribution of data
• Most data is not normal
• Good fit is critical
• Some data have natural distribution
Evaluate stability
• Unstable process is unpredictive
Use distribution to quantify capability
• Capability quantified using several statistics
Two Examples
I want to plan a 4th of July cookout
• Where should I have it?
• What factors should I consider?
• How likely is each location to satisfy my requirements?
We make high-strength cord used to secure
parachutes
• How long is each cord?
• How likely is each cord to be within my specs?
Two Examples
4th of July Cookout is in slides
• My locations:
– State College, PA
– Pasadena, CA
• My factors
– Temperature
– Precipitation
Cord will be done here
• Evaluate Length
Cookout: State College, PA
What is the capability of State College to produce good
weather on July 4th?
Average Temperature should be between 65 and 85
Precipitation should be <0.1 in.
Cookout: State College, PA
To assess capability:
• If necessary, verify measurement system
• Collect data
• Look at the data
• Evaluate stability using a Control Chart
• Determine the distribution
• Perform a Capability Analysis
Measurement System Analysis (MSA)
Do prior to collecting and analyzing data
Two types:
• Continuous (Length, Time, Temperature, etc.)
• Attribute (Yes/No, Poor/Fair/Good, etc.)
Establishes how much variability is coming from parts
versus operators
Measurement System Analysis (MSA)
In God we trust;
All others bring
data
Cord: MSA in Class
To test whether our Measurement System is sufficient:
• 3 Operators (volunteers?)
• 6 Parts
• 2 Measurements per part per operator
Randomize!
We will do Attribute Gage R&R later
Cord: MSA in Class
(Do MSA now…)
Cookout: State College, PA
For our weather data, no MSA will be done
Data has already been collected
Next steps:
•
•
•
•
Look at the data
Evaluate stability using a Control Chart
Determine the distribution
Perform a Capability Analysis
Cookout: State College, PA
Look at the data:
Summary for TAVE (F)
A nderson-D arling N ormality Test
55
60
65
70
75
80
85
A -S quared
P -V alue
0.20
0.870
M ean
S tDev
V ariance
S kew ness
Kurtosis
N
69.888
5.881
34.582
0.0962166
-0.0008702
80
M inimum
1st Q uartile
M edian
3rd Q uartile
M aximum
55.000
66.000
70.000
74.000
85.000
95% C onfidence Interv al for M ean
68.579
71.196
95% C onfidence Interv al for M edian
68.000
71.221
95% C onfidence Interv al for S tDev
9 5 % C onfidence Inter vals
5.089
Mean
Median
68.0
68.5
69.0
69.5
70.0
70.5
71.0
6.965
Cookout: State College, PA
Summary for TAVE (F)
Data appears
“normal”
A nderson-D arling N ormality Test
Symmetry
55
60
65
70
75
80
85
A -S quared
P -V alue
0.20
0.870
M ean
S tDev
V ariance
S kew ness
Kurtosis
N
69.888
5.881
34.582
0.0962166
-0.0008702
80
M inimum
1st Q uartile
M edian
3rd Q uartile
M aximum
55.000
66.000
70.000
74.000
85.000
95% C onfidence Interv al for M ean
68.579
Mean ~ Median
71.196
95% C onfidence Interv al for M edian
68.000
71.221
95% C onfidence Interv al for S tDev
9 5 % C onfidence Inter vals
5.089
Mean
Median
68.0
68.5
69.0
69.5
70.0
70.5
71.0
6.965
Cookout: State College, PA
Evaluate Stability using a Control Chart:
I-MR Chart of TAVE (F)
Individual V alue
90
U C L=88.79
80
_
X=69.89
70
60
LC L=50.99
50
1
9
17
25
33
41
O bser vation
49
57
65
73
U C L=23.22
M oving Range
20
15
10
__
M R=7.11
5
0
LC L=0
1
9
17
25
33
41
O bser vation
49
57
65
73
Cookout: State College, PA
Evaluate Stability using a Control Chart:
I-MR Chart of TAVE (F)
Random, stable
No “out of control”
Individual V alue
90
U C L=88.79
80
_
X=69.89
70
60
LC L=50.99
50
1
9
17
25
33
41
O bser vation
49
57
65
73
U C L=23.22
M oving Range
Location/Spread
20
15
10
__
M R=7.11
5
0
LC L=0
1
9
17
25
33
41
O bser vation
49
57
65
73
Cookout: State College, PA
Determine Distribution
What is the “Normal” distribution?
Other distributions:
• Weibull
• Largest/smallest extreme value
• Exponential
Cookout: State College, PA
Use a Probability Plot to Determine Distribution:
Probability Plot of TAVE (F)
Normal
99.9
Mean
StDev
N
AD
P-Value
99
95
Percent
90
80
70
60
50
40
30
20
10
5
1
0.1
50
60
70
TAVE (F)
80
90
69.89
5.881
80
0.204
0.870
Cookout: State College, PA
Use a Probability Plot to Determine Distribution
Probability Plot of TAVE (F)
Normal
“Fat Pencil” test
99.9
Mean
StDev
N
AD
P-Value
99
95
Anderson-Darling
• P-value
Percent
“Squinty Eye” test
90
80
70
60
50
40
30
20
10
5
1
0.1
50
60
70
TAVE (F)
80
90
69.89
5.881
80
0.204
0.870
Cookout: State College, PA
Finally, perform Capability Analysis
• Specs: 65 to 85 degrees
Key assumptions:
• Data is from a stable process
• Data is well-fit by distribution
We will learn:
• Characteristics of data
• Likelihood of “bad” parts
• Short-term vs. Long-term performance
Cookout: State College, PA
Finally, perform Capability Analysis
Process Capability of TAVE (F)
LSL
USL
P rocess D ata
LS L
65
Target
*
USL
85
S ample M ean
69.8875
S ample N
80
S tDev (Within)
6.16079
S tDev (O v erall) 5.8993
Within
Ov erall
P otential (Within) C apability
Cp
0.54
C P L 0.26
C P U 0.82
C pk
0.26
O v erall C apability
Pp
PPL
PPU
P pk
C pm
55
O bserv ed P erformance
P P M < LS L
187500.00
PPM > USL
0.00
P P M Total
187500.00
E xp.
PPM
PPM
PPM
60
65
Within P erformance
< LS L 213794.53
> USL
7083.23
Total
220877.75
70
75
80
E xp. O v erall P erformance
P P M < LS L 203696.86
PPM > USL
5207.36
P P M Total
208904.23
85
0.57
0.28
0.85
0.28
*
Cookout: State College, PA
Finally, perform Capability Analysis
Process Capability of TAVE (F)
LSL
USL
P rocess D ata
LS L
65
Target
*
USL
85
S ample M ean
69.8875
S ample N
80
S tDev (Within)
6.16079
S tDev (O v erall) 5.8993
Within
Ov erall
P otential (Within) C apability
Cp
0.54
C P L 0.26
C P U 0.82
C pk
0.26
O v erall C apability
Pp
PPL
PPU
P pk
C pm
Characteristics
of Data55 60
O bserv ed P erformance
P P M < LS L
187500.00
PPM > USL
0.00
P P M Total
187500.00
E xp.
PPM
PPM
PPM
65
Within P erformance
< LS L 213794.53
> USL
7083.23
Total
220877.75
70
75
80
E xp. O v erall P erformance
P P M < LS L 203696.86
PPM > USL
5207.36
P P M Total
208904.23
85
0.57
0.28
0.85
0.28
*
Cookout: State College, PA
Finally, perform Capability Analysis
Process Capability of TAVE (F)
LSL
USL
P rocess D ata
LS L
65
Target
*
USL
85
S ample M ean
69.8875
S ample N
80
S tDev (Within)
6.16079
S tDev (O v erall) 5.8993
Within
Ov erall
P otential (Within) C apability
Cp
0.54
C P L 0.26
C P U 0.82
C pk
0.26
O v erall C apability
Pp
PPL
PPU
P pk
C pm
Likelihood of
“bad” parts
55
O bserv ed P erformance
P P M < LS L
187500.00
PPM > USL
0.00
P P M Total
187500.00
E xp.
PPM
PPM
PPM
60
65
Within P erformance
< LS L 213794.53
> USL
7083.23
Total
220877.75
70
75
80
E xp. O v erall P erformance
P P M < LS L 203696.86
PPM > USL
5207.36
P P M Total
208904.23
85
0.57
0.28
0.85
0.28
*
Cookout: State College, PA
Finally, perform Capability Analysis
Process Capability of TAVE (F)
LSL
USL
P rocess D ata
LS L
65
Target
*
USL
85
S ample M ean
69.8875
S ample N
80
S tDev (Within)
6.16079
S tDev (O v erall) 5.8993
Within
Ov erall
P otential (Within) C apability
Cp
0.54
C P L 0.26
C P U 0.82
C pk
0.26
O v erall C apability
Pp
PPL
PPU
P pk
C pm
55
O bserv ed P erformance
P P M < LS L
187500.00
PPM > USL
0.00
P P M Total
187500.00
E xp.
PPM
PPM
PPM
60
65
Within P erformance
< LS L 213794.53
> USL
7083.23
Total
220877.75
Short-term
vs.
70
75
80
85
Long-term
E xp. O v erall P erformance
P P M < LS L 203696.86
PPM > USL
5207.36
P P M Total
208904.23
0.57
0.28
0.85
0.28
*
Cookout: State College, PA
Now let’s take a look at Precipitation
Recall we want <0.1 in.
We will follow the same procedure:
•
•
•
•
Look at the data
Evaluate stability
Determine distribution
Perform Capability Analysis
Cookout: State College, PA
Look at the data:
Summary for PRCP (in)
A nderson-D arling N ormality Test
-0.0
0.2
0.4
0.6
0.8
A -S quared
P -V alue <
15.00
0.005
M ean
S tDev
V ariance
S kew ness
Kurtosis
N
0.11025
0.21408
0.04583
2.05593
2.95297
80
M inimum
1st Q uartile
M edian
3rd Q uartile
M aximum
0.00000
0.00000
0.00000
0.07750
0.82000
95% C onfidence Interv al for M ean
0.06261
0.15789
95% C onfidence Interv al for M edian
0.00000
0.02000
95% C onfidence Interv al for S tDev
9 5 % C onfidence Inter vals
0.18528
Mean
Median
0.000
0.025
0.050
0.075
0.100
0.125
0.150
0.25357
Cookout: State College, PA
Data appears
“skewed”
Summary for PRCP (in)
A nderson-D arling N ormality Test
No symmetry
-0.0
0.2
0.4
0.6
0.8
A -S quared
P -V alue <
15.00
0.005
M ean
S tDev
V ariance
S kew ness
Kurtosis
N
0.11025
0.21408
0.04583
2.05593
2.95297
80
M inimum
1st Q uartile
M edian
3rd Q uartile
M aximum
0.00000
0.00000
0.00000
0.07750
0.82000
95% C onfidence Interv al for M ean
Mean ≠ Median
0.06261
0.15789
95% C onfidence Interv al for M edian
0.00000
0.02000
95% C onfidence Interv al for S tDev
9 5 % C onfidence Inter vals
0.18528
Mean
Median
0.000
0.025
0.050
0.075
0.100
0.125
0.150
0.25357
Cookout: State College, PA
Evaluate Stability using a Control Chart:
I-MR Chart of PRCP (in)
1
Individual V alue
0.8
1
1
1
0.6
1
1
1
1
1
0.4
1
1
0.2
U C L=0.2675
_
X=0.1103
0.0
LB=0
1
9
17
25
33
41
O bser vation
49
57
65
73
11
0.8
1
1
M oving Range
1
1
0.6
11
11
11
11
11
1
1
11
1
0.4
11
11
0.2
U C L=0.1932
__
M R=0.0591
LC L=0
0.0
1
9
17
25
33
41
O bser vation
49
57
65
73
Cookout: State College, PA
Evaluate Stability using a Control Chart:
I-MR Chart of PRCP (in)
1
Unstable
Individual V alue
0.8
1
1
1
0.6
1
1
1
1
1
0.4
1
1
U C L=0.2675
_
X=0.1103
0.2
0.0
“Out of control”
LB=0
1
9
25
33
41
O bser vation
49
1
1
M oving Range
17
57
65
73
11
0.8
Non-predictive
1
1
0.6
11
11
11
11
11
1
1
11
1
0.4
11
11
0.2
U C L=0.1932
__
M R=0.0591
LC L=0
0.0
1
9
17
25
33
41
O bser vation
49
57
65
73
Cookout: State College, PA
STOP!
Cookout: State College, PA
Assumptions are not met
No stability = No capability
At this point:
• Special causes
• Other factors
Cookout: State College, PA
Is State College a good location?
Temperature
• Average temperature stable year-to-year
• Normal distribution
• 79% chance of “good”
Precipitation
• Precipitation is unstable
• Cannot determine capability
Cookout: Pasadena, CA
How about Pasadena?
Evaluate same criteria
• Temperature (65 to 85)
Precipitation (<0.1 in.)
Remember our process:
•
•
•
•
•
Verify measurement system, Collect data (MSA)
Look at the data (Histogram)
Evaluate stability (Control Chart)
Determine distribution (Probability Plot)
Perform Capability Analysis
Cookout: Pasadena, CA
Look at the data:
Summary for TAVE (F)
A nderson-D arling N ormality Test
64
68
72
76
80
A -S quared
P -V alue <
1.78
0.005
M ean
S tDev
V ariance
S kew ness
Kurtosis
N
73.013
4.571
20.896
0.857208
0.462320
78
M inimum
1st Q uartile
M edian
3rd Q uartile
M aximum
84
64.000
70.000
72.000
76.000
86.000
95% C onfidence Interv al for M ean
71.982
74.043
95% C onfidence Interv al for M edian
71.000
73.000
95% C onfidence Interv al for S tDev
9 5 % C onfidence Inter vals
3.949
Mean
Median
71.0
71.5
72.0
72.5
73.0
73.5
74.0
5.427
Cookout: Pasadena, CA
Data appears
partly skewed
Summary for TAVE (F)
A nderson-D arling N ormality Test
Some Asymmetry
64
68
72
76
80
A -S quared
P -V alue <
1.78
0.005
M ean
S tDev
V ariance
S kew ness
Kurtosis
N
73.013
4.571
20.896
0.857208
0.462320
78
M inimum
1st Q uartile
M edian
3rd Q uartile
M aximum
84
64.000
70.000
72.000
76.000
86.000
95% C onfidence Interv al for M ean
Mean ≠ Median
71.982
74.043
95% C onfidence Interv al for M edian
71.000
73.000
95% C onfidence Interv al for S tDev
9 5 % C onfidence Inter vals
3.949
Mean
Median
71.0
71.5
72.0
72.5
73.0
73.5
74.0
5.427
Cord: Look at data
First we need to collect data
Need a good distribution fit
• Generally 25-50 points
Use Histogram
Cookout: Pasadena, CA
Evaluate Stability using a Control Chart:
I-MR Chart of TAVE (F)
U C L=86.03
Individual V alue
84
78
_
X=73.01
72
66
60
LC L=59.99
1
9
17
25
M oving Range
20
33
41
O bser vation
49
57
65
73
1
U C L=16.00
15
10
5
__
M R=4.90
0
LC L=0
1
9
17
25
33
41
O bser vation
49
57
65
73
Cookout: Pasadena, CA
Evaluate Stability using a Control Chart:
I-MR Chart of TAVE (F)
U C L=86.03
Mostly stable
Individual V alue
84
One “out of control”
78
_
X=73.01
72
66
60
LC L=59.99
1
9
17
25
Can we proceed?
M oving Range
20
33
41
O bser vation
49
57
65
73
1
U C L=16.00
15
10
__
M R=4.90
5
0
LC L=0
1
9
17
25
33
41
O bser vation
49
57
65
73
Cord: Evaluate Stability
(Evaluate stability using Control Chart…)
Out of Control Points
Many out of control points:
• Unstable process
• Special causes
• Other factors
Very few out of control:
• Look for special cause
• Only if legitimate, remove
Cookout: Pasadena, CA
Use a Probability Plot to Determine Distribution:
Probability Plot of TAVE (F)
Normal
99.9
Mean
StDev
N
AD
P-Value
99
95
Percent
90
80
70
60
50
40
30
20
10
5
1
0.1
60
65
70
75
TAVE (F)
80
85
90
73.01
4.571
78
1.782
<0.005
Cookout: Pasadena, CA
Use Probability Plots to Determine Distribution:
Probability Plot for TAVE (F)
G oodness of F it Test
Weibull - 95% C I
99.9
99.9
99
90
90
50
P er cent
P er cent
N ormal - 95% C I
50
10
N ormal
A D = 1.782
P -V alue < 0.005
Weibull
A D = 3.491
P -V alue < 0.010
10
1
Largest E xtreme V alue
A D = 0.544
P -V alue = 0.174
1
0.1
60
70
80
T A VE (F)
0.1
90
Largest E xtreme V alue - 95% C I
40
60
T A V E (F)
80
3-P arameter Loglogistic
A D = 0.556
P -V alue = *
3-P arameter Loglogistic - 95% C I
99.9
99.9
99
P er cent
P er cent
99
90
50
50
10
1
10
0.1
90
70
80
90
T A VE (F)
100
0.1
1
10
T A V E ( F) - T hr eshold
100
Cookout: Pasadena, CA
Use a Probability Plot to Determine Distribution
Probability Plot of TAVE (F)
Largest Extreme Value - 95% CI
“Fat Pencil” test
99.9
Loc
Scale
N
AD
P-Value
“Squinty Eye” test
Anderson-Darling
• P-value
Percent
99
98
97
95
90
80
70
60
50
40
30
20
10
1
0.1
60
70
80
TAVE (F)
90
100
70.94
3.628
78
0.544
0.174
Cord: Determine Distribution
(Determine distribution using Probability Plot…)
Cookout: Pasadena, CA
Finally, perform Capability Analysis
• Specs: 65 to 85 degrees
Key assumptions:
 Data is from a stable process
 Data is well-fit by distribution
We will learn:
• Characteristics of data
• Likelihood of “bad” parts
• Long-term performance only
Cookout: Pasadena, CA
Finally, perform Capability Analysis
Process Capability of TAVE (F)
Calculations Based on Largest Extreme Value Distribution Model
LSL
USL
P rocess D ata
LS L
65
Target
*
USL
85
S ample M ean 73.0128
S ample N
78
Location
70.9361
S cale
3.62756
O v erall C apability
Pp
0.65
PPL
0.89
PPU
0.56
P pk
0.56
E xp. O v erall P erformance
P P M < LS L
5877.92
P P M > U S L 20500.38
P P M Total
26378.30
O bserv ed P erformance
P P M < LS L 12820.51
P P M > U S L 12820.51
P P M Total
25641.03
64
68
72
76
80
84
88
Cookout: State College, PA
Finally, perform Capability Analysis
Process Capability of TAVE (F)
Calculations Based on Largest Extreme Value Distribution Model
LSL
USL
P rocess D ata
LS L
65
Target
*
USL
85
S ample M ean 73.0128
S ample N
78
Location
70.9361
S cale
3.62756
O v erall C apability
Pp
0.65
PPL
0.89
PPU
0.56
P pk
0.56
E xp. O v erall P erformance
P P M < LS L
5877.92
P P M > U S L 20500.38
P P M Total
26378.30
O bserv ed P erformance
P P M < LS L 12820.51
P P M > U S L 12820.51
P P M Total
25641.03
Characteristics
of Data
64
68
72
76
80
84
88
Cookout: State College, PA
Finally, perform Capability Analysis
Process Capability of TAVE (F)
Calculations Based on Largest Extreme Value Distribution Model
LSL
P rocess D ata
LS L
65
Target
*
USL
85
S ample M ean 73.0128
S ample N
78
Location
70.9361
S cale
3.62756
USL
O v erall C apability
Pp
0.65
PPL
0.89
PPU
0.56
P pk
0.56
Likelihood of
“bad” parts
E xp. O v erall P erformance
P P M < LS L
5877.92
P P M > U S L 20500.38
P P M Total
26378.30
O bserv ed P erformance
P P M < LS L 12820.51
P P M > U S L 12820.51
P P M Total
25641.03
64
68
72
76
80
84
88
Cookout: State College, PA
Finally, perform Capability Analysis
Process Capability of TAVE (F)
Calculations Based on Largest Extreme Value Distribution Model
LSL
USL
P rocess D ata
LS L
65
Target
*
USL
85
S ample M ean 73.0128
S ample N
78
Location
70.9361
S cale
3.62756
O v erall C apability
Pp
0.65
PPL
0.89
PPU
0.56
P pk
0.56
E xp. O v erall P erformance
P P M < LS L
5877.92
P P M > U S L 20500.38
P P M Total
26378.30
O bserv ed P erformance
P P M < LS L 12820.51
P P M > U S L 12820.51
P P M Total
25641.03
Long-term only
64
68
72
76
80
84
88
Cord: Capability Analysis
(Perform Capability Analysis now…)
Cookout: Pasadena, CA
How about Precipitation?
Evaluate same criteria
• Precipitation (<0.1 in.)
Remember our process:
•
•
•
•
•
Verify measurement system, Collect data (MSA)
Look at the data (Histogram)
Evaluate stability (Control Chart)
Determine distribution (Probability Plot)
Perform Capability Analysis
Cookout: Pasadena, CA
Look at the data:
Summary for PRCP (in)
A nderson-D arling N ormality Test
0.00
0.01
0.02
0.03
0.04
0.05
0.06
A -S quared
P -V alue <
29.19
0.005
M ean
S tDev
V ariance
S kew ness
Kurtosis
N
0.000769
0.006794
0.000046
8.8318
78.0000
78
M inimum
1st Q uartile
M edian
3rd Q uartile
M aximum
0.000000
0.000000
0.000000
0.000000
0.060000
95% C onfidence Interv al for M ean
-0.000763
0.002301
95% C onfidence Interv al for M edian
0.000000
0.000000
95% C onfidence Interv al for S tDev
9 5 % C onfidence Inter vals
0.005869
Mean
Median
-0.0010
-0.0005
0.0000
0.0005
0.0010
0.0015
0.0020
0.008066
Cookout: Pasadena, CA
Unusual data
Summary for PRCP (in)
A nderson-D arling N ormality Test
Nearly all values
equal or nearly
equal
0.00
0.01
0.02
0.03
0.04
0.05
0.06
A -S quared
P -V alue <
29.19
0.005
M ean
S tDev
V ariance
S kew ness
Kurtosis
N
0.000769
0.006794
0.000046
8.8318
78.0000
78
M inimum
1st Q uartile
M edian
3rd Q uartile
M aximum
0.000000
0.000000
0.000000
0.000000
0.060000
95% C onfidence Interv al for M ean
-0.000763
0.002301
95% C onfidence Interv al for M edian
0.000000
Mean ≠ Median
0.000000
95% C onfidence Interv al for S tDev
9 5 % C onfidence Inter vals
0.005869
Mean
Median
-0.0010
-0.0005
0.0000
0.0005
0.0010
0.0015
0.0020
0.008066
Cookout: Pasadena, CA
Evaluate Stability using a Control Chart:
I-MR Chart of PRCP (in)
1
Individual V alue
0.060
0.045
0.030
0.015
_ C L=0.00491
U
X=0.00077
LC L=-0.00338
0.000
1
9
17
25
33
41
O bser vation
49
57
65
11
0.060
M oving Range
73
0.045
0.030
0.015
__
U C L=0.00509
M R=0.00156
LC
L=0
0.000
1
9
17
25
33
41
O bser vation
49
57
65
73
Cookout: Pasadena, CA
Evaluate Stability using a Control Chart:
I-MR Chart of PRCP (in)
1
Mostly stable?
Individual V alue
0.060
0.045
0.030
0.015
_ C L=0.00491
U
X=0.00077
LC L=-0.00338
0.000
One “out of control”
1
9
17
25
33
41
O bser vation
49
57
65
11
M oving Range
0.060
Can we proceed?
73
0.045
0.030
0.015
__C L=0.00509
U
M
LCR=0.00156
L=0
0.000
1
9
17
25
33
41
O bser vation
49
57
65
73
Out of Control Points
Many out of control points:
• Unstable process
• Special causes
• Other factors
Very few out of control:
• Look for special cause
• Only if legitimate, remove
Cookout: Pasadena, CA
Our process is out of control:
Binary process?
Can evaluate capability for binary (later)
Not enough data…
Cookout: Pasadena, CA
STOP!
Cookout: Pasadena, CA
Is Pasadena a good location?
Temperature
• Average temperature stable year-to-year
• Non-normal distribution
• 97.4% chance of “good”
Precipitation
• Precipitation is unstable
• Cannot determine capability
Cookout Comparison
Which city is better
Temperature
• State College = 79%
• Pasadena = 97.4%
Precipitation
• Precipitation is unstable for both
• Relative rate is much lower in Pasadena
Cookout Comparison
A quick graph:
Boxplot of TMIN (F), TAVE (F), TMAX (F)
110
100
Data
90
80
70
60
50
40
City
Pasadena State College
TMIN (F)
Pasadena State College
TAVE (F)
Pasadena State College
TMA X (F)
Pill Quality Example
We work for a pharma company, and pill quality is
critical
Need to evaluate our capability
Remember:
•
•
•
•
•
•
Verify measurement system
Collect data
Look at the data
Evaluate stability using a Control Chart
Determine the distribution
Perform a Capability Analysis
Pill Quality Example
First we need to do an Attribute Gage R&R
• 3 Operators
• A few pills
• 2 tests/pill
Criteria for “good” pill
• Logo is clear
• No chips or dings
• Color applied evenly
Pill Quality Example
Now to collect our data
Everyone open your pill bottle
Without ingesting the medication:
• Count the number of pills
• Count how many are defective
Pill Quality Example
Now we will:
• Look at the data
• Evaluate stability
• Determine the distribution
• Perform Capability Analysis
Circuit Board Example
We work for an electronics company, and circuit board
quality is critical
Need to evaluate our capability
Remember:
•
•
•
•
•
•
Verify measurement system
Collect data
Look at the data
Evaluate stability using a Control Chart
Determine the distribution
Perform a Capability Analysis
Circuit Board Example
Perform Gage R&R
• Approximated as continuous
Our criteria:
• How many “burn marks” are on the board
We will use
• 3 operators
• 6 parts
• 2 runs per part
Circuit Board Example
Now everyone please take on circuit board
Again without ingesting, record:
• How many burn marks there are
Destructive test
Recap
Verify Measurement System
• Error types
• Ability to measure accurately
• “Continuous” versus “Attribute”
Tools
• Gage R&R
• Attribute Gage R&R
Recap
Collect data
• Short-term and long-term
• Subgrouping
• Randomize collection of data
Look at the data
• Histograms
• Boxplots
• Other graphs
Recap
Determine distribution of data
•
•
•
•
Most data is not normal
Good fit is critical
Some data have natural distribution
Probability Plots
Evaluate stability
• Unstable process is unpredictive
• Control Charts
Recap
Perform capability analysis
• Capability quantified using several statistics
• Capability Analysis
Consider data type
• Continuous
• Binary
• Count
The End…
Joel Smith
Commercial Sales
Minitab, Inc.