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The Practical Difference Between
Ppk and Cpk
Mark DiMartino
Director Quality Engineering
Amgen Inc.
Agenda
• Overview of Performance/Capability Indices
• What is Statistical Control?
• Types of Variation and the impact on Cpk/Ppk
• Examples
2
Four Indices are Typically Used in Industry to
Measure Process Performance
Assumes
Centered
Process
Accounts for
Process
Average
Potential Performance
Measure
Actual Performance
Measure
Process Capability (Cp)
Process Performance
(Pp)
Process Capability
Adjusted for Process
Shift (Cpk)
Process Performance
Adjusted for Process
Shift (Ppk)
ASTM E22821 Standard Practice for Process and Measurement Capability Indices
3
Each Index is a Measure of Process
Performance Relative to a Specification
The output is an index standardized to a ±3 SD range, meaning a
Ppk/Cpk of 1.0 indicates that there are 3 SDs between the mean and
the closest specification range. Cp/Pp use the center of the
specification (i.e., the target) in lieu of the mean.
Specification Limits
Process Mean
LSL
X
Process and
Measurement
Variability
Target
3 SDs
Ppk = 1.0
4
USL
What Does This Performance Measure
Mean?
The performance measure can be converted to the probability of
observing an out of specification (OOS) result. The higher the
Index, the lower the probability of an
OOS*
2007
1.60
1.50
1.40
Ppk
1.30
1.20
1.10
1.00
0.90
0.80
0.70
0
5000
2700 ppm
10000
15000
20000
25000
30000
Estimated OOS (ppm)
*This interpretation applies to all process performance and process capability indices
5
The Index Value Is Driven by a Combination of
the Mean, SD, and Specification Limits
0 bias, acceptable variability
LSL
Target
Bias, low variability
USL
LSL
Target
USL
Large bias, very low variability
Slight bias, low variability
LSL
Target
USL
LSL
Cpk/Ppk = 1.0 for each instance
6
Target
USL
What is the Distinction Between Pp/Ppk and
Cp/Cpk?
• Per ASTM E2281:
• Process capability indices (Cp/Cpk) compare the variability of a
process quality measure against product specifications or
tolerances and assume the process is in a state of statistical
control.
• Process performance indices (Pp/Ppk) are useful in situations
when the process in not in a state of statistical control.
• Mathematically:
• Cp/Cpk uses short term variation, for batch processes with a
subgroup n=1 it is based on the average distance between
adjacent points.
• Pp/Ppk uses long term variation which is the normal “Excel”
standard deviation calculation.
7
What is Statistical Control?
• Statistical control or process “stability” is a state in
which only common cause variation is evident.
• Common cause variation is the normal expected
variation in a process that is:
•
•
•
•
Due to the process itself
Produced by interactions of variables within that process
Present in all processes
“In statistical control” (stable) provided it is the only
variation present
• Predictable
8
What Does it Mean to be Out of
Statistical Control?
• A process that is out of statistical control or “unstable”
demonstrates evidence of special cause variation.
• Special Cause Variation is...
• Due to a specific, assignable cause
• Caused by special circumstances not inherent in the
process.
• Generally easier to detect than common causes.
• Not predictable
9
How Do I Determine if Special Cause
Variation is Present?
• Statistical Process Control (SPC) techniques are used to determine
the state of statistical control.
• The individuals control chart is the most typical SPC approach, with
tests applied to identify special cause variation.
Individuals Chart
Moving Range Chart
6 in a row increasing
or decreasing
1
11000
800
600
UCL=10713.72
3
500
Moving Range
of Value
Value
10500
22
UCL=714.02
700
Avg=10132.57
10000
400
300
Avg=218.59
200
100
LCL=9551.42
9500
0
LCL=0.00
-100
3
6
9
12
15
18
21
24
27
3
30
Sample
Single Point outside
3 sigma limits
6
9
12
15
18
21
24
27
30
Sample
Single point above the UCL
for the MR chart
9 in a row above or
below centerline
10
How Does Statistical Control Relate to
Cpk/Ppk?
• Cp/Cpk provides an estimate of potential process
performance or capability
• How the process would perform in the absence of special cause
variation.
• Pp/Ppk provides the actual process performance given
all of the variance that is currently present in the
process
• Pp/Ppk is generally <= Cp/Cpk
11
But of Course it is Not That Simple
• There is a third type of variation that is often present,
especially when considering batch processing
• Some statisticians call this Long term common cause
variation
• Long term common cause variation is:
• Variation that a control chart may consider special cause, but is
expected and generally tolerated in manufacturing
• Also called autocorrelation, where observations that are close
together in time tend to look more similar than observations that
are further apart in time.
• Cp/Cpk generally underestimates the standard
deviation in these situations, thereby overestimating
performance.
12
Examples of Long Term Common Cause
Variability
• Campaign based manufacturing
• Same raw material lot used over multiple batches
• Equipment within a lab
• Analyst within a lab
• Column Packing
• Critical Reagents used over a long period of time
• Multiple purification lots from a single harvest lot
13
Example 1: Common Cause Variation
• Example 1: Parameter demonstrates statistical control,
all values exhibit random noise
Individuals Chart
Moving Range Chart
40
130
UCL=125.42
UCL=36.14
35
120
30
Moving Range of Result
110
Result
100
Avg=96.00
90
80
70
LCL=66.59
25
20
15
Avg=11.06
10
5
0
LCL=0.00
-5
60
3
9
6
12
18
15
21
24
27
30
33
3
6
9
12
Sample
18
21
24
27
30
33
Sample
Cpk
Ppk
Mean
-3s
+3s
Target
LSL
60
15
80
100
USL
120
Mean
-3s
Target
LSL
140
60
+3s
80
100
USL
120
14
140
Cp
Cpk
Pp
Ppk
1.00
0.88
0.99
0.87
Example 2: Special Cause Evident
• Special cause variation leads to a discrepancy in
Cpk/Ppk
Individuals Chart
Moving Range Chart
0.40
1.1
0.35
UCL=1.091
0.30
Moving Range of Result
1.0
Result
Avg=0.954
0.9
LCL=0.818
0.8
0.7
0.25
0.20
UCL=0.1678
0.15
0.10
0.05
Avg=0.0514
0.00
LCL=0.0000
-0.05
3
6
9
12 15
18 21 24
27
30
33 36
39
3
6
9
12 15
Sample
Cpk
27
30
33 36
39
Ppk
-3s
Mean
+3s
Target
LSL
0.6
18 21 24
Sample
0.8
USL
1
Mean
-3s
Target
LSL
1.2
0.6
+3s
0.8
USL
1
1.2
15
Cp
Cpk
Pp
Ppk
1.46
1.07
0.94
0.69
Example 3: Long Term Common Cause
• Long term common cause variation leads to a
discrepancy in Ppk/Cpk
Individuals Chart
Moving Range Chart
1000
11000
Moving Range of Value
Value
10500
Avg=10190.50
10000
LCL=9526.29
9500
UCL=816.07
800
UCL=10854.71
600
400
Avg=249.83
200
0
LCL=0.00
0 1 2 3 4 5 6 7 8 9 11 13 15 17 19 21 23 25 27 29
0 1 2 3 4 5 6 7 8 9 11 13 15 17 19 21 23 25 27 29
Sample
Sample
Cpk
Ppk
-3s
Mean
+3s
-3s
Mean
+3s
LSL
Target
USL
LSL
Target
USL
9000
10000
11000
9000
10000
11000
16
Cp
Cpk
Pp
Ppk
1.51
1.22
1.06
0.86
Summary
• Ppk and Cpk are both useful measures in assessing
how a particular parameter is performing vs
specification.
• The concept of long term common cause variation
needs to be taken into account when assessing
statistical control.
• Understanding the nature of the underlying data is
critical when interpreting Cpk or Ppk.
17
THANK YOU!
Any Questions?
18