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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! 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