Cpk index
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Cpk index is a type of process capability index. It is sensitive to whether the process is centered, but insensitive to special cause. As a formula:
![Cpk = \min \Bigg[ {USL-Mean \over 3 \sigma} , { Mean-LSL \over 3 \sigma} \Bigg]](../../../math/9/9/6/9965503f9383d400672f9a622202a8de.png)
(where USL is Upper Spec Limit and LSL is Lower Spec Limit and sigma is the standard deviation of the process)
In simplest terms, Cpk indicates how many times you can fit three standard deviations of the process between the mean of the process and the nearest specification limit. Assuming that the process is stable and predictable, if you can do this once, Cpk is 1, and your process probably needs attention. If you can do it 1.5 times, your process is excellent, and you are on the path to being able to discontinue final inspection. If you can do it 2 times, you have an outstanding process. If Cpk is negative, the process mean is outside the specification limits.
There is a more sophisticated way to calculate Cpk, using a sum of squares estimate of within-subgroup standard deviation. In the more common case shown here, the same formula is used to calculate both Cpk and Ppk. The difference is in how standard deviation is estimated. For Cpk, the moving range method is used, and for Ppk the sum of squares for all the data is used.
Since the moving range method of estimating standard deviation is insensitive to "shifts and drifts" (special cause), Cpk tends to be an estimate of the capability of the process assuming special cause is not present. Anyone who wants you to accept Cpk as an indicator of process capability automatically owes you a Control Chart (Process Behavior Chart) demonstrating that the process is stable and predictable. ( Ppk will equal Cpk.) If not, Ppk is the correct indicator of capability.
The confidence interval around an estimate of standard deviation tends to be larger than many users expect. This uncertainty becomes part of the calculation. Even with a few dozen samples, the estimates of any of the quality indices may not be very precise.
While normality of the data is not a concern in Control Charts (Wheeler, Normality and the Process Behavior Chart, www.spcpress.com), it is of concern in interpreting the results of a Process Capability Study. Data should be tested for non-normality. If the data are non-normal, estimates of defective parts per million may be improved by applying the Box-Cox transform to the data.
Competent texts on the subject include the AIAG books, particularly Production Part Approval Process, p6-7; and Pyzdek's The Complete Guide to the CQE, pages 437-451.
