Process Capability Index, CpkCpk is a short term process index that numerically describes the "within subgroup" or "potential" capability (Ppk is long term indicator) of a process assuming it was analyzed and stays in control. Both Cpk and Ppk relate the standard deviation and centering of the process about the midpoint to the allowable tolerance specifications. The Cp is the best a process can perform if that process is centered on the midpoint and the Cp = Cpk. Cpk will never exceed the Cp. It is an option (along with Z-score and PPM) when describing process baseline measurement in the MEASURE phase or in the CONTROL phase when obtaining the final performance analysis. As with all the process capability indices, the process should be in control before assessing capability. Use time-series and SPC charts to determine process control. If the process is out of control (i.e. still rising with upward trend), then assessing the current process is not likely to reflect the long term performance. Similar to Ppk, the Cpk capability index is only a function of the standard deviation and mean of the data, not a nominal (target) value that may be historical or provided by the customer. It also requires input from the customer for the lower specification limit (LSL) and upper specification limit (LSL). The Cpm capability calculation accounts for a nominal value.
There are two calculations from the abover formula providing two values for Cpk. Select the MINIMUM value as the Cpk and to serve as the baseline value. This minimum value must be equal to or greater than the mininum acceptability level. Unlike Cp (and Pp), the Cpk (and Ppk) index can be calculated using unilateral or bilateral tolerances. If only one specification is provided (unilateral) the use the value that involves that specification limit. There won't be a minimum (or maximum), just calculate using the formula that has a specification and use it for the Cpk value. The standard Cpk level is 2.0 for a process in six sigma quality control . The acceptability levels for Cpk depends on your customer.
Read more about the process capability indices, their meanings, and relationships.
Converting from Cpk to a Z-scoreWith a normally distributed set of data an approximation of Z from Cpk and vice versa can be made in substituting and solving within these two formulas.What is the Cpk approximated from a 6 sigma performance? Substituting the Z formula in Cpk (USL) and plugging in 6 for Z from the given data gives:
Cpk of 2 corresponds to 6 sigma (short term) performance. The Z in the above formula refers to a short term sigma, short term Z.
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