Process performance index

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In process improvement efforts, the process performance index is an estimate of the process capability of a process during its initial set-up, before it has been brought into a state of statistical control.^[1]

Formally, if the upper and lower specifications of the process are USL and LSL, the estimated mean of the process is ${\displaystyle {\hat {\mu }}}$, and the estimated variability of the process (expressed as a standard deviation) is ${\displaystyle {\hat {\sigma }}}$, then the process performance index is defined as:

${\displaystyle {\hat {P}}_{pk}=\min {\Bigg [}{USL-{\hat {\mu }} \over 3{\hat {\sigma }}},{{\hat {\mu }}-LSL \over 3{\hat {\sigma }}}{\Bigg ]}}$

${\displaystyle {\hat {\sigma }}}$ is estimated using the sample standard deviation. P_pk may be negative if the process mean falls outside the specification limits (because the process is producing a large proportion of defective output).

Some specifications may only be one sided (for example, strength). For specifications that only have a lower limit, ${\displaystyle {\hat {P}}_{p,lower}={{\hat {\mu }}-LSL \over 3{\hat {\sigma }}}}$; for those that only have an upper limit, ${\displaystyle {\hat {P}}_{p,upper}={USL-{\hat {\mu }} \over 3{\hat {\sigma }}}}$.

Practitioners may also encounter ${\displaystyle {\hat {P}}_{p}={\frac {USL-LSL}{6{\hat {\sigma }}}}}$, a metric that does not account for process performance not exactly centered between the specification limits, and therefore is interpreted as what the process would be capable of achieving if it could be centered and stabilized.