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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]].<REF>{{cite book | last = Montgomery | first = Douglas | title = Introduction to Statistical Quality Control | publisher = [[John Wiley & Sons]] | date = 2004 | ___location = [[New York, New York]] | pages = 348 – 349 | url = http://www.eas.asu.edu/~masmlab/montgomery/ | isbn = 9780471656319 | oclc = 56729567}}</REF>
Formally, if the upper and lower [[Specification (technical standard)|specifications]] of the process are USL and LSL, the estimated mean of the process is <MATH>\hat{\mu}</MATH>, and the estimated variability of the process (expressed as a [[standard deviation]]) is <MATH>\hat{\sigma}</MATH>, then the process performance index is defined as:
:<MATH>\hat{P}_{pk} = \min \Bigg[ {USL - \hat{\mu} \over 3 \times \hat{\sigma}}, { \hat{\mu} - LSL \over 3 \times \hat{\sigma}} \Bigg]</MATH>
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Once a process is put into a state of statistical control, process capability is described using [[Process capability index|process capability indices]], which are formulaically identical to P<SUB>pk</SUB> (and P<SUB>p</SUB>). The indices are named differently to call attention to whether the process under study is believed to be in control or not.
==See also==
*[[Process capability index]]
==References==
{{reflist}}
[[Category:Index numbers]]
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