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Hello. In [[process improvement]] efforts, the '''process performance index''' is an estimate of the [[process capability]] of a [[Process (engineering)|process]] during its initial set-up, ''before'' it has been brought into a state of [[statistical control]].<ref>{{Citation | last = Montgomery | first = Douglas | title = Introduction to Statistical Quality Control | publisher = [[John Wiley & Sons]] | year = 2005 | ___location = [[Hoboken, New Jersey]] | pages = 348 – 349 | url = http://www.eas.asu.edu/~masmlab/montgomery/ | isbn = 978-0-471-65631-9 | 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:
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