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{{Disputed|date=February 2021}}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 | url-status = dead | archiveurl = https://web.archive.org/web/20080620095346/http://www.eas.asu.edu/~masmlab/montgomery/ | archivedate = 2008-06-20 }}</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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==Interpretation==
Larger values of P<SUB>pk</SUB> may be interpreted to indicate that a process is more capable of producing output within the specification limits, though this interpretation is controversial.{{Citation needed|date=April 2010}} Strictly speaking, from a statistical standpoint, P<SUB>pk</SUB> is meaningless if the process under study is not in control because one cannot reliably estimate the process underlying [[probability distribution]], let alone parameters like <MATH>\hat{\mu}</MATH> and <MATH>\hat{\sigma}</MATH>.<ref>{{Citation | last = Montgomery | first = Douglas | title = Introduction to Statistical Quality Control | publisher = [[John Wiley & Sons]] | year = 2005 | ___location = [[Hoboken, New Jersey]] | page = 349 | url = http://www.eas.asu.edu/~masmlab/montgomery/ | isbn = 978-0-471-65631-9 | oclc = 56729567 | quote = However, please note that if the process is '''not''' in control, the indices P<SUB>p</SUB> and P<SUB>pk</SUB> have no meaningful interpretation relative to process capability, because they cannot predict process performance. | url-status = dead | archiveurl = https://web.archive.org/web/20080620095346/http://www.eas.asu.edu/~masmlab/montgomery/ | archivedate = 2008-06-20 }}</ref>{{Disputed inline|date=February 2021}} Furthermore, using this metric of past process performance to predict future performance is highly suspect.<ref>{{Citation | last = Montgomery | first = Douglas | title = Introduction to Statistical Quality Control | publisher = [[John Wiley & Sons]] | year = 2005 | ___location = [[Hoboken, New Jersey]] | page = 349 | url = http://www.eas.asu.edu/~masmlab/montgomery/ | isbn = 978-0-471-65631-9 | oclc = 56729567 | quote = Unless the process is stable (in control), no index is going to carry useful predictive information about process capability or convey any information about future performance. | url-status = dead | archiveurl = https://web.archive.org/web/20080620095346/http://www.eas.asu.edu/~masmlab/montgomery/ | archivedate = 2008-06-20 }}</ref>{{Disputed inline|date=February 2021}}
From a management standpoint, when an organization is under pressure to set up a new process quickly and economically, P<SUB>pk</SUB> is a convenient metric to gauge how set-up is progressing (increasing P<SUB>pk</SUB> being interpreted as "the process capability is improving"). The risk is that P<SUB>pk</SUB> is taken to mean a process is ready for production before all the kinks have been worked out of it.
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>).{{Disputed inline|date=February 2021}} The indices are named differently in order to call attention to whether the process under study is believed to be in control or not.
==Example==
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[[Category:Index numbers]]
[[Category:Statistical process control]]
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