Process capability indices and non-normal distributions

Steven E. Somerville, Douglas Montgomery

Research output: Contribution to journalArticlepeer-review

122 Scopus citations


Capability indices are becoming increasingly popular in industry. One of the problems associated with these indices is the underlying assumption of normality. Four non-normal distributions were examined for their effect on inferences made using the standard capability indices. The gamma, lognormal, Weibull, and t distributions were analyzed. Various shapes of each of the four distributions were considered. The errors associated with a normal-distribution assumption when the distribution is non-normal were evaluated and tabulated. The errors were obtained by applying a standard index to the subject distribution as if it were normal. The expected proportion nonconforming, in parts per million, were compared to those obtained with the normal distribution. The errors were found to be extremely large in most instances. The skewness and kurtosis of the non-normal distributions contribute to a significant difference in the expected defect percentage. Consequently, we recommend that a sample distribution for which a capability estimate is desired should be evaluated for departures from normality. Methods which compensate for non-normality must be considered if a high degree of confidence is to be placed on the capability estimates.

Original languageEnglish (US)
Pages (from-to)305-316
Number of pages12
JournalQuality Engineering
Issue number2
StatePublished - 1996


  • Departures from assumptions
  • Normal probability plots
  • Process capability analysis
  • Process capability index

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Industrial and Manufacturing Engineering


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