Assessing the actual Gamma process quality - A curve-fitting approach for modifying the non-normal flexible index

Mou Yuan Liao*, W.l. Pearn, Yen Lun Liu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Process capability indices (PCIs) have been widely adopted for quality assurance activities. By analysing PCIs, a production department can trace and improve a poor process to enhance product quality level and satisfy customer requirements. Among these indices, Cpk remains the most prevalent for facilitating managerial decisions because it can provide bounds on the process yield for normally distributed processes. However, processes are often non-normal in practice, and Cpk may quite likely misrepresent the actual product quality. Hence, the flexible index Cjkp, which considers possible differences in the variability above and below the target value, has been developed for practical use. However, Cjkp continues to suffer from serious bias in assessing actual capability, especially when the process distribution is highly skewed. In this paper, we modify Cjkp for assessing the actual process quality of a Gamma process. A correction factor is obtained by the curve-fitting method. The results show that our proposed method can significantly reduce the bias for calculation of actual nonconformities. Moreover, we introduce a sample estimator for our modified index. The ratio of this estimators average value and the modified index is approximately 1. This implies that our proposed estimator can provide an appropriate estimation for assessing the actual Gamma process quality.

Original languageEnglish
Pages (from-to)4720-4734
Number of pages15
JournalInternational Journal of Production Research
Issue number15
StatePublished - 3 Aug 2015


  • Gamma distribution
  • curve fitting
  • flexible capability index
  • non-normal


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