Estimation of a modified capability index for non-normal distributions

W.l. Pearn, Y. T. Tai*, H. T. Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Process capability indices (PCIs), which are very important in quality control have been one of a numerical measure index in manufacturing processes. Index Cpk is the most popular one used in the manufacturing industry. It is applied under the assumption that the processes are normally distributed. In real-world applications, non-normal processes may occur in industries, and the index CNpk has been proposed for non-normal processes in which its exact sampling distribution is mathematically intractable. Quality practitioners commonly use the existing NCPPM (non-conformities in parts per million) table of Cpk to obtain process yields. However, the table could not be applied directly via the value of index CNpk. For the consistency of NCPPM mapping, we propose procedures to obtain the modified index CNpk and its approximately unbiased estimator ∼CNpk for three non-normal distributions, involving Log-normal, Gamma, and Weibull distributions. The values of modified index CNpk could be used to inquire the existing popular NCPPM table of Cpk. In addition, four bootstrap methods were used to construct the lower confidence bounds of the index CNpk, which are useful to the practitioners for making reliable decisions regarding process performance based on process yield.

Original languageEnglish
Pages (from-to)1998-2009
Number of pages12
JournalJournal of Testing and Evaluation
Issue number5
StatePublished - 1 Sep 2016


  • Lower confidence bound
  • Non-normal process
  • Process capability index
  • Surface fitting

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