The asymptotic distribution of the estimated process capability index C̃pk

Sy Mien Chen*, W.l. Pearn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Bissell (1990) proposed an estimator Ĉ′pk for the process capability index Cpk assuming that P(μ ≥ m) = 0, or 1, where μ is the process mean, and m is the midpoint between the upper and lower specification limits. Pearn and Chen (1996) considered a new estimator C̃pk, which relaxes Bissell's assumption on the process mean. The evaluation of C̃pk only requires the knowledge of P(μ ≥ m) = p, where 0 ≤ p ≤ 1. The new estimator C̃pk is unbiased, and the variance is smaller than that of Bissell's. In this paper, we investigated the asymptotic properties of the estimator C̃pk under general conditions. We derived the limiting distribution of C̃pk for arbitrary population assuming the fourth moment exists. The asymptotic distribution provides some insight into the properties of C̃pk which may not be evident from its original definition.

Original languageEnglish
Pages (from-to)2489-2497
Number of pages9
JournalCommunications in Statistics - Theory and Methods
Issue number10
StatePublished - 1 Jan 1997


  • Asymptotic distribution
  • Process capability index
  • Process mean
  • Process standard deviation

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