Estimating process capability index C″pmk for asymmetric tolerances: Distributional properties

W.l. Pearn, P. C. Lin, K. S. Chen

Research output: Contribution to journalArticle

20 Scopus citations

Abstract

Pearn et al. (1999) considered a capability index C″pmk, a new generalization of Cpmk, for processes with asymmetric tolerances. In this paper, we provide a comparison between C″pmk and other existing generalizations of Cpmk on the accuracy of measuring process performance for processes with asymmetric tolerances. We show that the new generalization C″pmk is superior to other existing generalizations of Cpmk. Under the assumption of normality, we derive explicit forms of the cumulative distribution function and the probability density function of the estimated index Ĉ″pmk. We show that the cumulative distribution function and the probability density function of the estimated index Ĉ″pmk can be expressed in terms of a mixture of the chi-square distribution and the normal distribution. The explicit forms of the cumulative distribution function and the probability density function considerably simplify the complexity for analyzing the statistical properties of the estimated index Ĉ″pmk.

Original languageEnglish
Pages (from-to)261-277
Number of pages17
JournalMetrika
Volume54
Issue number3
DOIs
StatePublished - 1 Jan 2001

Keywords

  • Asymmetric loss function
  • Bias
  • Departure ratio
  • Mean square error
  • Normally distributed process

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