A comparison of methods for estimating loss-based capability index

Chien Wei Wu*, Ming Hung Shu, W.l. Pearn, Feng Tsung Cheng

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


The process capability index Cpm, sometimes called the loss-based index, has been proposed to the manufacturing industry for measuring process reproduction capability. This index incorporates the variation of production items with respect to the target value and the specification limits preset in the factory. To estimate the loss-based index properly and accurately, certain frequentist and Bayesian perspectives have been proposed to obtain lower confidence bounds (LCBs) for providing minimum process capability. The LCBs not only provide critical information regarding process performance but are also used to determine whether an improvement was made in a capability index and by extension in reducing the fraction of non-conforming items. In this paper, under the assumption of normality, based on frequentist and Bayesian senses, several existing approaches for constructing LCBs of Cpm are presented. Depending on the statistical methods used, we then classify these existing approaches into three categories and compared them in terms of the coverage rates and the mean values of the LCBs via simulations. The relative advantages and disadvantages of these approaches are summarized with some highlights of the relevant findings.

Original languageEnglish
Pages (from-to)1129-1141
Number of pages13
JournalJournal of Statistical Computation and Simulation
Issue number9
StatePublished - 1 Sep 2009


  • Coverage rate
  • Loss-based capability index
  • Lower confidence bound
  • Performance comparison

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