Distributional and inferential properties of the process accuracy and process precision indices

W.l. Pearn*, G. H. Lin, K. S. Chen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

88 Scopus citations


Process capability indices such as Cp, k, and Cpk, have been widely used in manufacturing industry to provide numerical measures on process potential and performance. While Cp measures overall process variation, k measures the degree of process departure. In this paper, we consider the index Cp and a transformation of k defined as Ca = 1 - k which measures the degree of process centering. We refer to Cp as the process precision index, and Ca as the process accuracy index. We consider the estimators of Cp and Ca, and investigate their statistical properties. For Cp, we obtain the UMVUE and the MLE. We show that this UMVUE is consistent, and asymptotically efficient. For Ca, we investigate its natural estimator. We obtain the first two moments of this estimator, and show that the natural estimator is the MLE, which is asymptotically unbiased and asymptotically efficient. We also propose an efficient test based on the UMVUE of Cp. We show that the proposed test is the UMP test.

Original languageEnglish
Pages (from-to)985-1000
Number of pages16
JournalCommunications in Statistics - Theory and Methods
Issue number4
StatePublished - 1 Jan 1998


  • Process accuracy index
  • Process mean
  • Process precision index
  • Process standard deviation
  • Process yield

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