On the distributional properties of the estimated process accuracy index Ca

G. H. Lin*, W.l. Pearn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Pearn et al. (1998) introduced the process accuracy index Ca to measure the degree of process centering (the ability to cluster around the center). Assuming that the process runs under uniform process condition, so that the process mean may be assumed as an unknown constant, the distributional and inferential properties of the estimator of Ca are investigated for normal processes. In this paper, the distributional properties of an estimator are investigated under a different but practical condition for stable normal processes, in which the knowledge P {μ ≥ m} = p ε [0, 1] is available. The sampling distribution of the new estimator is derived. It is shown that the proposed estimator under the new process condition investigated, follows the normal distribution. Consequently, process accuracy testing based on the ability to cluster around the center, can be easily performed. The expected value and the mean square error of the new estimator are also calculated for various values of two commonly-used process characteristic parameters, (μ - m)/σ = 0.0(0.5)2.0, and d/σ = 2(1)6. Significance: The sampling distribution of the proposed new estimator is derived. Consequently, process accuracy testing based on the ability to cluster around the center, can be easily performed, and decisions therefore can be made on wether actions should be taken to improve the International process quality.

Original languageEnglish
Pages (from-to)169-177
Number of pages9
JournalInternational Journal of Industrial Engineering : Theory Applications and Practice
Volume11
Issue number2
StatePublished - 1 Jun 2004

Keywords

  • Process accuracy estimation
  • Process centering

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