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Distributions of the Estimated Process Capability Index Cpk

Author

Listed:
  • Lin G. H.

    (Department of Transportation & Logistic Management, National Penghu Institute of Technology, Taiwan)

  • Pearn W. L.

    (Department of Industrial Engineering & Management, National Chiao Tung University, Taiwan)

Abstract

Process capability indices Cp and Cpk have been widely used to provide numerical measures on process potential and process performance. While Cp measures process variation relative to the specification tolerance, which only reflects process potential, Cpk considers process variation as well as process centering, which gives an approximate measure of process yield. In this paper, the statistical properties of the estimated Cpk for two classes of stable processes are investigated under different real-world conditions: (1) normal processes with constant mean, and (2) normal processes with known probability P(μ ≥ m) = p, 0 ≤ p ≤ 1, where m is the mid-point of the specification interval. For the two classes of processes, the distributions, the probability density functions, the asymptotic behaviors, and other statistical properties of their estimators are derived.

Suggested Citation

  • Lin G. H. & Pearn W. L., 2003. "Distributions of the Estimated Process Capability Index Cpk," Stochastics and Quality Control, De Gruyter, vol. 18(2), pages 263-279, January.
    • Handle: RePEc:bpj:ecqcon:v:18:y:2003:i:2:p:263-279:n:8
    DOI: 10.1515/EQC.2003.263
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    References listed on IDEAS

    as
    1. Samuel Kotz & Wen Lea Pearn & N. L. Johnson, 1993. "Some Process Capability Indices are More Reliable than One Might Think," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 42(1), pages 55-62, March.
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