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Some Process Capability Indices are More Reliable than One Might Think

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  • Samuel Kotz
  • Wen Lea Pearn
  • N. L. Johnson

Abstract

In this paper we obtain formulae for exact expected values and standard deviations of estimators of certain process capability indices discussed by Bissell. In particular, we show that for the index Cpk Bissell's formula gives values for the standard deviation which are too high especially when the actual population mean value is close to (or equal to) the average of the upper and lower specification limits.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssc:v:42:y:1993:i:1:p:55-62
    DOI: 10.2307/2347409
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    Cited by:

    1. Chang, Y.C. & Wu, Chien-Wei, 2008. "Assessing process capability based on the lower confidence bound of Cpk for asymmetric tolerances," European Journal of Operational Research, Elsevier, vol. 190(1), pages 205-227, October.
    2. Hsi-Tien Chen & Kuen-Suan Chen, 2016. "Assessing the assembly quality of a T-bar ceiling suspension by using an advanced multi-process performance analysis chart with asymmetric tolerance," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 10(2), pages 264-283.
    3. Wu, Chien-Wei & Pearn, W.L. & Kotz, Samuel, 2009. "An overview of theory and practice on process capability indices for quality assurance," International Journal of Production Economics, Elsevier, vol. 117(2), pages 338-359, February.
    4. Wu, Chien-Wei, 2008. "Assessing process capability based on Bayesian approach with subsamples," European Journal of Operational Research, Elsevier, vol. 184(1), pages 207-228, January.
    5. Lin, Gu-Hong, 2007. "A Bayesian approach based on multiple samples for measuring process performance with incapability index," International Journal of Production Economics, Elsevier, vol. 106(2), pages 506-512, April.
    6. W. L. Pearn, 1998. "New generalization of process capability index Cpk," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(6), pages 801-810.
    7. Wu, Chien-Wei, 2009. "Decision-making in testing process performance with fuzzy data," European Journal of Operational Research, Elsevier, vol. 193(2), pages 499-509, March.
    8. Prasad, Sameer & Bramorski, Tom, 1998. "Robust Process Capability Indices," Omega, Elsevier, vol. 26(3), pages 425-435, June.
    9. Rendao Ye & Tiefeng Ma & Songgui Wang, 2011. "Generalized confidence intervals for the process capability indices in general random effect model with balanced data," Statistical Papers, Springer, vol. 52(1), pages 153-169, February.
    10. Pearn, W.L. & Wu, Chien-Wei, 2007. "An effective decision making method for product acceptance," Omega, Elsevier, vol. 35(1), pages 12-21, February.
    11. Shiau, Jyh-Jen Horng & Hung, Hui-Nien & Chiang, Chun-Ta, 1999. "A note on Bayesian estimation of process capability indices," Statistics & Probability Letters, Elsevier, vol. 45(3), pages 215-224, November.
    12. 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.
    13. Jessenberger, Jutta & Weihs, Claus, 1998. "A note on a multivariate analogue of the process capability index Cp," Technical Reports 1998,07, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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