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An overview of theory and practice on process capability indices for quality assurance

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  • Wu, Chien-Wei
  • Pearn, W.L.
  • Kotz, Samuel

Abstract

Process capability indices (PCIs), Cp, Ca, Cpk, Cpm, and Cpmk have been developed in certain manufacturing industry as capability measures based on various criteria, including process consistency, process departure from a target, process yield, and process loss. It is noted in certain recent quality assurance and capability analysis works that the three indices, Cpk, Cpm, and Cpmk provide the same lower bounds on the process yield. In this paper, we investigate the behavior of the actual process yield, in terms of the number of non-conformities (in ppm), for processes with fixed index values of Cpk=Cpm=Cpmk, possessing different degrees of process centering. We also extend Johnson's [1992. The relationship of Cpm to squared error loss. Journal of Quality Technology 24, 211-215] result formulating the relationship between the expected relative squared loss and PCIs. Also a comparison analysis among PCIs is carried out based on various criteria. The result illustrates some advantages of using the index Cpmk over the indices Cpk and Cpm in measuring process capability (yield and loss), since Cpmk always provides a better protection for the customers. Additionally, several extensions and applications to real world problem are also discussed. The paper contains some material presented in the Kotz and Johnson [2002. Process capability indices--a review, 1992-2000. Journal of Quality Technology 34(1), 1-19] survey but from a different perspective. It also discusses the more recent developments during the years 2002-2006.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:proeco:v:117:y:2009:i:2:p:338-359
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    References listed on IDEAS

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    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. 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.
    3. Wang, F. K. & Du, T. C. T., 2000. "Using principal component analysis in process performance for multivariate data," Omega, Elsevier, vol. 28(2), pages 185-194, April.
    4. Arjun Gupta & S. Kotz, 1997. "A new process capability index," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 45(1), pages 213-224, January.
    5. Wright, Peter A., 2000. "The cumulative distribution function of process capability index Cpm," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 249-251, April.
    6. K. Palmer & K.-L. Tsui, 1999. "A review and interpretations of process capability indices," Annals of Operations Research, Springer, vol. 87(0), pages 31-47, April.
    7. 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.
    8. Pearn, W. L. & Wu, Chien-Wei, 2005. "A Bayesian approach for assessing process precision based on multiple samples," European Journal of Operational Research, Elsevier, vol. 165(3), pages 685-695, September.
    9. W. L. Pearn, 1998. "New generalization of process capability index Cpk," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(6), pages 801-810.
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