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The C” pk index for asymmetric tolerances: Implications and inference

Author

Listed:
  • W. L. Pearn
  • P. C. Lin
  • K. S. Chen

Abstract

The process capability index C pk has been widely used in the manufacturing industry to provide numerical measures on process performance. Since C pk is a yield-based index which is independent of the target T, it fails to account for process centering with symmetric tolerances, and presents an even greater problem with asymmetric tolerances. Pearn and Chen (1998) considered a new generalization C” pk which was shown to be superior to other existing generalizations of C pk for processes with asymmetric tolerances. In this paper, we investigate the relation between the fraction nonconforming and the value of C” pk . Furthermore, we derive explicit forms of the cumulative distribution function and the probability density function for the natural estimator ” pk , under the assumption of normality. We also develop a decision making rule based on the natural estimator ” pk , which can be used to test whether the process is capable or not. Copyright Springer-Verlag 2004

Suggested Citation

  • W. L. Pearn & P. C. Lin & K. S. Chen, 2004. "The C” pk index for asymmetric tolerances: Implications and inference," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(2), pages 119-136, September.
    • Handle: RePEc:spr:metrik:v:60:y:2004:i:2:p:119-136
    DOI: 10.1007/s001840300300
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    Citations

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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. 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.
    3. Kuen-Suan Chen & Chun-Min Yu, 2024. "Developing a novel fuzzy testing model for capability index with asymmetric tolerances," Annals of Operations Research, Springer, vol. 340(1), pages 149-162, September.
    4. K. Kurian & Thomas Mathew & G. Sebastian, 2008. "Generalized confidence intervals for process capability indices in the one-way random model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(1), pages 83-92, January.

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