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A Bayesian procedure for assessing process performance based on the third-generation capability index

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  • Chien-Wei Wu
  • Tsai-Yu Lin

Abstract

Capability indices that qualify process potential and process performance are practical tools for successful quality improvement activities and quality program implementation. Most existing methods to assess process capability were derived on the basis of the traditional frequentist point of view. This paper considers the problem of estimating and testing process capability based on the third-generation capability index Cpmk from the Bayesian point of view. We first derive the posterior probability p for the process under investigation is capable. The one-sided credible interval, a Bayesian analog of the classical lower confidence interval, can be obtained to assess process performance. To investigate the effectiveness of the derived results, a series of simulation was undertaken. The results indicate that the performance of the proposed Bayesian approach depends strongly on the value of ξ=(μ-T)/σ. It performs very well with the accurate coverage rate when μ is sufficiently far from T. In those cases, they have the same acceptable performance even though the sample size n is as small as 25.

Suggested Citation

  • Chien-Wei Wu & Tsai-Yu Lin, 2009. "A Bayesian procedure for assessing process performance based on the third-generation capability index," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(11), pages 1205-1223.
    • Handle: RePEc:taf:japsta:v:36:y:2009:i:11:p:1205-1223
    DOI: 10.1080/02664760802582298
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    References listed on IDEAS

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    1. 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.
    2. W. L. Pearn & Chien-Wei Wu, 2005. "Process capability assessment for index C pk based on bayesian approach," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(2), pages 221-234, April.
    3. Wright, Peter A., 2000. "The cumulative distribution function of process capability index Cpm," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 249-251, April.
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    Citations

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    Cited by:

    1. Sanku Dey & Mahendra Saha & M. Z. Anis & Sudhansu S. Maiti & Sumit Kumar, 2023. "Estimation and confidence intervals of $$C_{Np}(u,v)$$ C Np ( u , v ) for logistic-exponential distribution with application," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 14(1), pages 431-446, March.
    2. Sajid Ali & Muhammad Riaz, 2014. "On the generalized process capability under simple and mixture models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(4), pages 832-852, April.

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