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Assessing process capability based on the lower confidence bound of Cpk for asymmetric tolerances

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  • Chang, Y.C.
  • Wu, Chien-Wei

Abstract

It has been proved that process capability indices provide very efficient measures of the capability of processes from many different perspectives. At the present time, the Cpk index is used more than any other index for measuring process capability. However, most existing research works for capability testing have focused on processes with symmetric tolerances, but not for asymmetric tolerances. A lower confidence bound estimates the minimum process capability, conveying critical information regarding product quality, which is essential to quality assurance. The sample size determination, which provides the sample sizes necessary to achieve a desired lower confidence bound, is directly related to the cost of the data collection plan. This paper provides explicit formulas with efficient algorithms to obtain the lower confidence bounds and sample sizes required for specified precision of the estimation on Cpk for processes with asymmetric tolerances. A Matlab computer program using a binary search method is developed. For the practitioners to use in their in-plant applications, we tabulate lower confidence bounds for some commonly used capability requirement and the sampling accuracy of Cpk for sample sizes determination. A realistic example of forging process is presented to illustrate the applicability of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:190:y:2008:i:1:p:205-227
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    References listed on IDEAS

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    1. W. L. Pearn & Y. C. Chang & Chien-Wei Wu, 2004. "Distributional and Inferential Properties of the Process Loss Indices," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(9), pages 1115-1135.
    2. 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.
    3. 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.
    4. 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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    1. 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.
    2. CHEN, Piao & YE, Zhi-Sheng, 2018. "A systematic look at the gamma process capability indices," European Journal of Operational Research, Elsevier, vol. 265(2), pages 589-597.
    3. Kuen-Suan Chen & Hsi-Tien Chen & Tsang-Chuan Chang, 2017. "The construction and application of Six Sigma quality indices," International Journal of Production Research, Taylor & Francis Journals, vol. 55(8), pages 2365-2384, April.
    4. Li, Der-Chiang & Lin, Liang-Sian, 2013. "A new approach to assess product lifetime performance for small data sets," European Journal of Operational Research, Elsevier, vol. 230(2), pages 290-298.
    5. 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.
    6. 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.

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