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New generalization of process capability index Cpk

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  • W. L. Pearn

Abstract

The process capability index Cpk has been widely used in manufacturing industry to provide numerical measures of process potential and performance. As noted by many quality control researchers and practitioners, Cpk is yield-based and is independent of the target T. This fails to account for process centering with symmetric tolerances, and presents an even greater problem with asymmetric tolerances. To overcome the problem, several generalizations of Cpk have been proposed to handle processes with asymmetric tolerances. Unfortunately, these generalizations understate or overstate the process capability in many cases, so reflect the process potential and performance inaccurately. In this paper, we first introduce a new index Cp"k, which is shown to be superior to the existing generalizations of Cpk. We then investigate the statistical properties of the natural estimator of Cp"k, assuming that the process is normally distributed.

Suggested Citation

  • W. L. Pearn, 1998. "New generalization of process capability index Cpk," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(6), pages 801-810.
    • Handle: RePEc:taf:japsta:v:25:y:1998:i:6:p:801-810
    DOI: 10.1080/02664769822783
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    References listed on IDEAS

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    1. 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.
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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. W. L. Pearn & Y. C. Chang & Chien-Wei Wu, 2006. "Measuring Process Performance Based on Expected Loss with Asymmetric Tolerances," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(10), pages 1105-1120.
    3. Dja-Shin Wang & Tong-Yuan Koo & Chao-Yu Chou, 2009. "Yield measure for the process with multiple streams," Quality & Quantity: International Journal of Methodology, Springer, vol. 43(4), pages 661-668, July.
    4. 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.
    5. Kuen-Suan Chen & Chun-Min Yu & Jin-Shyong Lin & Tsun-Hung Huang & Yun-Syuan Zhong, 2024. "Fuzzy Radar Evaluation Chart for Improving Machining Quality of Components," Mathematics, MDPI, vol. 12(5), pages 1-18, February.
    6. Daniel Dasig Jr, 2017. "A frontier in organizational and business process innovation in service management through lean six sigma Kaizen project implementation," Journal of Administrative and Business Studies, Professor Dr. Usman Raja, vol. 3(6), pages 263-283.
    7. Chen, K.S. & Yu, K.T. & Sheu, S.H., 2006. "Process capability monitoring chart with an application in the silicon-filler manufacturing process," International Journal of Production Economics, Elsevier, vol. 103(2), pages 565-571, October.
    8. V�ctor Leiva & Carolina Marchant & Helton Saulo & Muhammad Aslam & Fernando Rojas, 2014. "Capability indices for Birnbaum-Saunders processes applied to electronic and food industries," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(9), pages 1881-1902, September.
    9. Moutushi Chatterjee & Ashis Kumar Chakraborty, 2017. "Unification of some multivariate process capability indices for asymmetric specification region," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 71(4), pages 286-306, November.

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