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Estimation of the Six Sigma Quality Index

Author

Listed:
  • Chun-Chieh Tseng

    (School of Internet Economics and Business, Fujian University of Technology, Fuzhou 350014, China)

  • Kuo-Ching Chiou

    (Department of Finance, Chaoyang University of Technology, Taichung 413310, Taiwan)

  • Kuen-Suan Chen

    (Department of Industrial Engineering and Management, National Chin-Yi University of Technology, Taichung 411030, Taiwan
    Department of Business Administration, Chaoyang University of Technology, Taichung 413310, Taiwan
    Department of Business Administration, Asia University, Taichung 413305, Taiwan)

Abstract

The measurement of the process capability is a key part of quantitative quality control, and process capability indices are statistical measures of the process capability. Six Sigma level represents the maximum achievable process capability, and many enterprises have implemented Six Sigma improvement strategies. In recent years, many studies have investigated Six Sigma quality indices, including Q p k . However, Q p k contains two unknown parameters, namely δ and γ , which are difficult to use in process control. Therefore, whether a process quality reaches the k sigma level must be statistically inferred. Moreover, the statistical method of sampling distribution is challenging for the upper confidence limits of Q p k . We address these two difficulties in the present study and propose a methodology to solve them. Boole’s inequality, Demorgan’s theorem, and linear programming were integrated to derive the confidence intervals of Q p k , and then the upper confidence limits were used to perform hypothesis testing. This study involved a case study of the semiconductor assembly process in order to verify the feasibility of the proposed method.

Suggested Citation

  • Chun-Chieh Tseng & Kuo-Ching Chiou & Kuen-Suan Chen, 2022. "Estimation of the Six Sigma Quality Index," Mathematics, MDPI, vol. 10(19), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3458-:d:922413
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    References listed on IDEAS

    as
    1. K. Chen & L. Ouyang & C. Hsu & C. Wu, 2009. "The communion bridge to Six Sigma and process capability indices," Quality & Quantity: International Journal of Methodology, Springer, vol. 43(3), pages 463-469, May.
    2. Kuen-Suan Chen & Tsang-Chuan Chang, 2020. "Construction and fuzzy hypothesis testing of Taguchi Six Sigma quality index," International Journal of Production Research, Taylor & Francis Journals, vol. 58(10), pages 3110-3125, May.
    3. Hoang Pham, 2019. "A New Criterion for Model Selection," Mathematics, MDPI, vol. 7(12), pages 1-12, December.
    4. 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.
    5. Mei-Fang Wu & Hsuan-Yu Chen & Tsang-Chuan Chang & Chih-Feng Wu, 2019. "Quality evaluation of internal cylindrical grinding process with multiple quality characteristics for gear products," International Journal of Production Research, Taylor & Francis Journals, vol. 57(21), pages 6687-6701, November.
    Full references (including those not matched with items on IDEAS)

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