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Fuzzy Evaluation Models for Accuracy and Precision Indices

Author

Listed:
  • 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)

  • Tsun-Hung Huang

    (Department of Industrial Engineering and Management, National Chin-Yi University of Technology, Taichung 411030, Taiwan)

  • Ruey-Chyn Tsaur

    (Department of Management Sciences, Tamkang University, New Taipei City 25137, Taiwan)

  • Wen-Yang Kao

    (Office of Physical Education, National Chin-Yi University of Technology, Taichung 411030, Taiwan)

Abstract

The random variable X is used to represent the normal process containing two important parameters—the process average and the process standard deviation. The variable is transformed using Y = ( X − T )/d, where T is the target value and d is the tolerance. The average of Y is then called the accuracy index, and the standard deviation is called the precision index. If only the values of the accuracy index and the process precision index are well controlled, the process quality level as well as the process yield are ensured. Based on this concept, this paper constructed a control chart for the accuracy index and the precision index and derived the confidence intervals of the accuracy index and the precision index using in-control data, as the process was stable. This paper aims to control process quality via monitoring the accuracy and precision of the process. At the same time, fuzzy tests are developed for the indicators of process accuracy and precision to evaluate whether the process quality can reach the k -sigma quality level, as well as offer suggestions about directions of improvement when it fails to reach the k -sigma quality level. Obviously, the model in this paper cannot only evaluate whether the process meets the requirements of the quality level; it can also provide a decision regarding whether the process should be improved. It is very helpful for the enhancement of enterprises’ process capabilities.

Suggested Citation

  • Kuen-Suan Chen & Tsun-Hung Huang & Ruey-Chyn Tsaur & Wen-Yang Kao, 2022. "Fuzzy Evaluation Models for Accuracy and Precision Indices," Mathematics, MDPI, vol. 10(21), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:3961-:d:952462
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    References listed on IDEAS

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    1. Lepore, A. & Palumbo, B. & Castagliola, P., 2018. "A note on decision making method for product acceptance based on process capability indices Cpk and Cpmk," European Journal of Operational Research, Elsevier, vol. 267(1), pages 393-398.
    2. 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.
    3. 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.
    4. Chun-Min Yu & Kuen-Suan Chen & Ting-Hsin Hsu, 2022. "Confidence-Interval-Based Fuzzy Testing for the Lifetime Performance Index of Electronic Product," Mathematics, MDPI, vol. 10(9), pages 1-10, April.
    5. Kuen-Suan Chen & Tzung-Hua Hsieh, 2022. "Novel Physical Fitness Fuzzy Evaluation Model for Individual Health Promotion," IJERPH, MDPI, vol. 19(9), pages 1-12, April.
    6. Kuen-Suan Chen, 2022. "Fuzzy testing of operating performance index based on confidence intervals," Annals of Operations Research, Springer, vol. 311(1), pages 19-33, April.
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    Cited by:

    1. Kuo-Ching Chiou, 2023. "Building Up of Fuzzy Evaluation Model of Life Performance Based on Type-II Censored Data," Mathematics, MDPI, vol. 11(17), pages 1-12, August.

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