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Two-Tailed Fuzzy Hypothesis Testing for Unilateral Specification Process Quality Index

Author

Listed:
  • Chun-Min Yu

    (Department of Industrial Engineering and Management, National Chin-Yi University of Technology, Taichung 41170, Taiwan)

  • Win-Jet Luo

    (Graduate institute of precision manufacturing technology, National Chin-Yi University of Technology, Taichung 41170, Taiwan)

  • Ting-Hsin Hsu

    (Department of Finance, National Taichung University of Science and Technology, Taichung 40401, Taiwan)

  • Kuei-Kuei Lai

    (Department of Business Administration, Chaoyang University of Technology, Taichung 41349, Taiwan)

Abstract

The quality characteristics with unilateral specifications include the smaller-the-better (STB) and larger-the-better (LTB) quality characteristics. Roundness, verticality, and concentricity are categorized into the STB quality characteristics, while the wire pull and the ball shear of gold wire bonding are categorized into the LTB quality characteristics. In terms of the tolerance, zero and infinity ( ∞ ) can be viewed as the target values in line with the STB and LTB quality characteristics, respectively. However, cost and timeliness considerations, or the restrictions of practical technical capabilities in the industry, mean that the process mean is generally far more than 1.5 standard deviations away from the target value. Researchers have accordingly proposed a process quality index conforming to the STB quality characteristics. In this study, we come up with a process quality index conforming to the LTB quality characteristics. We refer to these two types of indices as the unilateral specification process quality indices. These indices and the process yield have a one-to-one mathematical relationship. Besides, the process quality levels can be completely reflected as well. These indices possess unknown parameters. Therefore, sample data are required for calculation. Nevertheless, interval estimates can lower the misjudgment risk resulting from sampling errors more than point estimates can. In addition, considering cost and timeliness in the industry, samples are generally small, which lowers estimation accuracy. In an attempt to increase the accuracy of estimation as well as overcome the uncertainty of measured data, we first derive the confidence interval for unilateral specification process quality indices, and then propose a fuzzy membership function on the basis of the confidence interval to establish the two-tailed fuzzy testing rules for a single indicator. Lastly, we determine whether the process quality has improved.

Suggested Citation

  • Chun-Min Yu & Win-Jet Luo & Ting-Hsin Hsu & Kuei-Kuei Lai, 2020. "Two-Tailed Fuzzy Hypothesis Testing for Unilateral Specification Process Quality Index," Mathematics, MDPI, vol. 8(12), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2129-:d:452888
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    References listed on IDEAS

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    Cited by:

    1. Kuen-Suan Chen & Chun-Min Yu, 2022. "Lifetime performance evaluation and analysis model of passive component capacitor products," Annals of Operations Research, Springer, vol. 311(1), pages 51-64, April.

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