IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i12p2129-d452888.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/12/2129/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/12/2129/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Wang, Ching-Hsin & Chen, Kuen-Suan, 2020. "New process yield index of asymmetric tolerances for bootstrap method and six sigma approach," International Journal of Production Economics, Elsevier, vol. 219(C), pages 216-223.
    2. Kun-Tzu Yu & Kuen-Suan Chen, 2016. "Testing and analysing capability performance for products with multiple characteristics," International Journal of Production Research, Taylor & Francis Journals, vol. 54(21), pages 6633-6643, November.
    3. Kuen-Suan Chen & Kung-Jeng Wang & Tsang-Chuan Chang, 2017. "A novel approach to deriving the lower confidence limit of indices , , and in assessing process capability," International Journal of Production Research, Taylor & Francis Journals, vol. 55(17), pages 4963-4981, September.
    4. Otsuka, Akimasa & Nagata, Fusaomi, 2018. "Quality design method using process capability index based on Monte-Carlo method and real-coded genetic algorithm," International Journal of Production Economics, Elsevier, vol. 204(C), pages 358-364.
    5. 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.
    6. 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.
    7. Tsang-Chuan Chang & Kuen-Suan Chen, 2019. "Testing process quality of wire bonding with multiple gold wires from viewpoint of producers," International Journal of Production Research, Taylor & Francis Journals, vol. 57(17), pages 5400-5413, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kuen-Suan Chen & Tsang-Chuan Chang & Chien-Che Huang, 2020. "Supplier Selection by Fuzzy Assessment and Testing for Process Quality under Consideration with Data Imprecision," Mathematics, MDPI, vol. 8(9), pages 1-14, August.
    2. Kuen-Suan Chen & Ming-Chieh Huang & Chun-Min Yu & Hsuan-Yu Chen, 2022. "Quality-Based Supplier Selection Model for Products with Multiple Quality Characteristics," Sustainability, MDPI, vol. 14(14), pages 1-17, July.
    3. Wei Lo & Chun-Ming Yang & Kuei-Kuei Lai & Shao-Yu Li & Chi-Han Chen, 2021. "Developing a Novel Fuzzy Evaluation Model by One-Sided Specification Capability Indices," Mathematics, MDPI, vol. 9(10), pages 1-11, May.
    4. Kuen-Suan Chen & Tsun-Hung Huang, 2021. "A Fuzzy Evaluation Model Aimed at Smaller-the-Better-Type Quality Characteristics," Mathematics, MDPI, vol. 9(19), pages 1-13, October.
    5. Kuen-Suan Chen & Chin-Chia Liu & Chi-Han Chen, 2022. "Fuzzy Evaluation of Process Quality with Process Yield Index," Mathematics, MDPI, vol. 10(14), pages 1-11, July.
    6. 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.
    7. 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.
    8. Chen, Kuen-Suan & Wang, Ching-Hsin & Tan, Kim-Hua, 2019. "Developing a fuzzy green supplier selection model using six sigma quality indices," International Journal of Production Economics, Elsevier, vol. 212(C), pages 1-7.
    9. Chen, Kuen-Suan & Wang, Ching-Hsin & Tan, Kim Hua & Chiu, Shun-Fung, 2019. "Developing one-sided specification six-sigma fuzzy quality index and testing model to measure the process performance of fuzzy information," International Journal of Production Economics, Elsevier, vol. 208(C), pages 560-565.
    10. Wang, Ching-Hsin & Chen, Kuen-Suan, 2020. "New process yield index of asymmetric tolerances for bootstrap method and six sigma approach," International Journal of Production Economics, Elsevier, vol. 219(C), pages 216-223.
    11. Kuen-Suan Chen & Tsang-Chuan Chang, 2022. "Fuzzy testing model for the lifetime performance of products under consideration with exponential distribution," Annals of Operations Research, Springer, vol. 312(1), pages 87-98, May.
    12. Kuen-Suan Chen & Chun-Min Yu, 2024. "Confidence-interval-based fuzzy supplier selection model with lifetime performance index," Annals of Operations Research, Springer, vol. 340(1), pages 133-147, September.
    13. Stolze, Hannah J. & Brusco, Michael J. & Smith, Jeffery S., 2021. "Exploring the social mechanisms for variation reduction for direct store delivery (DSD) and vendor managed inventory performance: An integrated network governance and coordination theory perspective," International Journal of Production Economics, Elsevier, vol. 234(C).
    14. 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.
    15. Huijian Han & Ye Yang & Rui Zhang & Brekhna Brekhna, 2020. "Factors and Paths of Transformation and Upgradation of Chemical Industry in Shandong, China," Sustainability, MDPI, vol. 12(8), pages 1-20, April.
    16. Tai-Shan Lee & Ching-Hsin Wang & Chun-Min Yu, 2019. "Fuzzy Evaluation Model for Enhancing E-Learning Systems," Mathematics, MDPI, vol. 7(10), pages 1-11, October.
    17. 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.
    18. Jung-Fa Tsai & Chin-Po Wang & Ming-Hua Lin & Shih-Wei Huang, 2021. "Analysis of Key Factors for Supplier Selection in Taiwan’s Thin-Film Transistor Liquid-Crystal Displays Industry," Mathematics, MDPI, vol. 9(4), pages 1-18, February.
    19. 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.
    20. Tomohiro, Ryosuke & Arizono, Ikuo & Takemoto, Yasuhiko, 2020. "Economic design of double sampling Cpm control chart for monitoring process capability," International Journal of Production Economics, Elsevier, vol. 221(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2129-:d:452888. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.