IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i19p3458-d922413.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/19/3458/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/19/3458/
    Download Restriction: no
    ---><---

    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)

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Mingyuan Li & Kuen-Suan Chen & Chun-Min Yu & Chun-Ming Yang, 2021. "A Fuzzy Evaluation Decision Model for the Ratio Operating Performance Index," Mathematics, MDPI, vol. 9(3), pages 1-12, January.
    7. 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.
    8. 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.
    9. 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.
    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 & 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.
    12. 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.
    13. Piotr Michalak, 2023. "Simulation and Experimental Study on the Use of Ventilation Air for Space Heating of a Room in a Low-Energy Building," Energies, MDPI, vol. 16(8), pages 1-17, April.
    14. Ahmad Al Humssi & Maria Petrovskaya & Milana Abueva, 2022. "Modelling the Impact of World Oil Prices and the Mining and Quarrying Sector on the United Arab Emirates’ GDP," Mathematics, MDPI, vol. 11(1), pages 1-22, December.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. Mohammad Rasoul Nazari Sendi & Iraj Hassanzad Navroodi & Aman Mohammad Kalteh, . "Estimation of Fagus orientalis Lipsky height using nonlinear models in Hyrcanian forests, Iran," Journal of Forest Science, Czech Academy of Agricultural Sciences, vol. 0.
    20. Kanthilanka, H. & Ramilan, T. & Farquharson, R.J. & Weerahewa, J., 2023. "Optimal nitrogen fertilizer decisions for rice farming in a cascaded tank system in Sri Lanka: An analysis using an integrated crop, hydro-nutrient and economic model," Agricultural Systems, Elsevier, vol. 207(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:10:y:2022:i:19:p:3458-:d:922413. 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.