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The Assessment of the Overall Lifetime Performance Index of Chen Products with Multiple Components

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  • Shu-Fei Wu

    (Department of Statistics, Tamkang University, Tamsui, Taipei 251037, Taiwan)

  • Yu-Lun Huang

    (Department of Statistics, Tamkang University, Tamsui, Taipei 251037, Taiwan)

Abstract

Process capability indices are widely utilized to evaluate process performance and drive continuous improvements in quality and productivity. Among these indices, the the-larger-the-better lifetime performance index is particularly noteworthy. For products with multiple components, an overall lifetime performance index is used, since it is a monotonically increasing function of the overall conforming rate and the relationship with each individual lifetime performance index can be determined. For products with the lifetime of the i th component following the Chen distribution, we investigate the maximum likelihood estimator for the overall lifetime performance index and the individual lifetime performance index based on the progressive type I interval censoring sample. Their asymptotic distributions for all lifetime performance indices are also derived. Once the target level for the overall lifetime performance index is specified, the desired level of individual lifetime performance index can be specified. By using the maximum likelihood estimator as the test statistic, a testing procedure to test whether the overall lifetime performance index has reached the target level is developed. The power analysis of the testing procedure is shown with figures, and some findings are summarized. At last, we use one practical example with two components to demonstrate how to implement this testing algorithmic procedure to test if the overall production process has reached the pre-assigned target level.

Suggested Citation

  • Shu-Fei Wu & Yu-Lun Huang, 2024. "The Assessment of the Overall Lifetime Performance Index of Chen Products with Multiple Components," Mathematics, MDPI, vol. 12(13), pages 1-21, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:2140-:d:1430806
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    References listed on IDEAS

    as
    1. Shu-Fei Wu & Meng-Zong Song, 2023. "Experimental Design for Progressive Type I Interval Censoring on the Lifetime Performance Index of Chen Lifetime Distribution," Mathematics, MDPI, vol. 11(6), pages 1-16, March.
    2. N. Balakrishnan, 2007. "Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 211-259, August.
    3. N. Balakrishnan, 2007. "Rejoinder on: Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 290-296, August.
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