Reliability Sampling Design for the Lifetime Performance Index of Gompertz Lifetime Distribution under Progressive Type I Interval Censoring

Shu-Fei Wu, Yi-Jun Xie, Mao-Feng Liao and Wei-Tsung Chang
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Shu-Fei Wu: Department of Statistics, Tamkang University, Taipei 251301, Taiwan
Yi-Jun Xie: Department of Statistics, Tamkang University, Taipei 251301, Taiwan
Mao-Feng Liao: Department of Statistics, Tamkang University, Taipei 251301, Taiwan
Wei-Tsung Chang: Department of Computer Science, University of Taipei, Taipei 100234, Taiwan

Mathematics, 2021, vol. 9, issue 17, 1-18

Abstract: In this artificial intelligence era, the constantly changing technology makes production techniques become sophisticated and complicated. Therefore, manufacturers are dedicated to improving the quality of products by increasing the lifetime in order to achieve the quality standards demanded by consumers. For products with lifetime following a Gompertz distribution, the lifetime performance index was used to measure the performance of manufacturing process under progressive type I interval censoring. The sampling design is investigated to reach the given level of significance and power level. When inspection interval length is fixed and the number of inspection intervals is not fixed, the required number of inspection intervals and sample size with minimum total cost are determined and tabulated. When the termination time is not fixed, the required number of inspection intervals, sample size, and equal interval length reaching the minimum total cost are determined and tabulated. The optimal parameter values are tabulated for the practical use of users. Finally, one practical example is given for the illustrative aim to show the implementation of this sampling design to collect data and the collected data are used to conduct the testing procedure to see if the process is capable.

Keywords: censored sample; Gompertz distribution; maximum likelihood estimator; process capability indices; testing algorithmic procedure; sampling design (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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