Reliability sampling design for the lifetime performance index of Burr XII lifetime distribution under progressive type I interval censoring

2021 ◽  
pp. 1-15
Author(s):  
Shu-Fei Wu ◽  
Yi-Wun Cheng ◽  
Che-Wei Kang ◽  
Wei-Tsung Chang
Keyword(s):  
Performance Index ◽  
Sampling Design ◽  
Interval Censoring ◽  
Lifetime Distribution ◽  
Type I ◽  
Lifetime Performance ◽  
Progressive Type

scholarly journals Experimental Design for the Lifetime Performance Index of Weibull Products Based on the Progressive Type I Interval Censored Sample

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1691
Author(s):  
Shu-Fei Wu ◽  
Yu-Cheng Wu ◽  
Chi-Han Wu ◽  
Wei-Tsung Chang
Keyword(s):  
Experimental Design ◽  
Performance Index ◽  
Sampling Design ◽  
Testing Procedure ◽  
Interval Censoring ◽  
Type I ◽  
Lifetime Performance ◽  
Progressive Type ◽  
Interval Censored ◽  
Censored Sample

In this study, the experimental design is developed based on the testing procedure for the lifetime performance index of products following Weibull lifetime distribution under progressive type I interval censoring. This research topic is related to asymmetrical probability distributions and applications across disciplines. The asymptotic distribution of the maximum likelihood estimator of the lifetime performance index is utilized to develop the testing procedure. In order to reach the given power level, the minimum sample size is determined and tabulated. In order to minimize the total cost that occurred under progressive type I interval censoring, the sampling design is investigated to determine the minimum number of inspection intervals and equal interval lengths when the termination time of experiment is fixed or not fixed. For illustrative aims, one practical example is given for the implementation of our proposed sampling design to collect the progressive type I interval censored sample so that the users can use this sample to test if the lifetime performance index exceeds the desired target level.

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

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2109
Author(s):  
Shu-Fei Wu ◽  
Yi-Jun Xie ◽  
Mao-Feng Liao ◽  
Wei-Tsung Chang
Keyword(s):  
Sample Size ◽  
Performance Index ◽  
Sampling Design ◽  
Optimal Parameter ◽  
Interval Censoring ◽  
Interval Length ◽  
Type I ◽  
Total Cost ◽  
Lifetime Performance ◽  
Progressive Type

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.

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