A hypothesis testing procedure for the evaluation on the lifetime performance index of products with Burr XII distribution under progressive type I interval censoring

2017 ◽  
Vol 47 (9) ◽  
pp. 2670-2683 ◽  
Author(s):  
Shu-Fei Wu ◽  
Tzu-Chin Chen ◽  
Wen-Jui Chang ◽  
Chia-Wei Chang ◽  
Chen Lin
Keyword(s):  
Hypothesis Testing ◽  
Performance Index ◽  
Testing Procedure ◽  
Interval Censoring ◽  
Type I ◽  
Burr Xii Distribution ◽  
Lifetime Performance ◽  
Progressive Type ◽  
Hypothesis Testing Procedure

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 Bayesian Testing Procedure on the Lifetime Performance Index of Products Following Chen Lifetime Distribution Based on the Progressive Type-II Censored Sample

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1322
Author(s):  
Shu-Fei Wu ◽  
Wei-Tsung Chang
Keyword(s):  
Hypothesis Testing ◽  
Performance Index ◽  
Testing Procedure ◽  
Lifetime Distribution ◽  
Type Ii ◽  
Lifetime Performance ◽  
Progressive Type ◽  
Hypothesis Testing Procedure ◽  
Censored Sample ◽  
Type Ii Censored Sample

With the high demands on the quality of high-tech products for consumers, assuring the lifetime performance is a very important task for competitive manufacturing industries. The lifetime performance index CL is frequently used to monitor the larger-the-better lifetime performance of products. This research is related to the topic of asymmetrical probability distributions and applications across disciplines. Chen lifetime distribution with a bathtub shape or increasing failure rate function has many applications in the lifetime data analysis. We derived the uniformly minimum variance unbiased estimator (UMVUE) for CL, and we used this estimator to develop a hypothesis testing procedure of CL under a lower specification limit based on the progressive type-II censored sample. The Bayesian estimator for CL is also derived, and it is used to develop another hypothesis testing procedure. A simulation study is conducted to compare the average confidence levels for two procedures. Finally, one practical example is given to illustrate the implementation of our proposed non-Bayesian and Bayesian testing procedure.

scholarly journals The Evaluation on the Process Capability Index CL for Exponentiated Frech’et Lifetime Product under Progressive Type I Interval Censoring

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1032
Author(s):  
Shu-Fei Wu ◽  
Wei-Tsung Chang
Keyword(s):  
Probability Distributions ◽  
Testing Procedure ◽  
Interval Censoring ◽  
Type I ◽  
Lifetime Distributions ◽  
Lifetime Performance ◽  
Progressive Type ◽  
Computational Testing ◽  
Lower Specification Limit ◽  
Level Of Significance

We present the likelihood inferences on the lifetime performance index CL to evaluate the performance of lifetimes of products following the skewed Exponentiated Frech’et distribution in many manufacturing industries. This research is related to the topic of skewed Probability Distributions and Applications across Disciplines. Exponentiated Frech’et distribution is a generalization of some lifetime distributions. The maximum likelihood estimator for CL for lifetimes with exponentiated Frech’et distribution is derived to develop a computational testing procedure so that experimenters can implement it to test whether the lifetime performance reached the pre-assigned level of significance with a given lower specification limit under progressive type I interval censoring. At the end, two examples are provided to demonstrate the implementation on the algorithm for our proposed computational testing procedure.

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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