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 Assessing the Lifetime Performance Index of Burr Type III Distribution under Progressive Type II Censoring

2021 ◽  
pp. 633-647
Author(s):  
Amal Hassan ◽  
Salwa Assar ◽  
Amany Selmy
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Performance Index ◽  
Testing Procedure ◽  
Type Ii ◽  
Likelihood Estimator ◽  
Significance Level ◽  
Type Iii ◽  
Lifetime Performance ◽  
Progressive Type

Process capability analysis has been widely applied in the field of quality control to monitor the performance of industrial processes. Hence, lifetime performance index CL is used to measure the potential and performance of a process. In the present study, we construct a maximum likelihood estimator of CL under Burr Type III distribution based on the progressive Type II censored sample. The maximum likelihood estimator of CL is then utilized to develop the hypothesis testing procedure in the condition of known L. Finally, one practical example and Monte Carlo simulation are given to assess the behavior of the lifetime performance index under given significance level.

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.

Evaluating the lifetime performance index with the inverted exponentiated Rayleigh distribution based on censored sample

2019 ◽  
Vol 10 (05) ◽  
pp. 1950028
Author(s):  
Shuo Gao ◽  
Wenhao Gui
Keyword(s):  
Performance Index ◽  
Hypothesis Test ◽  
Rayleigh Distribution ◽  
Likelihood Method ◽  
Lifetime Performance ◽  
Progressive Type ◽  
Speed Up ◽  
Extensive Numerical Simulation ◽  
Censored Sample ◽  
The Cost

Lifetime performance index is a powerful and effective way to analyze whether a product achieves the specified standards. In this paper, we investigate the lifetime performance index for the inverted exponential Rayleigh distribution using progressive type II censored sample data. The censored sample is able to greatly save the cost of the experiment and speed up the experiment. We derive the estimation value of lifetime performance index using the maximum likelihood method, and conduct the hypothesis test. Based on extensive numerical simulation, the power function is utilized to assess effectiveness of hypothesis testing. The simulation results show that lifetime performance index is good for determining whether the lifetime of the product reaches the criterion. Finally, a practical dataset is provided to give a demonstration for the procedures of lifetime performance evaluation.

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