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

Shu-Fei Wu,Wei-Tsung Chang

doi:10.3390/sym13081322

Shu-Fei Wu, Wei-Tsung Chang

Open Access

https://doi.org/10.3390/sym13081322

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Journal: Symmetry	Publication Date: Jul 22, 2021
Citations: 4	License type: CC BY 4.0

Affiliation: Tamkang University, University of Taipei

Abstract

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.

Highlights

Introduction de Córdoba Castellá and CalogeroIn the competitive industry of manufacturing, evaluating whether the performance of products meets the desired quality level is crucial in order to get a larger market share.Process capability indices have been widely utilized as the measurement of the larger-thebetter type quality characteristics (See Montgomery [1] for more examples and details). μ− LMontgomery [1] proposed a lifetime performance index denoted by CL = σ, where μ represents the process mean, σ denotes the process standard deviation, and L is the known pre-specified lower specification limit
We develop a statistical testing procedure based on the uniformly minimum variance unbiased estimator (UMVUE) of CL given by eL = 1 − m−1 kL to assess whether the lifetime performance index exceeds the pre-specified
Wu and Chang [8] derived the maximum likelihood estimator (MLE) for the lifetime performance index based on the progressive type-I interval censored sample and built a testing procedure about CL with the lifetime of products following an exponentiated

Summary

Introduction

In the competitive industry of manufacturing, evaluating whether the performance of products meets the desired quality level is crucial in order to get a larger market share. Montgomery [1] proposed a lifetime performance index denoted by CL = σ , where μ represents the process mean, σ denotes the process standard deviation, and L is the known pre-specified lower specification limit. This lifetime performance index is usually used to evaluate the lifetime performance of products. The lifetimes of all products cannot be observed in the life test due to the limited material resources or experimental time. The application of progressive censored data is referring to Balakrishnan and Cramer [3], Aggarwala [4], Wu [5], and Wu et al [6]

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Discussion

Conclusion