Likelihood Inference for the Lifetime Performance Index under Progressive Type-II Censoring

Laumen, Benjamin; Cramer, Erhard

doi:10.1515/eqc-2015-0008

Cited by 15 publications

(4 citation statements)

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“…Under the progressive type-II censoring, the experiment terminates when the mth failure time is observed and the failure times for the first m units, excluding the progressive censored units, are collected. Laumen and Cramer [10] derived the MLE for the lifetime performance index from gamma distributions and built a testing procedure under the same censoring. For the exponential lifetime model, Lee et al [11] derived the UMVUE for the lifetime performance index and utilized it to build a hypothesis testing procedure for C L .…”

Section: Discussionmentioning

confidence: 99%

“…Wu and Hsieh [9] assessed the lifetime performance index of products following the Gompertz distribution. For the progressive type-II censored data, Laumen and Cramer [10] proposed the inferences for the lifetime performance index from gamma distributions. Lee et al [11] evaluated the lifetime performance index for products with an exponential distribution, and Wu et al [12] considered the Bayesian test for the lifetime performance index.…”

Section: Introductionmentioning

confidence: 99%

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

Chang

2021

Symmetry

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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.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Chang

2021

Symmetry

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“…Using the max p-value method, Ahmadi et al (2013) discussed statistical inference for C L on the basis of a progressively first-failure-censored sample coming from a Weibull distribution with known shape parameter. For more details, see Day et al (2017), Lee et al (2010), Wu et al (2007, Liu and Ren (2013), Wu and Lin (2016), Yan et al (2015) and Laumen and Cramer (2015).…”

Section: Introductionmentioning

confidence: 99%

Evaluating the lifetime performance index of products based on generalized order statistics from two-parameter exponential model

Ahmadi

Abdi³

2019

Int J Syst Assur Eng Manag

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Assessing the lifetime performance of products is one of the most important topics in the manufacturing industries. In this paper, we assume that the lifetimes of products are independent and have a common two-parameter exponential distribution. The lifetime performance index (C L ) provides a means for evaluating the performance of a process under a known lower lifetime limit L. We consider a sample of generalized order statistics (GOS), introduced by Kamps (A concept of generalized order statistics. Teubner, Stuttgart, 1995), which contains several models of ordered random variables, e.g. ordinary order statistics, progressively censored order statistics and record values. Then, we obtain the maximum likelihood estimator and the uniformly minimum variance unbiased estimator (UMVUE) of C L on the basis of a GOS sample. These estimators are compared in terms of mean squared error and Pitman measure of closeness criteria. The UMVUE of C L is utilized to develop a novel hypothesis testing procedure in the condition of known L. Finally, in order to illustrate the results, two real data sets due to Lawless (Statistical model and methods for lifetime data, 2nd edn. Wiley, New York, 2003) and Proschan (Technometrics 15:375-383, 1963), and a simulated sample are analyzed.

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“…Bhattacharya et al [8] proposed an optimum life-testing plans under Type-II progressive censoring scheme using variable neighborhood search algorithm. Laumen and Cramer [9] discussed the likelihood inference and statistical test procedure for the lifetime performance index in the presence of progressive censoring. Khorram and Farahani [10] considered the maximum likelihood estimation and bayes estimation of parameters of weighted exponential distribution based on progressively Type-II censored sample.…”

Section: Introductionmentioning

confidence: 99%

Admissibility Estimation of Pareto Distribution Under Entropy Loss Function Based on Progressive Type-II Censored Sample

Fan¹

2016

PAMJ

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Abstract:The aim of this paper is to study the estimation of Pareto distribution on the basis of progressive type-II censored sample. First, the maximum likelihood estimator (MLE) is derived. Then the Bayes estimator of the unknown parameter of Pareto distribution is derived on the basis of Gamma prior distribution under entropy loss function. Further the empirical Bayes estimator also obtained by using maximum likelihood on the basis of Bayes estimator. Finally, the admissibility of a class of inverse linear estimators are discussed under suitable conditions.

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Likelihood Inference for the Lifetime Performance Index under Progressive Type-II Censoring

Abstract: Likelihood inference for the lifetime performance index

Cited by 15 publications

References 0 publications

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

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

Evaluating the lifetime performance index of products based on generalized order statistics from two-parameter exponential model

Admissibility Estimation of Pareto Distribution Under Entropy Loss Function Based on Progressive Type-II Censored Sample

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