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

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Abstract

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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Acknowledgements

The authors would like to thank the Editor and reviewers for their valuable comments and suggestions to improve the presentation of the paper. The research of J. Ahmadi was supported by Ferdowsi University of Mashhad [Grant Number 2/45621].

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Authors and Affiliations

  1. Department of Statistics, University of Bojnord, Bojnord, Iran

    Mohammad Vali Ahmadi

  2. Department of Statistics, Ferdowsi University of Mashhad, Mashhad, Iran

    Jafar Ahmadi

  3. Department of Statistics, Higher Education Complex of Bam, Bam, Iran

    Mousa Abdi

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  1. Mohammad Vali Ahmadi
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  2. Jafar Ahmadi
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  3. Mousa Abdi
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Correspondence to Jafar Ahmadi.

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Ahmadi, M.V., Ahmadi, J. & Abdi, M. Evaluating the lifetime performance index of products based on generalized order statistics from two-parameter exponential model. Int J Syst Assur Eng Manag 10, 251–275 (2019). https://doi.org/10.1007/s13198-019-00780-2

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  • DOI: https://doi.org/10.1007/s13198-019-00780-2

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