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

Author

Listed:
  • Mohammad Vali Ahmadi

    (University of Bojnord)

  • Jafar Ahmadi

    (Ferdowsi University of Mashhad)

  • Mousa Abdi

    (Higher Education Complex of Bam)

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 ( $$C_L$$ 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 $$C_L$$ 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 $$C_L$$ 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.

Suggested Citation

  • Mohammad Vali Ahmadi & Jafar Ahmadi & Mousa Abdi, 2019. "Evaluating the lifetime performance index of products based on generalized order statistics from two-parameter exponential model," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(2), pages 251-275, April.
    • Handle: RePEc:spr:ijsaem:v:10:y:2019:i:2:d:10.1007_s13198-019-00780-2
    DOI: 10.1007/s13198-019-00780-2
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    References listed on IDEAS

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    1. Hsiu-Mei Lee & Jong-Wuu Wu & Chia-Ling Lei & Wen-Liang Hung, 2011. "Implementing lifetime performance index of products with two-parameter exponential distribution," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(8), pages 1305-1321.
    2. Sanku Dey & Vikas Kumar Sharma & M. Z. Anis & Babita Yadav, 2017. "Assessing lifetime performance index of Weibull distributed products using progressive type II right censored samples," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 318-333, June.
    3. Lee, Hsiu-Mei & Lee, Wen-Chuan & Lei, Chia-Ling & Wu, Jong-Wuu, 2011. "Computational procedure of assessing lifetime performance index of Weibull lifetime products with the upper record values," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1177-1189.
    4. Mohammad Vali Ahmadi & Mahdi Doostparast & Jafar Ahmadi, 2015. "Statistical inference for the lifetime performance index based on generalised order statistics from exponential distribution," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(6), pages 1094-1107, April.
    5. Aboeleneen, Z.A., 2010. "Inference for Weibull distribution under generalized order statistics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(1), pages 26-36.
    6. A. Childs & B. Chandrasekar & N. Balakrishnan & D. Kundu, 2003. "Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(2), pages 319-330, June.
    7. Wu, Shu-Fei & Lin, Ying-Po, 2016. "Computational testing algorithmic procedure of assessment for lifetime performance index of products with one-parameter exponential distribution under progressive type I interval censoring," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 120(C), pages 79-90.
    8. Lee, Wen-Chuan & Wu, Jong-Wuu & Hong, Ching-Wen, 2009. "Assessing the lifetime performance index of products from progressively type II right censored data using Burr XII model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2167-2179.
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