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Statistical inference for the lifetime performance index based on generalised order statistics from exponential distribution

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  • Mohammad Vali Ahmadi
  • Mahdi Doostparast
  • Jafar Ahmadi

Abstract

In manufacturing industries, the lifetime of an item is usually characterised by a random variable X and considered to be satisfactory if X exceeds a given lower lifetime limit L. The probability of a satisfactory item is then ηL := P(X ≥ L), called conforming rate. In industrial companies, however, the lifetime performance index, proposed by Montgomery and denoted by CL, is widely used as a process capability index instead of the conforming rate. Assuming a parametric model for the random variable X, we show that there is a connection between the conforming rate and the lifetime performance index. Consequently, the statistical inferences about ηL and CL are equivalent. Hence, we restrict ourselves to statistical inference for CL based on generalised order statistics, which contains several ordered data models such as usual order statistics, progressively Type-II censored data and records. Various point and interval estimators for the parameter CL are obtained and optimal critical regions for the hypothesis testing problems concerning CL are proposed. Finally, two real data-sets on the lifetimes of insulating fluid and ball bearings, due to Nelson (1982) and Caroni (2002), respectively, and a simulated sample are analysed.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:tsysxx:v:46:y:2015:i:6:p:1094-1107
    DOI: 10.1080/00207721.2013.809611
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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. Ching-Wen Hong & Wen-Chuan Lee & Jong-Wuu Wu, 2012. "Computational Procedure of Performance Assessment of Lifetime Index of Products for the Weibull Distribution with the Progressive First-Failure-Censored Sampling Plan," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, July.
    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. 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.
    5. 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.
    6. Wen-Chuan Lee, 2011. "Inferences on the lifetime performance index for Weibull distribution based on censored observations using the max -value method," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(6), pages 931-937.
    7. Jiang, R. & Murthy, D.N.P., 2011. "A study of Weibull shape parameter: Properties and significance," Reliability Engineering and System Safety, Elsevier, vol. 96(12), pages 1619-1626.
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    Cited by:

    1. 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.
    2. Tzong-Ru Tsai & Hua Xin & Ya-Yen Fan & Yuhlong Lio, 2022. "Bias-Corrected Maximum Likelihood Estimation and Bayesian Inference for the Process Performance Index Using Inverse Gaussian Distribution," Stats, MDPI, vol. 5(4), pages 1-18, November.

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