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Reliability analysis of log-normal distribution with nonconstant parameters under constant-stress model

Author

Listed:
  • Wei Cui

    (Jilin University of Finance and Economics)

  • Zai-zai Yan

    (Inner Mongolia University of Technology
    Inner Mongolia Key Laboratory of Statistical Analysis Theory for Life Data and Neural Network Modeling)

  • Xiu-yun Peng

    (Inner Mongolia University of Technology
    Inner Mongolia Key Laboratory of Statistical Analysis Theory for Life Data and Neural Network Modeling)

  • Gai-mei Zhang

    (Huhhot First Hospital)

Abstract

Under constant-stress accelerated life test, the general progressive type-II censoring sample and the two parameters following the linear Arrhenius model, the point estimation and interval estimation of the two parameters log-normal distribution were discussed. The unknown parameters of the model as well as reliability and hazard rate functions are estimated by using Maximum likelihood (ML) and Bayesian methods. The maximum-likelihood estimates are derived by the Newton–Raphson method and the corresponding asymptotic variance is derived by the Fisher information matrix. Since the Bayesian estimates (BEs) of the unknown parameters cannot be expressed explicitly, the approximate BEs of the unknown parameters. The approximate highest posterior density confidence intervals are calculated. The practicality of the proposed method is illustrated by simulation study and real data application analysis.

Suggested Citation

  • Wei Cui & Zai-zai Yan & Xiu-yun Peng & Gai-mei Zhang, 2022. "Reliability analysis of log-normal distribution with nonconstant parameters under constant-stress 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. 13(2), pages 818-831, April.
    • Handle: RePEc:spr:ijsaem:v:13:y:2022:i:2:d:10.1007_s13198-021-01343-0
    DOI: 10.1007/s13198-021-01343-0
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    References listed on IDEAS

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    1. A.C. Kimber, 1990. "Exploratory Data Analysis for Possibly Censored Data from Skewed Distributions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 39(1), pages 21-30, March.
    2. W. R. Gilks & P. Wild, 1992. "Adaptive Rejection Sampling for Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 337-348, June.
    3. Seo, J.H. & Jung, M. & Kim, C.M., 2009. "Design of accelerated life test sampling plans with a nonconstant shape parameter," European Journal of Operational Research, Elsevier, vol. 197(2), pages 659-666, September.
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