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Bayesian analysis for step-stress accelerated life testing using weibull proportional hazard model

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  • Naijun Sha
  • Rong Pan

Abstract

In this paper, we present a Bayesian analysis for the Weibull proportional hazard (PH) model used in step-stress accelerated life testings. The key mathematical and graphical difference between the Weibull cumulative exposure (CE) model and the PH model is illustrated. Compared with the CE model, the PH model provides more flexibility in fitting step-stress testing data and has the attractive mathematical properties of being desirable in the Bayesian framework. A Markov chain Monte Carlo algorithm with adaptive rejection sampling technique is used for posterior inference. We demonstrate the performance of this method on both simulated and real datasets. Copyright Springer-Verlag Berlin Heidelberg 2014

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  • Naijun Sha & Rong Pan, 2014. "Bayesian analysis for step-stress accelerated life testing using weibull proportional hazard model," Statistical Papers, Springer, vol. 55(3), pages 715-726, August.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:3:p:715-726
    DOI: 10.1007/s00362-013-0521-2
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    References listed on IDEAS

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    1. Ronghua Wang & Heliang Fei, 2004. "Conditions for the coincidence of the TFR, TRV and CE models," Statistical Papers, Springer, vol. 45(3), pages 393-412, July.
    2. René Van Dorp, J. & Mazzuchi, Thomas A., 2005. "A general Bayes weibull inference model for accelerated life testing," Reliability Engineering and System Safety, Elsevier, vol. 90(2), pages 140-147.
    3. 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.
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    Cited by:

    1. Ling, M.H. & Hu, X.W., 2020. "Optimal design of simple step-stress accelerated life tests for one-shot devices under Weibull distributions," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    2. Fode Zhang & Hon Keung Tony Ng & Yimin Shi & Ruibing Wang, 2019. "Amari–Chentsov structure on the statistical manifold of models for accelerated life tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 77-105, March.
    3. Kabir, Golam & Tesfamariam, Solomon & Sadiq, Rehan, 2015. "Predicting water main failures using Bayesian model averaging and survival modelling approach," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 498-514.
    4. Rui Hua & Wenhao Gui, 2022. "Inference for copula-based dependent competing risks model with step-stress accelerated life test under generalized progressive hybrid censoring," Computational Statistics, Springer, vol. 37(5), pages 2399-2436, November.
    5. Wang, Huan & Wang, Guan-jun & Duan, Feng-jun, 2016. "Planning of step-stress accelerated degradation test based on the inverse Gaussian process," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 97-105.
    6. Naijun Sha, 2018. "Statistical Inference for Progressive Stress Accelerated Life Testing with Birnbaum-Saunders Distribution," Stats, MDPI, vol. 1(1), pages 1-15, December.
    7. Chunhui Guo & Chuan Lyu & Jiayu Chen & Dong Zhou, 2018. "A multi-event combination maintenance model based on event correlation," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-24, November.
    8. Abdullah AH Ahmadini & Frank PA Coolen, 2020. "Statistical inference for the Arrhenius-Weibull accelerated life testing model with imprecision based on the likelihood ratio test," Journal of Risk and Reliability, , vol. 234(2), pages 275-289, April.
    9. Yin, Yi-Chao & Coolen, Frank P.A. & Coolen-Maturi, Tahani, 2017. "An imprecise statistical method for accelerated life testing using the power-Weibull model," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 158-167.

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