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Statistical inference for the Arrhenius-Weibull accelerated life testing model with imprecision based on the likelihood ratio test

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  • Abdullah AH Ahmadini
  • Frank PA Coolen

Abstract

In this article, we present a new imprecise statistical inference method for accelerated life testing data, where nonparametric predictive inferences at normal stress levels are integrated with a parametric Arrhenius-Weibull model. The method includes imprecision based on the likelihood ratio test which provides robustness with regard to the model assumptions. We use the likelihood ratio test to obtain an interval for the parameter of the Arrhenius link function providing imprecision into the method. The imprecision leads to observations at increased stress levels being transformed into interval-valued observations at the normal stress level, where the width of an interval is larger for observations from higher stress levels. If the model fits well, our method has relatively little imprecision. However, if the model fits poorly, it leads to more imprecision. Simulation studies are presented to investigate the performance of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:risrel:v:234:y:2020:i:2:p:275-289
    DOI: 10.1177/1748006X19884860
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    References listed on IDEAS

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    1. Han, David, 2015. "Time and cost constrained optimal designs of constant-stress and step-stress accelerated life tests," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 1-14.
    2. 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.
    3. Elsayed, E.A. & Zhang, Hao, 2007. "Design of PH-based accelerated life testing plans under multiple-stress-type," Reliability Engineering and System Safety, Elsevier, vol. 92(3), pages 286-292.
    4. Nasir, Ehab A. & Pan, Rong, 2015. "Simulation-based Bayesian optimal ALT designs for model discrimination," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 1-9.
    5. 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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    1. Frank P. A. Coolen & Abdullah A. H. Ahmadini & Tahani Coolen-Maturi, 2021. "Imprecise inference based on the log-rank test for accelerated life testing," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(6), pages 913-925, August.

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