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A Bayesian approach to estimate the failure time distribution of a log-logistic degradation model

Author

Listed:
  • Aymen Rawashdeh

    (Yarmouk University)

  • Mohammed Hassan Al-Haj Ebrahem

    (Yarmouk University)

  • Ayat Momani

    (Yarmouk University)

Abstract

This paper presents a Bayesian approach, using differential evolution Markov chain method, to estimate the parameters of the failure time distribution and its percentiles based on grouped and non-grouped degradation data. The observed failure times are modeled by linear degradation path model with random degradation rates follow log-logistic distribution. Two Monte Carlo simulation studies are conducted. The first one is devoted to assess the performance of the proposed method with respect to the mean squared error (MSE) for different values of the scale and shape parameters of the degradation model using small, moderate and large sample sizes. The proposed method performs better when applied to non-grouped data compared with grouped data. The second simulation study is conducted to compare the proposed log-logistic model with a Weibull degradation model. More importantly, the log-logistic model outperforms the Weibull model. The proposed methods are demonstrated by modeling real life times of laser devices.

Suggested Citation

  • Aymen Rawashdeh & Mohammed Hassan Al-Haj Ebrahem & Ayat Momani, 2018. "A Bayesian approach to estimate the failure time distribution of a log-logistic degradation model," METRON, Springer;Sapienza Università di Roma, vol. 76(2), pages 155-176, August.
    • Handle: RePEc:spr:metron:v:76:y:2018:i:2:d:10.1007_s40300-018-0141-7
    DOI: 10.1007/s40300-018-0141-7
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    References listed on IDEAS

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    1. David D. Hanagal & Richa Sharma, 2015. "Analysis of Bivariate Survival Data using Shared Inverse Gaussian Frailty Model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(7), pages 1351-1380, April.
    2. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
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