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

Aymen Rawashdeh (), Mohammed Hassan Al-Haj Ebrahem and Ayat Momani
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Aymen Rawashdeh: Yarmouk University
Mohammed Hassan Al-Haj Ebrahem: Yarmouk University
Ayat Momani: Yarmouk University

METRON, 2018, vol. 76, issue 2, No 2, 155-176

Abstract: 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.

Keywords: Degradation model; Bayesian analysis; Differential evolution Markov chain (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s40300-018-0141-7

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