Load-Sharing Model under Lindley Distribution and Its Parameter Estimation Using the Expectation-Maximization Algorithm

Date
2020-11-22
Authors
Park, Chanseok
Wang, Min
Alotaibi, Refah Mohammed
Rezk, Hoda
Journal Title
Journal ISSN
Volume Title
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Abstract

A load-sharing system is defined as a parallel system whose load will be redistributed to its surviving components as each of the components fails in the system. Our focus is on making statistical inference of the parameters associated with the lifetime distribution of each component in the system. In this paper, we introduce a methodology which integrates the conventional procedure under the assumption of the load-sharing system being made up of fundamental hypothetical latent random variables. We then develop an expectation maximization algorithm for performing the maximum likelihood estimation of the system with Lindley-distributed component lifetimes. We adopt several standard simulation techniques to compare the performance of the proposed methodology with the Newton–Raphson-type algorithm for the maximum likelihood estimate of the parameter. Numerical results indicate that the proposed method is more effective by consistently reaching a global maximum.

Description
Keywords
expectation-maximization algorithm, hypothetical latent random variable, Lindley distribution, maximum likelihood estimation, Newton–Raphson method
Citation
Entropy 22 (11): 1329 (2020)
Department
Management Science and Statistics