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BAYESIAN ANALYSIS OF DOUBLY STOCHASTIC MARKOV PROCESSES IN RELIABILITY

Published online by Cambridge University Press:  08 April 2020

Atilla Ay Open the ORCID record for Atilla Ay [Opens in a new window] ,
Refik Soyer ,
Joshua Landon  and
Süleyman Özekici
Atilla Ay
Affiliation:
Department of Decision Sciences, The George Washington University, Washington, DC 20052, USA E-mail: aay@gwu.edu
Refik Soyer
Affiliation:
Department of Decision Sciences, The George Washington University, Washington, DC 20052, USA E-mail: aay@gwu.edu
Joshua Landon
Affiliation:
Department of Statistics, The George Washington University, Washington, DC 20052, USA
Süleyman Özekici
Affiliation:
Department of Industrial Engineering, Koç University, 34450 İstanbul, Turkey
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Abstract

Markov processes play an important role in reliability analysis and particularly in modeling the stochastic evolution of survival/failure behavior of systems. The probability law of Markov processes is described by its generator or the transition rate matrix. In this paper, we suppose that the process is doubly stochastic in the sense that the generator is also stochastic. In our model, we suppose that the entries in the generator change with respect to the changing states of yet another Markov process. This process represents the random environment that the stochastic model operates in. In fact, we have a Markov modulated Markov process which can be modeled as a bivariate Markov process that can be analyzed probabilistically using Markovian analysis. In this setting, however, we are interested in Bayesian inference on model parameters. We present a computationally tractable approach using Gibbs sampling and demonstrate it by numerical illustrations. We also discuss cases that involve complete and partial data sets on both processes.

Keywords

Bayesian inferenceBayesian reliability analysishidden Markov modelMarkov modulated Markov process
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 3 , July 2021 , pp. 708 - 729
Copyright
© Cambridge University Press 2020

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