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Entropy 2017, 19(6), 274; doi:10.3390/e19060274

Bayesian Hierarchical Scale Mixtures of Log-Normal Models for Inference in Reliability with Stochastic Constraint

Department of Statistics, Dongguk University-Seoul, Pil-Dong 3Ga, Chung-Gu, Seoul 100-715, Korea
Academic Editor: Brendon J. Brewer
Received: 2 May 2017 / Revised: 3 June 2017 / Accepted: 9 June 2017 / Published: 13 June 2017
(This article belongs to the Special Issue Maximum Entropy and Bayesian Methods)
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Abstract

This paper develops Bayesian inference in reliability of a class of scale mixtures of log-normal failure time (SMLNFT) models with stochastic (or uncertain) constraint in their reliability measures. The class is comprehensive and includes existing failure time (FT) models (such as log-normal, log-Cauchy, and log-logistic FT models) as well as new models that are robust in terms of heavy-tailed FT observations. Since classical frequency approaches to reliability analysis based on the SMLNFT model with stochastic constraint are intractable, the Bayesian method is pursued utilizing a Markov chain Monte Carlo (MCMC) sampling based approach. This paper introduces a two-stage maximum entropy (MaxEnt) prior, which elicits a priori uncertain constraint and develops Bayesian hierarchical SMLNFT model by using the prior. The paper also proposes an MCMC method for Bayesian inference in the SMLNFT model reliability and calls attention to properties of the MaxEnt prior that are useful for method development. Finally, two data sets are used to illustrate how the proposed methodology works. View Full-Text
Keywords: Bayesian reliability analysis; Bayesian hierarchical model; MCMC method; scale mixtures of log-normal failure time model; stochastic constraint; two-stage MaxEnt prior Bayesian reliability analysis; Bayesian hierarchical model; MCMC method; scale mixtures of log-normal failure time model; stochastic constraint; two-stage MaxEnt prior
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Kim, H.-J. Bayesian Hierarchical Scale Mixtures of Log-Normal Models for Inference in Reliability with Stochastic Constraint. Entropy 2017, 19, 274.

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