Bayes Analysis and Comparison of Accelerated Weibull and Accelerated Birnbaum-Saunders Models

• Published in: Communications in statistics. Theory and methods Vol. 39; no. 2; pp. 195 - 213
• Main Authors: Upadhyay, S. K., Mukherjee, Bhaswati
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 01.01.2010; Taylor & Francis; Taylor & Francis Ltd
• Subjects: Accelerated testing; Bayesian analysis; BIC; Birnbaum-Saunders model; DIC; Distribution theory; Exact sciences and technology; Fractional Bayes Factor; General topics; Gibbs sampler; Hybrid strategy; Markov analysis; Markov processes; Mathematics; Metropolis algorithm; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Predictive simulation; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Statistics; Weibull model; Statistical distribution; Bayes model; Prediction theory; Birnbaum-Saunders model; Stochastic method; Statistical simulation; Markov chain; Statistical test; Predictive simulation; Approximation theory; Weibull distribution; BIC; Posterior distribution; Hybrid strategy; DIC; Bayes estimation; Accelerated testing; Metropolis algorithm; Monte Carlo method; Bayes factor; Weibull model; Gibbs sampling; Statistical method; Gibbs sampler; Numerical analysis; Mechanical stress; Fractional Bayes Factor
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610920802663323

Several models are proposed in the literature for modeling fatigue data resulting from materials subject to cyclic stress and strain. Accelerated Weibull and accelerated Birnbaum-Saunders distributions are most commonly used models. Whereas the accelerated Weibull model is easier compared to accelerated Birnbaum-Saunders, it fails to represent the situation equally well. The present article focuses on Bayes analysis of the two models and provides a comparison based on some important Bayesian tools. Model compatibility study using predictive simulation ideas is preceded by the said comparison. Throughout, the posterior simulations are carried out by Markov chain Monte Carlo procedure.