Bayesian estimation of system reliability in Brownian stress-strength models |
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Authors: | Sanjib Basu Rama T Lingham |
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Institution: | (1) Division of Statistics, Department of Mathematical Sciences, Northern Illinois University, 60115-2854 DeKalb, IL, USA |
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Abstract: | A stress-strength system fails as soon as the applied stress,X, is at least as much as the strength,Y, of the system. Stress and strength are time-varying in many real-life systems but typical statistical models for stress-strength
systems are static. In this article, the stress and strength processes are dynamically modeled as Brownian motions. The resulting
stress-strength system is then governed by a time-homogeneous Markov process with an absorption barrier at O. Conjugate as
well as non-informative priors are developed for the model parameters and Markov chain sampling methods are used for posterior
inference of the reliability of the stress-strength system. A generalization of this model is described next where the different
stress-strength systems are assumed to be exchangeable. The proposed Bayesian analyses are illustrated in two examples where
we obtain posterior estimates as well as perform model checking by cross-validation. |
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Keywords: | Cross-validation first-passage time Gibbs sampler hitting time non-informative prior prediction |
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