Application of Bayesian Methods for Age‐Dependent Reliability Analysis

Abstract

In this article, the authors present a general methodology for age‐dependent reliability analysis of degrading or ageing components, structures and systems. The methodology is based on Bayesian methods and inference—its ability to incorporate prior information and on ideas that ageing can be thought of as age‐dependent change of beliefs about reliability parameters (mainly failure rate), when change of belief occurs not only because new failure data or other information becomes available with time but also because it continuously changes due to the flow of time and the evolution of beliefs. The main objective of this article is to present a clear way of how practitioners can apply Bayesian methods to deal with risk and reliability analysis considering ageing phenomena. The methodology describes step‐by‐step failure rate analysis of ageing components: from the Bayesian model building to its verification and generalization with Bayesian model averaging, which as the authors suggest in this article, could serve as an alternative for various goodness‐of‐fit assessment tools and as a universal tool to cope with various sources of uncertainty. The proposed methodology is able to deal with sparse and rare failure events, as is the case in electrical components, piping systems and various other systems with high reliability. In a case study of electrical instrumentation and control components, the proposed methodology was applied to analyse age‐dependent failure rates together with the treatment of uncertainty due to age‐dependent model selection. Copyright © 2013 John Wiley & Sons, Ltd.

Bayesian estimation for a mortality model via the aging process

“…Then by the Remark 2.1 (2) q i (T ) = P(τ i ≤ T ) = 1 − e i exp (T Q)e, since τ i ∼ P H(e i , Q), where τ i is the random variable that models the time until the death for a person at physiological age i. Now, in order to calculate the death probability (2), we need to estimate the phase-type parameters.…”

“…Bayesian methods also deal with risk and reliability analysis considering the aging phenomena. In [2], the authors presented a general methodology for age-dependent reliability analysis of degrading or aging systems.…”

“…Figure 2 shows these estimates including the confidence intervals at 95% level of significance of the GS estimates. We can calculate the Mean Squared Error for both estimations: MSE(θ) = E(θ − θ) 2 . We obtain…”

A Bayesian model averaging method for software reliability modeling and assessment

“…Firstly, the prior probability of models and the prior distribution of model parameters are specified. Most of the research on Bayesian methods is related to the prior distribution, which represents the uncertainty that exists before the observed data 38 . We assume that the models’ prior probabilities are the situations with a lack of prior information, namely $$\pi ({M}_{GO}) = \pi ({M}_{GG}) = \pi ({M}_{Duane}) = 1/3$$.…”

Reliability assessment of complex electromechanical systems: A network perspective

“…The assumptions the assumptions of above approaches may not conform to most real-life systems. 11 Dynamic models: Markov model 12,13 ; dynamic fault tree [14][15][16] ; Petri net 17,18 ; Bayesian network 6,19,20 ; multivalued decision diagram 21,22 ; universal generating functions [23][24][25] ; and stochastic process approach 26,27 The problem of combinatorial explosion is intractable. Some of them have been criticized for the high computational complexity.…”