Combining discrete-time Markov processes and probabilistic fracture mechanics in RI-ISI risk estimates

Cronvall, Otso; Männistö, Ilkka

doi:10.1016/j.ijpvp.2009.07.004

Cited by 4 publications

(1 citation statement)

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“…To start with, the applications of Markov models in engineering practice are numerous. In reliability engineering and safety analysis, discrete Markov schemes, the states of which correspond to gradually degraded operating conditions, have for instance been used to assess the reliability of programmable electronic systems (Bukowski and Globe, 1995), cogeneration plants (El-Nashar, 2008), machineries of oil refineries (Cochran et al, 2001), water meters (Pasanisi and Parent, 2004), piping systems of power plants (Cronvall and Männistö, 2009) and welded structures submitted to fatigue damage (Lassen, 1991). In this paper, the example treated in Section 2.5 provides a real industrial use-case where a Markov model is used to assess the reliability of rotating machines.…”

Section: Introductionmentioning

confidence: 99%

Estimating discrete Markov models from various incomplete data schemes

Pasanisi¹,

Fu²,

Bousquet³

2012

Computational Statistics & Data Analysis

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The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a case, the estimation of transition probabilities is straightforwardly made by counting one-step moves from a given state to another. In many real-life problems, however, the inference is much more difficult as state sequences are not fully observed, namely the state of each individual is known only for some given values of the time variable. A review of the problem is given, focusing on Monte Carlo Markov Chain (MCMC) algorithms to perform Bayesian inference and evaluate posterior distributions of the transition probabilities in this missing-data framework. Leaning on the dependence between the rows of the transition matrix, an adaptive MCMC mechanism accelerating the classical Metropolis-Hastings algorithm is then proposed and empirically studied.

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