2013
DOI: 10.1109/tr.2013.2270421
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A Set-Theoretic Method for Parametric Uncertainty Analysis in Markov Reliability and Reward Models

Abstract: This paper proposes a set-theoretic method to capture the effect of parametric uncertainty in reliability and performability indices obtained from Markov reliability and reward models. We assume that model parameters, i.e., component failure and repair rates, are not perfectly known, except for upper and lower bounds obtained from engineering judgment or field data. Thus, the values that these parameters can take are constrained to lie within a set. In our method, we first construct a minimum volume ellipsoid … Show more

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Cited by 18 publications
(6 citation statements)
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“…denotes the first order partial derivative w.r.t. p R [33]. The same result applies for the k-th order derivative w.r.t.…”
Section: ) Large Deviations Principle (Ldp) For the Asymptotic Missesupporting
confidence: 52%
“…denotes the first order partial derivative w.r.t. p R [33]. The same result applies for the k-th order derivative w.r.t.…”
Section: ) Large Deviations Principle (Ldp) For the Asymptotic Missesupporting
confidence: 52%
“…For example [63] used statistical estimates of failure probability and the expected economic impact of failures in multi‐objective optimization, simultaneously minimising the maintenance costs and the predicted cost of unexpected failures to form an integrated framework of transformer maintenance management. In [64], Markov reliability and reward models are used to perform component failure and repair rates and follow the effect of parametric uncertainty in reliability and performability indices and the proposed method applied on sample system to apply preventative maintenance of an electric‐power distribution transformer. Paper [65] determines the optimum maintenance strategy and optimum power flow control based on condition monitoring and diagnostic results of the operating power apparatus.…”
Section: Components Of Distribution Systemsmentioning
confidence: 99%
“…In the case of power systems described by nonlinear differential algebraic equations (DAEs), reachability analysis is often limited to small 1-2 bus systems [48]. For larger power systems, the reachable set can be efficiently approximated by ellipsoidal techniques for linearized system models [49,50] and second-order Taylor-series approximations [51].…”
Section: ______________________________________________________________________________________________________mentioning
confidence: 99%