A set-theoretic method for parametric uncertainty analysis in markov reliability and reward models

Sairaj V. Dhople, Yu Christine Chen, Alejandro D. Domínguez-García

Research output: Contribution to journalArticlepeer-review


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 that upper bounds this set, and hence contains all possible values that the parameters can take. This ellipsoid is then propagated via set operations through a second-order Taylor series expansion of the Markov chain stationary distribution, resulting in a set that provides approximate bounds on reliability and performability indices of interest. Case studies pertaining to a two-component shared load system with common-cause failures, and preventative maintenance of an electric-power distribution transformer, are presented.

Original languageEnglish (US)
Article number6552225
Pages (from-to)658-669
Number of pages12
JournalIEEE Transactions on Reliability
Issue number3
StatePublished - 2013


  • Markov reliability models
  • Markov reward models
  • parametric uncertainty
  • unknown-but-bounded uncertainty models

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Electrical and Electronic Engineering


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