Monte Carlo simulation of Markov unreliability models

E. E. Lewis*, Franz Böhm

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

119 Scopus citations


A Monte Carlo method is formulated for the evaluation of the unrealibility of complex systems with known component failure and repair rates. The formulation is in terms of a Markov process allowing dependencies between components to be modeled and computational efficiencies to be achieved in the Monte Carlo simulation. Two variance reduction techniques, forced transition and failure biasing, are employed to increase computational efficiency of the random walk procedure. For an example problem these result in improved computational efficiency by more than three orders of magnitudes over analog Monte Carlo. The method is generalized to treat problems with distributed failure and repair rate data, and a batching technique is introduced and shown to result in substantial increases in computational efficiency for an example problem. A method for separating the variance due to the data uncertainty from that due to the finite number of random walks is presented.

Original languageEnglish (US)
Pages (from-to)49-62
Number of pages14
JournalNuclear Engineering and Design
Issue number1
StatePublished - Jan 1984

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Nuclear Energy and Engineering
  • Materials Science(all)
  • Safety, Risk, Reliability and Quality
  • Waste Management and Disposal
  • Mechanical Engineering


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