An Interval Approach for the Availability Optimization of Multi-State Systems in the Presence of Aleatory and Epistemic Uncertainties

Joanna Akrouche, Mohamed Sallak, Eric Châtelet, F-O Abdallah, H. Haj Chhadé

Research output: Contribution to journalArticlepeer-review


An essential step in the safe design of systems is choosing the system configuration that will maximize the overall availability of the system and minimize its overall cost. The main objective of this paper is to propose an optimization method of multistate system availability in the presence of both aleatory and epistemic uncertainties, to choose the best configuration for the system in terms of availability, cost, and imprecision. The problem is formulated as follows: let us consider several configurations of a system, with each configuration consisting of components with different working states, and imprecise failure and repair rates provided in the form of intervals. The aim is to find the best configuration regarding the system’s imprecise availability, cost, and imprecision. First, the imprecise steady availability of each configuration is computed by using an original method based on Markovian approaches combined with interval contraction techniques. Then an objective function incorporating cost, the lower and upper bounds of availability, and imprecision is defined and computed to provide the best configuration. To illustrate the proposed method, a use case is discussed.

Original languageEnglish
Article number021202
Number of pages11
JournalASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering
Issue number2
Publication statusPublished - Jun 2022


  • Imprecise availability
  • Imprecise Markov chain
  • Multi-state system
  • Safe design
  • Technique of contraction

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