Availability analysis of systems using random set theory

Abstract

In this paper, we introduce the use of random set theory for availability assessment of systems with rare failure events. Instead of using failure probabilities calculated directly from each component's observation, we propose to construct pseudo-system observations directly from components observations. We then applied operations defined in the random set framework (expectations, confidence intervals, etc.) to obtain upper and lower bounds and confidence intervals of system availability without assuming any prior distribution about failures of the system components. Finally, a case study is used to prove the efficiency of the proposed method and a comparison with imprecise probability approach based on Monte-Carlo simulations is also done.