Estimation of Imprecise Reliability of Systems Using Random Sets and Monte Carlo Resampling Procedures

摘要

This paper is divided into three parts. First, it introduces the use of random sets for reliability assessment of components with rare failure events. The proposed approach is based on the use of operations defined in the random set framework (expectations, confidence intervals, etc.) to obtain upper and lower bounds and confidence intervals of components reliability without assuming any prior distribution about their lifetimes. Then, instead of using failure probabilities calculated directly from each component’s observation in order to obtain system reliability, we propose to construct pseudo-system observations directly from components observations in order to obtain the interval system reliability. Finally, the proposed approach is applied on the evaluation of reliability of large-scale systems with very large fault trees and censored reliability data by using Monte Carlo resampling procedure. A comparison with classical probabilistic approaches is also done.