Interval-Valued Reliability Analysis of Multi-State Systems

In previous studies that analyzed the reliability of multi-state systems, the precise values of the state performance levels and state probabilities of multi-state components were required. In many cases, however, there are insufficient data to obtain the state probabilities of components precisely. A method is proposed in this paper to analyze the reliability of multi-state systems when the available data of components are insufficient. Based on the Bayesian approach and the imprecise Dirichlet model, the interval-valued state probabilities of components are obtained instead of precise values. The interval universal generating function is developed, and the corresponding operators are defined to estimate the interval-valued reliability of multi-state systems. Affine arithmetic is used to improve the interval-valued reliability. A numerical example illustrates the proposed method. The results show that the proposed method is efficient when state performance levels and/or state probabilities of components are uncertain and/or imprecise.