Application of Binary Decision Diagrams in Time-Dependent Reliability Analysis

Binary Decision Diagrams (BDDs) are often used in specific types of reliability analysis known as topological (or structure) analysis and time-independent analysis. The previous focuses only on the analysis of system topology, which is defined by structure function. The latter takes into account the structure function together with the time-independent reliabilities of components that the system is composed of. However, the most interesting type of reliability analysis is time-dependent analysis in which reliabilities of the components are time-dependent functions. In this paper, we first present the development of a mathematical model of a non-repairable system composed of independent non-repairable components and explain the properties of this model from the point of view of time-dependent, time-independent, and topological reliability analysis. In the second part of the paper, we present and experimentally compare two methods for time-dependent reliability analysis of the considered mathematical model. The first method is based on the direct application of BDDs and we label it as a basic approach. The second, symbolic approach, combines BDDs with expression trees. The experimental comparison implemented using opensource C++ libraries TeDDy and GiNaC shows that the first method based on the basic approach is much faster than the second method using expression trees.