An Improved Algorithm for Symbolic Reliability Analysis

The purpose of this paper is to describe an efficient Boolean algebraic algorithm to compute the probability of a union of non-disjoint sets as applied to symbolic reliability analysis. Coherent networks and fault-trees with statisticallyindependent components characterized by their minimal pathsets or cutsets are used as examples for generating the non-disjoint sets. The algorithm uses the concept of multiple variable inversion originally proposed by Grnarov, Meinrock, Gerla (1979). We fwst present our algorithm. Next, we illustrate our improvements in the use of multiple variable inversion technique for this problem using two examples. The algorithm is extended to compute the reliability importance of a given component (sensitivity of system reliability to the component reliability). Finally, a computer program implementing the modified algorithm is used to solve and obtain measured time complexities for a large set of network and fault tree models.