An improved algorithm for symbolic reliability analysis

The authors describe an efficient Boolean algebraic algorithm to compute the probability of a union of nondisjoint sets as applied to symbolic reliability analysis. Coherent networks and fault-trees with statistically-independent components characterized by their minimal pathsets or cutsets are used as examples for generating the nondisjoint sets. The algorithm uses the concept of multiple variable inversion originally proposed by A. Grnarov et al. (1979). The authors illustrate improvements in the use of the 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). 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