An efficient multi-variable inversion algorithm for reliability evaluation of complex systems using path sets

Abstract

Reliability evaluation of a large and complex system is quite an involved and time-consuming process and its state-of-art is far from being called as satisfactory. This is mainly due to the fact that unionizing path sets results in large number of terms in the reliability expression. Thereafter, the process of computing numerical value of system reliability from its expression is a task not free from the build up of round-off errors. The entire process also restricts the use of a low-end PC for computing system reliability of such systems. In this paper, we propose an efficient methodology to evaluate reliability of large and complex systems based on minimal path sets; the path sets enumeration procedure used in this paper generates path sets in lexicographic and increasing order of cardinality -a condition, which is helpful in obtaining sum of disjoint products (SDP) of the system reliability expression in a compact form. Although we make use of the system connection matrix but no complicated matrix operations are performed to obtain the results. The paper further presents an improved multi-variable inversion (MVI) algorithm to evaluate system reliability in a compact form. Our approach offers an extensive reduction in the number of mutually disjoint terms and provides a minimized and compact system reliability expression. The procedure not only results in substantial saving of CPU time but also can be run on a low-end PC. To demonstrate this capability, we solve several problems of varied complexities on a low-end PC and also provide a comparison of our approach with earlier techniques available for the purpose.