A Minimizing Algorithm for Sum of Disjoint Products

Abstract

This paper describes a minimizing version of the Abraham sum-of-disjoint products (sdp) algorithm, called the Abraham-Locks-Revised (ALR) method, as an improved technique for obtaining a disjoint system-reliability formula. The principal changes are: 1) Boolean minimization and rapid inversion are substituted for time-consuming search operations of the inner loop. 2) Paths and terms are ordered both according to size and alphanumerically. ALR reduces the computing cost and data processing effort required to generate the disjoint system formula compared to the seminal 1979 Abraham paper, and obtains a shorter formula than any other known sdp method. Very substantial savings are achieved in processing large paths of complex networks.