An efficient disjoint product algorithm for assessing the reliability bounds of a complex system’s lifetimes

A critical aspect of reliability analysis is selecting an appropriate structure-function to describe system behavior. Existing methods rely on identifying minimal path sets (MPSs) and minimal cut sets (MCSs) to model the reliability bounds of two-terminal systems. Accurate reliability bounds are crucial for analyzing critical system states. This article introduces a new algorithm that solves the sum of disjoint products (SDP) problem using a multivariable inversion technique to directly transform the structure-function into a simplified disjoint reliability expression. The proposed method combines two matrix-based algorithms that use the system graph's connection and adjacency matrices to efficiently find MPSs and cut MCSs. The primary objective is to determine accurate lower and upper reliability bounds for complex communication networks, including bridge and double-bridge types. The algorithms were implemented in Mathematica 13 and tested on 14 benchmark systems, demonstrating high accuracy and computational efficiency.