Computing the reliability of mixed uncertain random [formula omitted]-out-of-[formula omitted] systems with multiple possible states

Abstract

This paper presents an uncertain random multi-state k-out-of-n system (urm-k-out-of-n system, for short), where both random components and uncertain components coexist. States of the system and components display multiplicity and are defined as uncertain random variables. Since reliability is a crucial index to reflect system performance, this paper proves some formulas to calculate the reliability of urm-k-out-of-n systems in accordance with chance theory, which have two special cases, random systems and uncertain systems. Later, a mixed algorithm for multi-valued decision diagram (MDD) and binary search is designed to assess the reliability index. Compared to the general algorithm, it operates in significantly less time when the system becomes complex.