On the phase transition of k-out-of-n systems with applications to optimal maintenance

Abstract

An effective method for improving the reliability of a technical system is to build redundancy into it. A commonly used redundancy structure in reliability engineering is the k-out-of-n structure. A k-out-of-n structure, consisting of n components, operates if and only if at least k components operate. This paper studies a high-dimension feature of k-out-of-n systems consisting of independent and identical components. This phenomenon, commonly known as a phase transition in high-dimensional probability, shows that in a system consisting of a large number of components, if the components operate independently with common reliability, then the system reliability undergoes a ‘sharp transition’. That is, in a narrow interval, the value of the system reliability rapidly declines. We first consider the systems whose components have common static reliability p∈(0,1). Then we focus on k-out-of-n systems with time-dependent reliability. As an application of the results, we employ the phase transition property to propose optimal age-based maintenance for the system. © 2023 Elsevier B.V.