Reliability analysis of multi-state series systems with k-out-of-n: G subsystems considering performance sharing

Abstract

Motivated by real-world engineering systems, this paper presents an in-depth exploration of a novel reliability model for a complex multi-state series system (MSSS) that incorporates a performance sharing mechanism. Specifically, the MSSS is composed of m distinct subsystems featuring a k-out-of-n: G structure. The ith subsystem consists of ni elements, such that a minimum of ki functioning elements is required for normal operation. Transmission devices (TDs) are present between adjacent subsystems to share surplus performance. Both element performance and subsystem demand are treated as random variables, and the performance of all elements in each subsystem is cumulated to meet its individual random demand. Subsystem failure can result from either an inability to meet performance demands or an insufficient number of functioning elements. The surplus performance of a subsystem can only be transferred to its adjacent subsystem via the TD. The entire MSSS will fail if at least one subsystem does not work properly by using performance sharing mechanism. To analyze the reliability indexes of the MSSS, a new algorithm based on the generalized universal generating function (GUGF) has been developed. Numerical examples are provided to illustrate the accuracy and effectiveness of the proposed model and method.