Optimal element allocation and sequencing of multi-state series systems with two levels of performance sharing

Abstract

Motivated by real-world complex engineering systems, this research proposes a multi-state system with two levels of performance sharing. In this system, there exists a unique performance transmitter between any two adjacent subsystems and any two adjacent elements within each subsystem. Surplus performance of a subsystem or an element can only be transmitted to its adjacent subsystems or elements. We build the reliability model of the proposed system and suggest a corresponding reliability evaluation algorithm by extending the existing universal generating function technique. Since the performance sharing is only allowed between adjacent subsystems and elements, the element allocation and sequencing will affect the system reliability. Due to the complexity of the combinatorial optimization problem, we use the genetic algorithm to find the optimal allocation and sequencing of the elements. An analytical example is provided to illustrate the reliability evaluation algorithm. Numerical experiments are carried out to demonstrate how the optimal allocation and sequencing as well as the capacities of the performance transmitters affect the system reliability.