Optimal allocation and maintenance of multi-state elements in series–parallel systems with common bus performance sharing

•A new series–parallel system with common bus performance sharing is proposed.•A reliability evaluation algorithm is suggested.•Both preventive replacement and minimal repair are considered.•Multi-state elements allocation and maintenance are considered simultaneously.•Genetic algorithm is explored to solve the optimization problem.

This article considers the optimal allocation and maintenance of multi-state elements in series–parallel systems with common bus performance sharing. The surplus performance from a sub-system can be transmitted to any other sub-system which is experiencing performance deficiency. The amount that can be transmitted is subjected to a random transmission capacity. In order to increase the system availability, maintenance actions can be performed during the system lifetime and the system elements can be optimally allocated into the sub-systems. In this paper, we consider the element allocation and maintenance simultaneously in order to minimize the total maintenance cost subject to the pre-specified system availability requirement. An algorithm based on universal generating function is suggested to evaluate the system availability and the genetic algorithm is explored to solve the optimization problem. Numerical experiments are presented to illustrate the applications.