A bi-objective model for reliability analysis of a multi-state system with performance sharing mechanism

This study seeks to strike an equilibrium between system reliability and cost in a multi-state series-parallel structure by exploiting the performance sharing capacity in order to establish a tradeoff among redundancy levels in the relevant subsystems. To meet fixed demands on subsystems, the model opts for proper combinations of components in each subsystem and the deployment of proper transmitters to connect them. The assumptions made include a multi-state mode for all the components and transmitters, an unsatisfied demand leading to system failure, and the possibility for subsystems to share performance with adjacent ones directly through mediating transmitters. System reliability is computed using an efficient algorithm based on the universal generating function that has proved useful for analyzing multi-state systems. Moreover, a Non-dominating Sorting Genetic Algorithm (NSGA-II) is employed to find the Pareto frontier of the best solutions from the cheapest structure with the minimum reliability to one with the highest reliability and maximum cost. Finally, a numerical example is provided to illustrate the application of the proposed algorithm.