series-parallel systems

This paper develops an efficient non-dominated sorting genetic algorithm (NSGA-II) to solve the redundancy allocation problem (RAP) of series-parallel systems. The system consists of subsystem in series, where components are used in parallel for each subsystem. Both the system and its subsystems can only take two states of complete perfect and complete failure. Identical redundant components are included to achieve a desirable reliability. The components of each subsystem, which are chosen from a list that is available in the market, are characterized by their cost, weight, and reliability. To find the optimum combination of the number of components for each subsystem, the mathematical formulation for the maximal reliability and minimal cost of the system configuration under cost constraint is first obtained. Then, a modified NSGA-II is proposed to solve the model. In this algorithm, a heuristic method of generating a primary solution is integrated to achieve better solutions. Moreover, design of experiment approach is employed to calibrate the parameters of the algorithm. At the end, some numerical examples are used to validate the solution, to assess the performance of the proposed methodology under different configurations, and to compare the performance with the ones of two other meta-heuristic algorithms. The results of experiments are generally in favor of the proposed solution algorithm.

In this paper, we consider series-parallel and parallel-series systems with independent subsystems consisting of dependent homogeneous components whose joint lifetimes are modeled by an Archimedean copula. Then, by considering two such systems with different numbers of components within each subsystem, we establish hazard rate and reversed hazard rate orderings between the two system lifetimes, and also discuss how these systems age relative to each other in terms of hazard rate and reversed hazard rate functions.