A New Recursive Formulation for the Mixed Redundancy Strategy in Reliability Optimization Problems

One of the common approaches for improving the reliability of a specific system is to use parallel redundant components in subsystems. This approach, which is known as the redundancy allocation problem (RAP), includes the simultaneous selection of the component type and its level for each subsystem in order to maximize the system reliability.Traditionally, there are two redundancy strategies, namely active and standby, for the redundant components. Recently, a new powerful strategy called mixed strategy has been developed. It has been proved that the mixed strategy has a better performance when compared to both previous strategies. The main issue in utilizing the mixed strategy is its complicated formulation and sophisticated calculations, leading to a time-consuming procedure for solving the problems. Hence, in this paper, a new formulation based on the recursive approach is introduced to ease the calculation of the mixed strategy. In the new formulation, the complex double integral calculations are removed and the calculation times is reduced. The proposed recursive formulation provides a general statement for the mixed strategy formula which is not changed by altering the number of components in each subsystem. This flexibility and stability in the formula can be very important, especially for large scale cases. In order to evaluate the new approach and to compare its performances with the previous formulation, a benchmark problem with 14 subsystems is considered and the results of the two formulation are compared with each other.