Reliability optimization of series–parallel systems with mixed redundancy strategy in subsystems

Traditionally in redundancy allocation problem (RAP), it is assumed that the redundant components are used based on a predefined active or standby strategies. Recently, some studies consider the situation that both active and standby strategies can be used in a specific system. However, these researches assume that the redundancy strategy for each subsystem can be either active or standby and determine the best strategy for these subsystems by using a proper mathematical model. As an extension to this assumption, a novel strategy, that is a combination of traditional active and standby strategies, is introduced. The new strategy is called mixed strategy which uses both active and cold-standby strategies in one subsystem simultaneously. Therefore, the problem is to determine the component type, redundancy level, number of active and cold-standby units for each subsystem in order to maximize the system reliability. To have a more practical model, the problem is formulated with imperfect switching of cold-standby redundant components and k-Erlang time-to-failure (TTF) distribution. As the optimization of RAP belongs to NP-hard class of problems, a genetic algorithm (GA) is developed. The new strategy and proposed GA are implemented on a well-known test problem in the literature which leads to interesting results.