Optimal series–parallel topology of multi-state system with two failure modes

When considering systems built from units with two failure modes, changes in system topology that increases system reliability in open mode can decrease system reliability in closed mode and vice versa. For the given set of units composing a system there always exists a configuration which provides maximal reliability for the system experiencing both failure modes. In this paper, we suggest an algorithm for finding optimal series–parallel topology (configuration) for systems consisting of units characterized by different reliability and nominal performance rates. Such systems are multi-state because they can have different levels of output performance depending on the combination of units available at the moment. Reliability is defined as the probability of satisfaction of given constraints imposed on system performance in both modes. The procedure developed to solve this problem is based on the use of a universal moment generating function (UMGF) for the fast evaluation of multi-state system reliability and a genetic algorithm (GA) for optimization. Basic UMGF technique operators are developed for two different types of systems based, respectively, on transmitting capacity and processing time. Solution encoding for GA implementation is developed and basic GA procedures and parameters are chosen for the given problem. Examples of the optimization of series–parallel configurations for systems of both types are presented.