Multi-level redundancy optimization in series systems

Single-level systems have been considered in redundancy allocation problems. It may be the best policy in some specific situations, but not in general. In regards to reliability, it is most effective to duplicate the lowest objects, because parallel-series systems are more reliable than series-parallel systems. However, the smaller an object is, the more time and higher accuracy are needed for duplicating it, and so, redundancy cost can be decreased by using modular redundancy. Therefore, providing redundancy at high levels such as modules or subsystems, can be more economical than providing redundancy at low level of components. In this paper, the problem in which redundancy is available at all levels in a series system is addressed and a mixed integer programming model is presented. A heuristic algorithm and a genetic algorithm are proposed to solve the problem and some examples illustrate the procedure.