Abstract. Redundancy allocation problem (RAP) is a common technique for increasing the reliability of systems. In this paper, a new model for the RAP is introduced that takes into account the warm standby and mixed strategy, the model dynamics, and the type of the strategy in redundancy allocation prob- lems. A recursive formula is rst obtained for the reliability function in the dynamic warm standby and mixed redundancy strategies that leverages the success mode analysis and works for any arbitrary failure-time distribution. Failure rates for warm standby units change before and after their replacement with a damaged unit, and, therefore, the reliability function in warm standby varies with time (i.e., the model is dynamic). Although dynamic models are commonplace in practice, they are more challenging to assess than static mod- els, which have been mainly considered in the literature. An optimization problem is then formulated to select the best redundancy strategy and redun- dancy levels. Genetic algorithm and particle swarm optimization are leveraged to solve the problem. Finally, the eciency of the presented method is veried through a numerical example. The experimental results verify that the pro- posed model for RAP signicantly improves the system reliability, which can be of vital importance for system designers.

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