Some new results on redundancy allocation in series systems

This paper studies the problems of optimally allocating one/two active redundancies to series systems in the sense of stochastic orders. For the case of allocating one redundancy to a series system, we show that allocating the redundancy to the weaker component can lead a longer system’s lifetime in the sense of the hazard rate and reversed hazard rate orders. For two redundancies case, we also demonstrate that allocating the relatively stronger redundancy to the weaker component can lead a longer system’s lifetime in the sense of the hazard rate and reversed hazard rate orders. These results generalize and strengthen the results of several papers. Finally, two applications are also presented to illustrate our results.