On the optimal allocation of two active redundancies in a two-component series system

Components C1C1 and C2C2 form a series system. Suppose we can allocate the spare R1R1 in parallel with C1C1 and the spare R2R2 in parallel with C2C2, or otherwise, allocate R1R1 with C2C2 and R2R2 with C1C1. In this paper, we compare these two options using hazard rate ordering.