A revisit to two-component series and parallel systems with general standby redundancies

Abstract.: This note is devoted to a further study on series and parallel systems with general standby redundancies. We build a lower bound on the ratio of distribution functions for two parallel systems with a single redundancy, and, for the series system with two redundancies, we develop the usual stochastic order on their lifetimes under different allocating policies. The present results serve as either an improvement or a supplement to those ones in the literature. Some numerical examples are utilized to illustrate the new results as well.