General standby allocation in series and parallel systems

Stochastic orders are very useful tools to compare the lifetimes of two systems. Optimum lifetime of a series (resp. parallel) system with general standby component(s) depends on the allocation strategy of standby component(s) into the system. Here, we discuss three different models of one or more standby components. In each model, we compare different series (resp. parallel) systems (which are formed through different allocation strategies of standby component(s)) with respect to the usual stochastic order and the stochastic precedence order. The results related to the cold as well as the hot standby models are obtained as particular cases of the results discussed in this article because the model considered here is a general one.