Stochastic order inequalities for systems with standby units and parallel-series configurations

In this paper, we first consider stochastic orderings of lifetimes of series and parallel systems with cold standby units. The strategy is to find out whether the reliability of a series or parallel system improves when standby units are installed on the components or on the subsystem. We also study stochastic orderings between parallel-series systems and series-parallel systems with independent, non-identical component lifetimes. The results are applied to a set of lifetimes of electrical devices to investigate and illustrate the ordering properties.