Monotonicity properties of residual lifetimes of parallel systems and inactivity times of series systems with heterogeneous components (Q2894057)

Consider a parallel system that has components with independent, but not necessarily identically distributed, life times. Suppose that at time \(t\) there is some partial information about the number of components that are still alive. The authors prove some results which show that the conditional life time of the system is larger, in some stochastic sense, if the known partial information corresponds to a larger number of live components at time \(t\). Some variations of this type of results are also proven for series systems. Some results about stochastic monotonicity of the system life time, with respect to the time elapsed, are given as well.