Stochastic comparisons of residual lifetimes and inactivity times of coherent systems with dependent identically distributed components

In this paper we compare the residual lifetime of a used coherent system of age t>0 with the lifetime of the similar coherent system made up of used components of age t. Here ‘similar’ means that the system has the same structure and the component lifetimes have the same dependence (joint reliability copula). Some comparison results are obtained for the likelihood ratio order, failure rate order, reversed failure rate order and the usual stochastic order. Similar results are reported for comparing inactivity time of a coherent system with lifetime of similar coherent system having component lifetimes same as inactivity times of failed components.