A system model with interacting components:renewal type results

We consider a k-component system where the failure rates of the components interact, but where interaction depends only on the current ages of the components. We first formalize the concept of interaction and show that the k-variant age process can be defined as a MARKOV process on , and that it has the strong MARKOV property. Under simple conditions on the failure rates, we then show this process to be positively recurrent, and that the time-dependent distributions of the process converge exponentially quickly to a stationary distribution π further π admits a finite moment-generating function. These results are used to study the limiting behaviour of the residual lifetimes of the system. Finally, we link our analysis with the results of Franken and Streller (1980) obtained for stationary processes.