Asymptotic distribution of some multivariate “success run” renewal processes,applied to a 2-i.i.d. unit repairable system

If the probability of “failure” in a multivariate renewal process of the “success run” type is very small, then if certain conditions are imposed on the components of the renewals, the joint distribution of their total durations is approximately exponential with all mass along one line. This result is applied to a 2-i.i.d. unit repairable system of the “1 out of 2:G, Cold Standby” type.