General analysis of systems in which a 2-unit system is a sub-system

In this paper we consider a system which has three subsystems A, B and C. A and B are one unit systems and two unit systems respectively, and C is exposed to a damage process. The units of B have exponential life times. In model 1, A has a general life time and the damage process of C is Poisson and in model 2, A has an exponential life time and C is exposed to a renewal damage process. Introducing a repair facility which repairs all the failures one by one, this paper presents the joint Laplace-Stieltjes transforms of the ur> and down times. Marginal down time distributions an- calculated whon there exists a repair facility vor every damage.