Waiting time distribution for an exchangeable item repair system with two failed components

Models involving exchangeable component repair systems are widely treated in the literature. In such systems, a customer arrives at a repair queue with a failed component which is replaced from stocks of previously repaired components. Various strategies and service measures have been discussed. Customers who arrive with a single failed component type will be referred to the appropriate service queue which will exchange the failed component. The waiting time distribution for a single failed component has also been developed. The development of the waiting time distribution for a single queue servicing multiple component failures has been neglected. There are many instances where two distinct components are linked so that one failure will cause the failure of the second. Finding the waiting time distribution for the customer is important because it can lead to better facility planning and realistic service measures. For example, how many extra spares should be in the system so as to limit the probability of waiting more than an acceptable amount of time (the window fill rate). We limit our development to the case of two failed components; however, the ideas developed may be extendable to more than just two failed component.