Optimal Repair of a 2-Component Series-System with Partially Repairable Components

A 2-component series system is maintained by one repairman. The up-times of the components are s-independent r.v.´s with exponential distributions. The time required to repair a failed component is the sum of a number of s-independent, exponential r.v.´s. Components can be partially repaired, and a working component can fail even while the system as a whole is not functioning. The analysis finds repairman allocation policies which maximize the system availability. Under the assumption that it is permissible to reassign the repairman instantaneously among failed components, the explicit form of optimal policies is obtained. And, the optimal policies are characterized when the time for such a reassignment is allowed to be an exponential r.v.