General trigger‐off replacement procedures for two‐unit systems

A trigger‐off replacement policy, suggested and analyzed in [1], for two‐unit systems composed of identical units, is generalized and extended in this work in several ways. In the first part of the paper we obtain the appropriate integral equations for nonidentical units and then use them for a complete solution of the case of two units, whose lifetimes are distributed according to general Erlang distributions. In the second part of the paper we extend the trigger‐off policy itself by allowing preventive replacements of units which reach a certain critical age. The system stops working if either one of the two units fails or reaches its critical age. Both cases present natural replacement possibilities for the remaining unit, provided that its age exceeds a predetermined critical age. Finally, we consider the question of which policy parameters, i.e. control limits and critical ages, to choose when facing a real‐life situation. Using the criterion of expected costs per unit time in the long run, we show how to find the optimal parameters which minimize this objective function. The fact that a restricted optimization, within the class of trigger‐off replacement policies, leads to the global optimal policy has been proved in [2] by a different approach.