An age replacement policy with minimal repair and general random repair cost

An age replacement policy is introduced which incorporates minimal repair, replacement, and general random repair costs. If an operating unit fails at age y<T, it is either replaced by a new unit with probability p(y) at a cost c₀, or it undergoes minimal repair with probability q(y) = 1−p(y). Otherwise, a unit is replaced when it fails for the first time after age T. The cost of the i-th minimal repair of an unit at age y depends on the random part C(y) and the deterministic part c_i(y). The aim of the paper is to find the optimal T which minimizes the long run expected cost per unit time of the policy. Various special cases are considered.