Imperfect preventive maintenance policies for a cumulative damage model

This paper applies a sequential preventive maintenance (PM) Policy to a cumulative damage model where each PM is imperfect: Shocks occur at Poisson process and a unit fails with probability p(x) when the total damage is x. If a unit fails, it undergoes a minimal repair. The PM is done at fixed intervals T-k (k = 1, 2,..., n), and reduces the total damage according to its improvement factor a(k). The expected cost rate until replacement is derived when p(x) is exponential. Optimal PM times which minimize the expected cost rates are numerically computed for an infinite time and a finite time intervals, by solving simultaneous equations.