Periodic and Sequential Imperfect Preventive Maintenance Policies for Cumulative Damage Models

Abstract

This chapter applies periodic and sequential preventive maintenance (PM) policies to cumulative damage models where the total damage is additive. First, the PM is done at periodic times kT (k=1, 2,...) and an amount of damage incurred for each periodic interval has an identical distribution. A unit fails when the total damage has exceeded a failure level K. The PM reduces the total damage according to its improvement factor. Two replacement policies, where a unit is replaced at time nT and when the total damage has exceeded a managerial level Z are considered. An example is shown when an amount of damage is distributed exponentially. Next, the PM is done at sequential times T _k (k=1, 2,...): Shocks occur in a 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 expected cost rate until replacement is derived when p(x) is exponential. Optimal PM times that minimize the expected cost rates are numerically computed for an infinite time and a finite time intervals, by solving simultaneous equations.