Asymptotic replacement and preventive maintenance policies

This paper proposes asymptotic maintenance models by using the hazard rate function, i.e., the expected number of failures in the time interval, when the failure time has a Weibull distribution. First, when failures occur at a nonhomogeneous Poisson process, the mean times between failures are given by a simple equation. The expected cost rate and optimal replacement time for the age replacement policy are also given by simple equations. Both periodic replacements at time and number of failures are shown to be a simple identical equation. Finally, an optimal imperfect preventive policy is derived easily and simply. It is shown numerically that such asymptotic policies for four models have good approximations to the standard ones.