Comparison of Parametric Models for Estimating Maintenance Times from Small Samples

Abstract

The estimation of optimal preventive maintenance (PM) times is considered. When failure and PM cause the only costs of interest, and the steady state cost-rate is to be minimized, very small samples of times to failure can often be effectively used. In particular, with only 10 failures the mean extra cost, due to statistical uncertainty, is in many realistic cases just a small fraction of the true optimal cost. When the ratio of failure costs to PM costs is high, the gain of assuming a correct parametric model instead of an empirical one can be substantial when only a small sample is available. On the other hand, assuming a wrong parametric model can give a much higher extra cost than the empirical model. In this paper we give Monte Carlo results comparing empirical estimation with maximum likelihood estimation based on correct and wrong parametric assumptions. The study covers: three Weibull distributions, two bathtub distributions, one Gaussian distribution. Sample sizes: 10 and 50, with and without censoring. Failure cost to PM cost ratios: 4 and 50.