An efficient method for the estimation of parameters of stochastic gamma process from noisy degradation measurements

Abstract

The stochastic gamma process model is widely used in modeling a variety of degradation phenomena in engineering structures and components. If degradation in a component population can be accurately measured over time, the statistical estimation of gamma process parameters is a relatively straight-forward task. However, in most practical situations, degradation data are collected through in-service and non-destructive inspection methods, which invariably contaminate the data by adding random noises (or sizing errors) to the data. Therefore, a proper estimation method is needed to filter out the effect of sizing errors from the measured degradation data. This article presents an efficient method for estimating the parameters of the gamma process model based on a novel use of the Genz transform and quasi-Monte Carlo method in the maximum likelihood estimation. Examples presented show that the proposed method is very efficient compared with the Monte Carlo method currently used for this purpose in the literature.