Overhaul decision of repairable systems based on the power-law model fitted by a weighted least squares method

Abstract

The power law model has been widely used to analyze failure data from repairable systems and to optimize overhaul decision. However, it is not applicable for the situations where the empirical mean cumulative function displays complex shapes. It is noted that the failure observations in wear-out phase have larger influence on overhaul decision than the failure observations in early and normal use phases. This implies that the observations in different phases have different importance and the power-law model may be still appropriate for the overhaul decision optimization as long as the fitted model is mainly based on the observations in the wear-out phase. In this paper, we use a simple weight function, which is proportional to the normal density function, to reflect the importance of failure observations at different times. We propose a heuristic method to determine the parameters of the weight function so that it can appropriately stress the recent observations. The observed data are fitted to the power-law model using a weighted least squares method, and the fitted model is then used to optimize the overhaul decisions for the population and individual systems, respectively. The appropriateness of the proposed approach is illustrated by a real-world example.