Predicting distribution of time to degradation limit using a weighted approach

One of the key elements in condition-based maintenance is to predict the distribution of time to a pre-specified degradation limit based on the observed degradation paths. The prediction accuracy strongly depends on the method to fit the observed degradation paths to a mean degradation model. Since the recent observations contain more information about the future degradation trend than the earlier observations, a weight function can be used to represent the importance of an observation. As such, the prediction accuracy can be improved through using a weighted parameter estimation method. A key issue with the weighted method is to appropriately specify the form of the weight function and its parameters. This paper aims to address this issue. We adopt the Gaussian kernel function with parameters mu and sigma as the weight function. The mu is set at the last observation time and the value of sigma is optimally determined using a cross-validation approach. The appropriateness and usefulness of the proposed approach are illustrated by a real-world example.