Residual life estimation based on nonlinear-multivariate Wiener processes

Abstract

For some operable products with critical reliability constraints, it is important to estimate accurately their residual lives so that maintenance actions can be arranged suitably and efficiently. In the literature, most publications have dealt with this issue by only considering one-dimensional degradation data. However, this may be not reasonable in situations wherein a product may have two or more performance characteristics (PCs). In such situations, multi-dimensional degradation data should be taken into account. Here, for the target product with multivariate PCs, methods of residual life (RL) estimation are developed. This is done with the assumption that the degradation of PCs over time is governed by a multivariate Wiener process with nonlinear drifts. Both the population-based degradation information and the degradation history of the target product up-to-date are combined to estimate the RL of the product. Specifically, the population-based degradation information is first used to obtain the estimates of the unknown parameters of the model through the EM algorithm. Then, the degradation history of the target product is adopted to update the degradation model, based on which the RL is estimated accordingly. To illustrate the validity and the usefulness of the proposed method, a numerical example about fatigue cracks is finally presented and analysed.

Keywords:

• residual life
• performance characteristics
• multivariate Wiener process with nonlinear drifts
• degradation data

Acknowledgements

This research was supported by the National Science Foundation of China under agreement 201206110079 through a visit of the first author to McMaster University, Canada, for carrying out collaborative research with the second author. It is also co-supported by the National Science Foundation of China (Grant No. 71371182) and the Science Foundation of National University of Defense Technology, China (Grant No. JC13-02-05). Our sincere thanks also go to the anonymous reviews and the associated editor for their constructive comments and useful suggestions on an earlier version of this manuscript which led to this improved version.