A degradation path‐dependent approach for remaining useful life estimation with an exact and closed‐form solution

Remaining useful life (RUL) estimation is regarded as one of the most central components in prognostics and health management (PHM). Accurate RUL estimation can enable failure prevention in a more controllable manner in that effective maintenance can be executed in appropriate time to correct impending faults. In this paper we consider the problem of estimating the RUL from observed degradation data for a general system. A degradation path‐dependent approach for RUL estimation is presented through the combination of Bayesian updating and expectation maximization (EM) algorithm. The use of both Bayesian updating and EM algorithm to update the model parameters and RUL distribution at the time obtaining a newly observed data is a novel contribution of this paper, which makes the estimated RUL depend on the observed degradation data history. As two specific cases, a linear degradation model and an exponential‐based degradation model are considered to illustrate the implementation of our presented approach. A major contribution under these two special cases is that our approach can obtain an exact and closed‐form RUL distribution respectively, and the moment of the obtained RUL distribution from our presented approach exists. This contrasts sharply with the approximated results obtained in the literature for the same cases. To our knowledge, the RUL estimation approach presented in this paper for the two special cases is the only one that can provide an exact and closed‐form RUL distribution utilizing the monitoring history. Finally, numerical examples for RUL estimation and a practical case study for condition‐based replacement decision making with comparison to a previously reported approach are provided to substantiate the superiority of the proposed model.