Uncertain failure thresholds in cumulative damage models

This paper investigates the issues related to variability in degradation-based reliability models and how the variability affects the remaining useful life prognosis being made by those models. Particularly, uncertain failure thresholds in cumulative damage models are of primary interest in this study. Many degradation-based reliability approaches make use of a predefined deterministic value of the failure threshold. However, in real-world cases, the designer may not be aware of the precise critical degradation level. In such situations it is suitable to define the critical degradation level as a range of values having certain probabilities of being critical. If no prior information is available regarding the failure threshold; the critical value has to be estimated from experimental reliability data that are subject to uncertainty due to imperfect measurements and random deviations in reliability properties of the tested components. In these circumstances, it is desirable to model the critical threshold as a random variable. Otherwise, the model can be oversimplified since it neglects the failure threshold uncertainty, whose influence onto the reliability prediction can be significant. This paper presents uncertainty analysis regarding how variability in the failure threshold affects the reliability prediction in conjunction with cumulative damage models. Three types of cumulative damage models are investigated; these are a Markov chain-based model, a linear path degradation model, and a Wiener process with drift. Closed-form equations quantifying the threshold uncertainty propagation into the model prediction are given. A numerical example is presented to illustrate how the critical threshold uncertainty reshapes the predicted time-to-failure distribution, supporting the need for considering the critical threshold uncertainty in accurate reliability computations.