Predicting the Time To Failure of a randomly degrading component by a hybrid Monte Carlo and possibilistic method

The main goal of a prognostic system is to estimate the Time To Failure (TTF) of a structure, system or component (SSC), i.e. the lifetime remaining between the present and the instance when it can no longer perform its function. Such prediction on the time of loss of functionality is typically done on the basis of measurements of parameters representative of the SSC condition state and degradation process. Uncertainties from two different sources affect the prediction: randomness due to inherent variability in the SSC degradation behavior (aleatory uncertainty) and imprecision due to incomplete knowledge and information on the SSC stress and strength characteristics (epistemic uncertainty). Such uncertainties must be adequately represented and propagated in order for the prognostic results to have operative significance, e.g. in terms of maintenance and renovation decisions. This work illustrates an hybrid Monte Carlo and possibilistic method for the representation and propagation of aleatory and epistemic uncertainties, with reference to a case study of a component which is randomly degrading in time according to a stochastic fatigue crack growth model of literature. The crack depth is assumed as representative parameter of the component condition state and its limit value beyond which failure occurs is assumed to be affected by epistemic uncertainty, as represented by a possibility distribution.