The key goal in prognostics is to predict the remaining use- ful life (RUL) of engineering systems in order to guide dif- ferent types of decision-making activities such as path plan- ning, fault mitigation, etc. The remaining useful life of an engineering component/system is defined as the first future time-instant in which a set of safety threshold conditions are violated. The violation of these conditions may render the system inoperable or even lead to catastrophic failure. This paper develops a computational methodology to analyze the aforementioned set of safety threshold conditions, calculate the probability of failure, and in turn, proposes a new hy- pothesis to mathematically connect such probability to the re- maining useful life prediction. A significant advantage of the proposed methodology is that it is possible to learn important properties of the remaining useful life, without simulating the system until the occurrence of failure; this feature renders the proposed approach unique in comparison with existing direct- RUL-prediction approaches. The methodology also provides a systematic way of treating the different sources of uncer- tainty that may arise from imprecisely known future operating conditions, inaccurate state-of-health state estimates, use of imperfect models, etc. The proposed approach is developed using a model-based framework prognostics using principles of probability, and illustrated using a numerical example.
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