Underlying Probability Measure Approximated by Monte Carlo Simulations in Event Prognostics

Abstract

The prognostic of events, and particularly of failures, is a key step towards allowing preventive decision-making, as in the case of predictive maintenance in Industry 4.0, for example. However, the occurrence time of a future event is subject to uncertainty, so it is natural to think of it as a random variable. In this regard, the default procedure (benchmark) to compute its probability distribution is empirical, through Monte Carlo simulations. Nonetheless, the analytic expression for the probability distribution of the occurrence time of any future event was presented and demonstrated in a recent publication. In this article it is established a direct relationship between these empirical and analytical procedures. It is shown that Monte Carlo simulations numerically approximate the analytically known probability measure when the future event is triggered by the crossing of a threshold.