Computation of time probability distributions for the occurrence of uncertain future events

The determination of the time at which an event may take place in future is a well-studied problem number science and engineering disciplines. Indeed, for more than fifty years, researchers have tried to establish adequate methods characterize behaviour dynamic systems implement predictive decision-making policies. Most these efforts intend model evolution nonlinear terms stochastic processes; while defining occurrence events first-passage problems with thresholds that could be either deterministic or probabilistic nature. random variable associated such has been determined closed-form variety specific continuous-time diffusion models, being most available literature motivated by physical phenomena. Unfortunately, quite limited rigorous studies related discrete-time processes, despite tremendous amount digital information currently collected worldwide. In this regard, article provides mathematically formalization computing probability uncertain both discrete- extending notion fully “uncertain events” hazard zones”. We focus on applications showing how compute those measures validate proposed framework comparing results obtained Monte Carlo simulations; all fatigue crack growth prognosis.