New Probabilistic Modeling and Simulation Methods for Complex Time-Dependent Systems

摘要

This paper is a tutorial that presents a new method of modeling the probabilistic description of failure mechanisms in complex, time-dependent systems. The method of modeling employs a state vector differential equation representation of cumulative failure probabilities derived from Markov models associated with certain generic fault trees, and the method automatically includes common cause/common mode statistical dependencies, as well as time-related dependencies not considered in the literature previously. Simulations of these models employ a population dynamics representation of a probability space involving probability particle transitions among the Markov disjoint states. The particle transitions are governed by a random, Monte Carlo selection process. (ERA citation 10:033097)