System availability and reliability analysis by direct Monte Carlo with biasing

The quantitative analysis of the reliability and availability of an engineered system can be carried out analytically only for simple systems and under simplifying assumptions, such as the time-homogeneity in the Poisson processes governing the components' failure and repair behaviours. However, real systems are complex, the failure and repair behaviours of the components of a system may be quite different and time-dependencies may become significant in the various phases of components' life. The most suitable method to account for time-dependent failure and repair behaviours of components is the direct Monte Carlo simulation which amounts to sampling, from the corresponding distributions, one occurrence time for each possible transition of each component from its present state. These times are then ordered in a master schedule and the actually occurring transition is that corresponding to the shortest time. If the new system configuration belongs to a cut set, which makes the system fail, the occurring failure is recorded in appropriate counters. Otherwise, the simulation of the system trial proceeds by sampling a new transition time of the component which has undergone the transition and then the master schedule is updated accordingly. In this paper, the realistic time behaviours of components' failure and repair rates are described by means of various distributions of the transition times, such as the exponential, the Weibull, the normal. The effects of these different modelling hypotheses is examined. Moreover, an efficient biasing technique is introduced to guide the system to generate several realizations of failure, which would otherwise constitute a rather rare-event.