Cluster-Event Biasing in Monte Carlo Applications to Systems Reliability

Estimation of the probabilities of rare events with significant consequences, e.g., disasters, is one of the most difficult problems in Monte Carlo applications to systems engineering and reliability. The Bernoulli-type estimator used in analog Monte Carlo is characterized by extremely high variance when applied to the estimation of rare events. Variance reduction methods are, therefore, of importance in this field.

The present work suggests a parametric nonanalog probability measure based on the superposition of transition biasing and forced events biasing. The cluster-event model is developed providing an effective and reliable approximation for the second moment and the benefit along with a methodology of selecting near-optimal biasing parameters. Numerical examples show a considerable benefit when the method is applied to problems of particular difficulty for the analog Monte Carlo method.

The suggested model is applicable for reliability assessment of stochastic networks of complicated topology and high redundancy with component-level repair (i.e., repair applied to an individual failed component while the system is operational).