Partially unbiased estimators for reliability and availability calculations

In a Monte Carlo algorithm for transport calculations, partially unbiased estimators are estimators conserving the expected value of the score obtained from any possible starter, for the estimation of a given functional. Such estimators can be easily deduced for Monte Carlo reliability estimations from the analogy between neutron transport and Markovian reliability. This paper summarizes and further develops some results recently obtained in this case. They are then generalized to dynamic reliability, and adapted to unavailability calculations. Based on the second moment of the score, a comparison of the different sets of estimators is provided. The paper is concluded by a semi-Markov extension of this theory.

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