Monte-Carlo approximation for probability distribution of monotone Boolean function

The new method for probability of the value 1 evaluation for monotone Boolean function (for example for system reliability) is proposed. The method is based on a presentation of the function by its canonical disjunctive normal form. Monte-Carlo procedure assumes random choice of this form terms. Their arithmetical mean gives approximation for the probability of the value 1. Such an estimator is unbiased. The variance of this estimator has been calculated. It is shown that proposed method has less variance in comparison with the crude Monte-Carlo method.