Some advancements in Monte Carlo integration methods with applications to proximity fuze detection probabilities

Abstract

A simulation model is developed for estimating any quantity defined as a multiple integral with constant, variable or infinite limits of integration. The model evaluates multiple integrals by sampling uniformally over the multidimensional volume defined by the original region of integration, and employing the sample variance (associated with Monte Carlo methods) to obtain a probabilistic representation for the error bound. Uniform sampling over any region of integration is accomplished by determining the appropriate conditional probability density functions and integrating—an approach which is not shown in the simulation literature. The calculation of detection probabilities for a proximity fuze is used to illustrate the results (and to show how such problems arise), and comparison with alternative solution procedures (e.g. Gaussian quadrature) are discussed.