Probability of hitting a specified target region with three-dimensional correlated random variables and aim point offset from the target

This paper provides a numerical solution for calculating the probability of hitting a specified target region, with the assumptions: (1) the aim point has an offset from the target, (2) the surrounding area of the target can be spherical or ellipsoidal, and (3) the joint probability density function is trivariate normal with non-zero means and non-zero correlation coefficient. A less general form of this type of problem has been solved by approximation for the offset but uncorrelated case. More recently, D.Y. Hsu solved the no-offset but correlated case of this problem [1999], and the two dimensional version of this general problem [2000]. A summary of these previous methods is given in the Appendix. In this paper a method for solving the general probability-of-hitting problem is presented. The problem is general in that both the correlation between three sets of two random variables and the offset between the target and aim point are included in the problem formulation.