The variance of the coverage of a randomly located area target by a salvo of weapons

We derive formulas for the variance of that proportion of the value of a randomly located, circularly symmetric area target that is destroyed by N independently fired weapons of identical type whose damage functions are circularly symmetric about the respective impact points. The probability density functions of the target center location and of the weapon impact points are also circularly symmetric. The general results are specialized to uniform and Gaussian functions. In the latter case a closed‐form solution (triple integral) for the variance of the coverage is derived. Similar to some well‐known results on expected coverage, this expression for the variance of the coverage can be easily evaluated by numerical quadrature. Numerical results are given which indicate the target coverage variability caused by the combined effects of random target‐locating errors and weapon impact point fluctuations.