Normal approximation to a sum of geometric random variables with application to ammunition stockpile planning

The normal approximation for a sum of geometric random variables has been examined. This approximation is relevant to the determination of direct-fire ammunition stockpile levels in a defence setting. Among the methodologies available for this assessment, one is a target-oriented methodology. This approach calculates the number of rounds necessary to destroy a given fraction of the enemy force and infrastructure. The difficulty is that the number of rounds required cannot be determined analytically. An obvious numeric approach is Monte Carlo simulation. Another is the approximation approach which has several advantages like it is easy to implement. and is accurate even in the case where the number of targets is low.