Probability distribution function for damage expectancy

Damage expectancy (DE) is defined as the probability of damaging a target to a specified criterion. Often military planners apply event decomposition, which divides the process of delivering and executing the weapon into phases, to calculate DE as the product of independent conditional factors, sometimes referred to as a "kill chain." We propose a Bayesian approach, which treats the success rate in each phase (subevent) and the overall DE as random variables. The multiplicative central limit theorem indicates products of positive random variables asymptotically follow a lognormal distribution. We investigate the applicability of the lognormal distribution with few random variables in the product. We conclude that the lognormal distribution generally provides a very reasonable characterization of the uncertainty for DE. We also find that under some predictable circumstances, the beta distribution provides a more satisfactory characterization. This approach provides a statistical distribution indicating the certainty of a DE assessment. We recommend using the most conservative of the mean or the median as a point estimate for DE.