Combining Probabilistic Estimates to Reduce Uncertainty

Abstract Suppose we have contracted for or otherwise obtained n probabilistic estimates, expressed as random variables, independent of each other, of the same system or project. This assumption means that we have, for each estimate, a random variable having a probability distribution (likely something close to the lognormal), an S-curve, a mean, and a standard deviation. We want to combine these n estimates to obtain one estimate that contains less uncertainty than each of the n estimates individually. There are two questions that we have to answer: 1) How should we “combine” the estimates? and 2) Will the combined estimate actually be less uncertain than each of the n independent estimates individually? For this issue to be meaningful, we must assume that each of the estimates is “correct,” i.e., 1) they are neither too optimistic, nor too pessimistic, but are based on risk assessments validly drawn from the same risk information available to each estimating team; 2) each estimating team has applied appropriate mathematical techniques to the cost-risk analysis, including, for example, inter-element correlations when appropriate; and 3) each estimating team was working from the same ground rules but may have applied different estimating methods and made different assumptions when encountering the absence of some information required by their estimating method.