Treatment of Correlation for Risk Analysis of Engineering Projects

Treatment of correlations between variables is necessary to establish realistic quantifications of uncertainty of decision variables such as project duration, cost and internal rate of return during the planning stages of an engineering project. This paper highlights some often ignored theoretical requirements necessary for a rigorous consideration of correlations and presents a general analytical procedure for eliciting and treating correlations between variables which is applicable to a broad class of engineering problems. The general case of a decision variable Y expressed in terms of an arbitrary function g(X) is examined, where X is a vector of random variables, some or all of which may be correlated. The theoretical requirement for a positive definite correlation matrix is described, along with a two stage process that leads to the elicitation of such a matrix. A variable transformation approach for treating correlations in moment analysis is used to derive the first four moments of Y. The approach is verified using published results for the break-even analysis problem. A numerical example is used throughout the paper to demonstrate the approach and to highlight the importance of treating correlations in risk analysis.