The variance of elemental estimates

One of the factors affecting the success or otherwise of the procurement process is the quality of its financial management. In many cases, particularly in the early stages of a project, this is dependent on the accuracy of forecasts of future costs. For risk management purposes, what is most useful is the representation of future costs in the form of a probability distribution. In the case of early stage building contract price forecasts the approximate distribution of the likely error is usually obtained by the stochastic simulation of values from the distribution of known elemental rates under the simplifying assumption that the elemental rates are from independent random variables. This paper describes an empirical study aimed at investigating the accuracy of this method in comparison with one which incorporates the intervariable correlations. This confirms previous work in showing that the estimated second moment (variance) is considerably different when using the mean element rates as estimators, with the approximate method producing much lower estimates. It is then shown that, under the empirically supported assumption that element rates are normally distributed, the total project is also lognormally distributed and that this is completely specified. It is also shown that the coefficient of variation is unaffected by the size (floor area) of the project. The analysis then continues to examine the role of professional judgement and, with the simulated data used, the independent approximation is shown to be reasonably accurate – the professional judgement absorbing most of the intercorrelations involved. A final example is given involving the use of elemental unit quantities and rates. This shows how a unique project rate variance can be calculated for an individual future project, based on relevant data from previous projects and taking into account interelemental rate correlations. The results again suggests that the approximating method may be quite accurate.