Project activities are never truly independent from one another. In practice, common factors result in a tendency for activity outcomes (schedule or cost) to gravitate towards a similar region in the probability distributions that have been estimated for them. In other words, there is a positive correlation between the activity outcomes. Some common factors may pertain to the project as a whole, for example, the quality of the project management team, and the robustness of the estimating process. Other common factors may be contained within certain project areas, often because they are associated with a particular group of products.

Most Monte Carlo analysis tools use correlation functions to simulate statistical dependencies between activities. Truly independent activities would have a correlation coefficient of zero, whereas activities with a perfect positive correlation would have a correlation coefficient of 1. In practice, most project activities have interdependencies within this range. The figure below shows four scatter diagrams, illustrating correlation coefficients of 0.1, 0.3, 0.7 and 0.9 for the beta pert distribution.

Just occasionally, a negative correlation between activity outcomes might be expected. For example, if there is uncertainty as to what proportion of a certain area of the project will be subcontracted, there might be a negative correlation between the in-house and subcontract costs for the associated activities.

The risk analyst should consider the common factors that affect interdependencies between project activities and select a correlation co-efficient that is appropriate, either to apply to all project activities or to specified groups of activities. (If there are a small number of groups it is usually reasonable to simulate the groups as being independent of one another). The value selected for correlation coefficients should reflect the degree to which they are inter-related. Interdependencies within activity groups are likely to be stronger than interdependencies that apply to the project as a whole. Typically, experience shows that for schedule risk analysis, correlation coefficients in the region of 0.5 are appropriate, whereas for a simple cost risk analysis, this could rise to 0.7-0.8. However, if the structure of the cost risk model has been designed to take into account results from the schedule analysis, then the cost model correlation coefficients may be reduced accordingly

Research shows that there is always some degree of correlation within a project even where there appear to be no direct causal links between activities. Such research indicates the existence of hidden underlying factors (such as a common source of estimating bias) that tend to result in correlation of outcomes. Despite this evidence, failure to include correlation is a common fault in Monte Carlo analysis. The outcome is that the results for overall project risk have an unrealistically small variance; the s-curves don’t show a realistically wide spread. This is a fault that grows with the number of items being simulated and is a particular problem in cost risk analysis, where the simulation is based on an arithmetic total of a large number of line items.

Contact: martin.hopkinson@hvr-csl.co.uk