A method for treating dependencies between variables in a simulation risk analysis model

This thesis explores the need to recognise and represent accurately the interdependencies between uncertain quantitative components in a simulation model. Therefore, helping to fill the gap between acknowledging the importance of modelling correlation and the actual specification and implementation of a procedure for modelling accurate measures of Pearson's correlation became the main aim of this research. Two principal objectives are stated for the developed Research Correlation Model ("RCM"): (1) it is to generate Pearson-correlated paired samples of two continuous variables for which the sample correlation is a good approximation to the target correlation; and (2) the sampled values of the two individual variables must have very accurate means and variances. The research results conclude that the samples from the four chosen distributions that have been generated by the RCM have highly acceptable levels of precision when tested using x2 tests and others. The results also show that an average improvement in precision of correlation modelling was over 96 percent. Even with samples as small as 10 the worst case correction factor is only just less than 90 percent, with the average correction factor being over 96 percent overall, so that the contribution made by the RCM here is quite impressive. Overall the analysis shows that in the case when the sample size is 10, the RCM consistently generates samples whose correlation is so much more precise than that generated by @RISK. The smallest of all the observed ratios of improvements of the RCM in comparison with the use of @RISK is 2.3:1, in just one case when the medians were being compared. The average improvement ratio exceeded 100. It is concluded that the aim of specifying, formulating and developing a Pearson correlation model between a pair of continuous variables which can be incorporated into simulation models of complex applications has been achieved successfully.