Since – based on the above results – no analytical formulation for the resultant leakage current probability density distribution p(I) could be derived, an alternative way was to use the Monte Carlo technique. Monte Carlo simulation is a computerized mathematical technique that permits accounting for risk in quantitative analysis and decision making. It performs risk analysis by building models of possible results by substituting a range of values – a probability distribution – for any factor that has inherent uncertainty. It then calculates results over and over, each time using a different set of random values from the probability functions. Depending upon the number of uncertainties and the ranges specified for them, a Monte Carlo simulation could involve thousands or tens of thousands of recalculations before it is complete. Monte Carlo simulation produces distributions of possible outcome values. By using probability distributions, variables can have different probabilities of different outcomes occurring. It is emphasized in this paper that probability distributions are a much more realistic way of describing uncertainty in variables of a risk analysis.
This procedure is diagrammatically described in Fig. 5. Random numbers Rgi and Rci were first numerically generated. Random values of contamination layer conductivity (ci) and layer size (gi) were in turn generated. Random magnitudes of leakage current (Ii) using the two random ci and gi values were then generated using the numerical techniques described in this paper.