Once the probability and impact ranges have been established for each risk, the cost of risk retained by the public sector under Traditional and AFP delivery are calculated using the following formulas:
| Cost of RiskPSC = (Base Costs x Probability of Occurrence of Risk #1 under Traditional x Impact of Risk #1 under Traditional) + (Base Costs x Probability of Occurrence of Risk #2 under Traditional x Impact of Risk #2 under Traditional) + …+ (Base Costs x Probability of Occurrence of Risk #N under Traditional x Impact of Risk #N under Traditional); where the risk matrix has N defined risks under Traditional delivery |
| Cost of RiskAFP = (Base Costs x Probability of Occurrence of Risk #1 under AFP x Impact of Risk #1 under AFP) + (Base Costs x Probability of Occurrence of Risk #2 under AFP x Impact of Risk #2 under AFP) + …+ (Base Costs x Probability of Occurrence of Risk #N under AFP x Impact of Risk #N under AFP); where the risk matrix has N defined risks under AFP delivery |
On any project, the actual impact of any individual risk may fall somewhere along a continuum of impacts that includes the low, most likely and high ranges (the 10th, Most Likely and 90th percentile impacts quantified in the risk workshop). Since the impact will not necessarily be the same for each risk, without knowing in advance the exact combination of risks that might occur in the project being analysed, there are an infinite number of solutions to the above equations depending on the combination of impacts that are plugged into the equations. A well-established mathematical technique for dealing with such problems is the method of statistical simulation. Statistical simulation follows the following steps:
Step 1: Create a parametric model, y = f(x1, x2, ..., xN). In our problem, y is the cost of risk and the x'es are the risk impacts for each of the N risks.
Step 2: Generate a set of random inputs, xi1, xi2, ..., xiN. This is done by randomly picking a risk impact number for each of the N risks, from within the defined range for that risk8.
Step 3: Evaluate the model and store the results as yi. In other words, plug the randomly chosen set of impacts for each risk into the two equations above and record the resulting cost of risk number for Traditional and AFP delivery.
Step 4: Repeat steps 2 and 3 for i = 1 to a minimum of 10,000 times.
Step 5: Analyze the results using summary statistics, confidence intervals, etc. The statistical simulation exercise generates a full distribution of cost of risks under Traditional delivery and under AFP, as we now have 10,000 different possible costs of risks each under Traditional and AFP delivery. This distribution can be statistically analyzed for the mean (i.e. average or 50th percentile) cost of risk retained by the public sector under Traditional delivery and under AFP delivery. This mean cost of risk is used in the VFM analysis.
Most risk impact ranges, such as the Design Coordination and Completeness risk discussed in the section on retained risks, are positively (or rightward) skewed9 so the mode ("Most Likely" outcome) of the distribution is less than the mean (average or 50th percentile) of the distribution. Using the "Most Likely" impact to calculate the cost of the risk would thus understate the true cost of the risk on average.
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8 Risks are assumed to be completely uncorrelated and impact ranges are assumed to follow a triangular distribution.
9 In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable.