# Weighted Cost Reliability

Weighted cost is used as a method of predicting the actual risk costs that we can expect to occur on a project. How reliable is weighted cost as a means of prediction?

If there are several risks on a project, each with an associated cost effect, it is possible that none of the risks will occur, in which case the project risk cost would be zero. It is also possible that all of them will occur, in which case the project risk costs will simply be the sum of all the costs associated with each risk.

However, these two cases are statistically unlikely. If there are a reasonably large number of risks (not less than about 10) the most likely outcome is that some will occur and some will not occur. The more risks there are, the more likely is it that the overall risk cost will be about the same, regardless of which risks actually occur.

To illustrate this, a computer simulation of a project was set up in which there were 80 identified risks with associated costs. Each risk was randomly assigned a cost value between \$0 and \$100,000, and was also randomly assigned a probability. A large number (100,000) of different scenarios were then generated, thereby simulating the ‘parallel universe’ concept described above. In each scenario an overall project risk cost, i.e. the cost to the project of all the risks that occurred in that scenario, was calculated by including or not including each individual risk according to its probability. (A random number in the range 0-1 was generated for each risk and, if it was less than or equal to the probability, the risk was included, otherwise it was not included.) Project risk costs for each scenario were analysed statistically and the results displayed as a histogram, as shown below.

This figure also shows the calculated value of weighted cost. It will be seen that the calculated weighted cost occurs at or very close to the peak of the distribution, and that actual project risk costs are bunched quite closely in an approximately normal distribution. This indicates that the calculated weighted cost should give a good approximation to the actual risk costs that will occur, in this case.

The next four figures show the same distribution of project risk costs but for progressively fewer risks (40, 20, 10 and 5 risks respectively). It will be seen that, while the calculated weighted cost is always at or near the peak of the distribution, the width of the distribution increases as the number of risks decreases. This means that the fewer the identified risks, the more likely is the actual risk cost for the project to be significantly different from the calculated weighted cost.

The possible difference between the actual project risk cost and the calculated weighted cost is shown in the figure below. The horizontal axis of this graph shows the number of identified risks in the project while the vertical axis shows the 90% half-width of the risk cost distribution as a percentage of the total unweighted risk cost, i.e. the costs of all the risks added together without regard for their probabilities. Thus, for example, if there are 60 identified risks in the project, and the cost effect and probability of each one has been reliably established, the actual risk cost that will occur for the project as a whole will differ from the calculated weighted cost by about 10% of the total unweighted risk cost 9 times out of 10. (The other 1 time out of 10, the actual risk cost will differ from the calculated weighted cost by more than this amount.)

It can be seen from this graph that the usefulness of weighted cost as a program or project risk cost predictor rapidly decreases as the number of identified risks dips below about 20 or so. If there are only 10 risks with significant cost effects in the project, then weighted cost can only be relied upon to give an overall project risk cost indication within +/-25% of the total unweighted risk cost. This probably represents the lower limit of usefulness for weighted cost. With less than 10 risks, the utility of the weighted cost concept is doubtful.