In a previous blog, I presented a very simple way to allocate contingencies to uncertain cost elements in the project risk management process. However, that methodology works well when there are not risk events that affect a cost element or a group of cost elements.

A risk event is described by two elements: the probability of occurrence and the conditional impact to the project given its occurrence. For example, we have a risk that describes the possibility of a new regulation. If it occurs, it will increment the cost of group of cost elements by a minimum of 10%, most likely 15%, and a maximum 20%. If the risk does not occur, no impact will be observed. Using a Discrete and a PERT distribution, we can model such risk such as:

When sampling from this distribution approximately only 20% of the time will generate a multiplier with a minimum of 1.1, most likely 1.5 and a maximum of 1.2; in 80% of instances the multiplier will be 1. That means that only 20% of the time the risk will increment the cost of selected cost elements by the multiplier previously described as show in the figure below:

In addition to risk events in our cost risk analysis models, we often use distributions that describe cost uncertainties. These distributions model ranges are mostly in a different order of magnitude. Therefore, the variance will also be in a even greater order of magnitude. For example, the cost of Item 3 modeled using a 3-point estimate (i.e., min 100,000, ML 120,000, and max 150,000) has a variance of 87,698,412.70), while the variance of the risk event is 0.0036.

If we are to distribute the contingency using the % of contribution of the variance method, the risk event that we just modeled will be ignored even though we know that such risk event has an impact that we cannot dismiss. Given this practical scenario, the method of variance contribution will not work appropriately.

As an alternative, we can use a tornado diagram that results from @RISK’s sensitivity analysis. Here we can use the regression coefficients to understand what risk events or uncertainties are affecting the total cost in a more drastic way. In the case that you also incorporated events that represent an opportunity to reduce cost, you will observe that the coefficient is negative; in your allocation calculations you should not consider negative coefficients.

In the figure below you can observe the Regression Tornado. Here risk events and uncertainties are represented in a scale that goes from 0 to +/-1:

Knowing the regression coefficient of each input that affects the total cost in a negative way, we can construct a table and obtain a normalized percent that can be used to distribute contingency. If for example, we have a contingency of $100,000, it can be distributed to each input proportionally to the regression coefficient as shown below.

Some risk management experts do not distribute the entire amount of the calculated contingency. It is common practice to distribute only a percentage of it (i.e., 70%). The remaining amount will be used as a reserve that will handle unidentified risks.

Javier Ordóñez, Ph.D

Director of Custom Solutions