Calculating Probabilities, Risk, Decision Trees and Monetary Value

There are several areas where you might need to calculate probablities of an occurance. Most likely they are involved with calculating risk.

One of those areas is calculating the advantage of splitting an order. If you have an activity on the critical path and in order to start working you need at least part of the order completed it might be a good idea to split the order between two providers. While most of us think of this in the manufacturing scenario it is very applicable to software development. The calculation can be thought of in two ways:

• If provider A is on time 80% of the time and company B is on time 70% of the time then the overall assurance that I will get at least something is 80% + (20% x 70%) = 94%.



• The general parellel calcualtion rules is that for two components in parallel the availability is A = 1-(1-Ac)^2 where Ac is the availability of each component and they are equal.



• The more general case of this formula is then 1-(1-Ac1)*(1-Ac2) or 1-(1-.80)*(1-.70)=94%

A good question is how does this relate to decision trees. In a decision tree there are normally two types of branches/nodes the decision node and the chance node. The decision node is mutually exclusive. Mutually exclusive means that it is either A or B not A nor B or A and B. In other words the probablity of A and B should add up to 1. The results on the branch are usually done with expected monetary value where the probablity can add up to more than 1 or less than one since these are not exculsive and are simply possiblities which generate value on the node.

Can we have a parellel node on the chance node of a decision tree? Yes absolutely. But then we dont use the simple expected monetary value instead we use the 1- (1-Ac1)*(1-Ac2) formula above to find the monetary value.