Risk management - Evaluate - independent correlation
The Risk Management process
EVALUATE - independent correlation
We can show how two activities may combine with independent correlation.
Let us assume an identical probability distribution for both activity ‘A’ and ‘B’ with probabilities for values of 7, 9 and 11 weeks delay of 0.3, 0.5 and 0.2.
| Delay | Probability |
|---|---|
| 7 | 0.3 |
| 9 | 0.5 |
| 11 | 0.2 |
The combination of activities ‘A’ and ‘B’ can give possible values of 14, 16, 18, 20 and 22.
The calculations for their probabilities are shown below.
| Delay | Calculation | Probability | ||||
|---|---|---|---|---|---|---|
| 14 | 0.3 x 0.3 | 0.09 | ||||
| 16 | 0.3 x 0.5 | + | 0.5 x 0.3 | 0.30 | ||
| 18 | 0.3 x 0.2 | + | 0.5 x 0.5 | + | 0.2 x 0.3 | 0.37 |
| 20 | 0.5 x 0.2 | + | 0.2 x 0.5 | 0.20 | ||
| 22 | 0.2 x 0.2 | 0.04 | ||||
For both activities to cause a 7 week delay would be most unlikely and hence is reflected as the lowest probability of 0.09. The value of 14 can only be derived from the addition of 7 + 7.
A similar argument applies to 22 but the probability is slightly less at 0.04. This is because the initial estimate of a 11 week delay was less than for the 7 week delay.
In the case of a value of 16 weeks delay we can obtain this by 7 + 9 and 9 + 7. There are more possible combinations and the probability is correspondingly higher at 0.3.
The value of 18 can be formed by 7 + 11, 9 + 9 and 11 + 7 affording the highest probability of 0.37.
As each addition is added the extremes become less and less likely.
For example, if we had 5 additions the likelihood of each one being 7 and causing a 35 week delay would be 0.3 to the power 5.
That is, 0.3 x 0.3 x 0.3 x 0.3 x 0.3 x 0.3 x 0.3 = 0.0002187 which is very low.
For 10 additions the probability would be 0.3 to the power of 10 which is virtually impossible to occur.
Next, is shown the cumulative probability curves for the combination of ‘A’ and ‘B’ and on their own [see Cumulative probability graph].