Question

QUESTION FOR ALL - MY MEDIUM IMPACT TRUMPS YOUR HIGH PROBABILITY!

So, we are evaluating our probabilities on an ordinal scale of Very High, High, Medium, Low, Very Low. And we are using the same scale for impacts. A little combinatorial math will tell you that gives us 25 combinations of individual combined ratings.

We know that a Very High probability with a Very High impact will be the top of our list. Likewise, we know a very low probability with a very low impact will be at the bottom. It’s the stuff in the middle that gives us so much problem.

Is a High Probability Medium impact risk a bigger problem than a Medium Probability High impact risk, for example?   We have many of these pairs to sort through if we are going to come up with a combined risk rating for each identified risk.

How do we do that, people? And once we do, how do we document it clearly?

Thoughts, ideas, examples?

help please

Answer 1

If this would have been a problem of only a single series (i.e. Very High, High, Medium, Low, Very Low) - a simple ranking would like below have worked -

Very High	1
High	2
Medium	3
Low	4
Very Low	5

This problem can be broken down to determine ranking for each of the cells of a matrix of order 5 x 5. General idea to solve this problem can be based on calculating compensation for each cell for a fall in risk category on ordinal scale.

A very simple approach could be like below -

1. Count the total number of rows and columns (in this case both are equal to 5). Let this be S (equal to 10).
2. Compensation for each cell (i, j) = sum (i, j). Let this be C (i, j).
3. Rank of each cell on the matrix = S - C (i, j)
4. Higher the rank, lower the risk

For each of the combination of risk category, you will end up with the following -

	j	1	2	3	4	5
i		Very High	High	Medium	Low	Very Low
1	Very High	8	7	6	5	4
2	High	7	6	5	4	3
3	Medium	6	5	4	3	2
4	Low	5	4	3	2	1
5	Very Low	4	3	2	1	0

A weighted approach could also be used (provided we can associate weights for each of the risk category) -

1. Count the total number of rows and columns (in this case both are equal to 5). Let this be S (equal to 10).
2. Determine the weight for each of the risk category across row and column (this can be for example the average risk observed and can be different or same for row and column).
3. Standardize the weights so that sum is equal to 1. And then can calculate the cumulative weights across both row and column.
4. Cumulative weights observed above is the compensation, i.e. compensation for each cell (i, j) = sum (Cum. wts. i, Cum. wts. j). Let this be C (i, j).
5. Rank of each cell on the matrix = S - C (i, j).
6. Higher the rank, lower the risk

For each of the combination of risk category, you will end up with the following -

	j	1	2	3	4	5	Wts.	Std. Wts.	Compensation
i		Very High	High	Medium	Low	Very Low
1	Very High	7	6	5	5	5	25.0	1.7	1.7
2	High	6	5	4	4	4	16.0	1.1	2.7
3	Medium	5	4	4	4	3	9.0	0.6	3.3
4	Low	5	4	4	3	3	4.0	0.3	3.6
5	Very Low	5	4	3	3	3	1.0	0.1	3.7
Wts.		25.0	16.0	9.0	4.0	1.0
Std. Wts.		1.7	1.1	0.6	0.3	0.1
Compensation		1.7	2.7	3.3	3.6	3.7

The weighted approach is best suited when we can define the weights associated for each of the risk category. For the above table, I have randomly assigned weights as (25, 16, 9, 4, 1) for both row and column.