I have a program that creates a pool of equations with some variety of variables. I want to test the sensitivity of each equation to fluctuations in any of the variables. Basically, I haven't gone looking for some standard approach, but have been playing with different measures of sensitivity, and am looking for suggestions.

The simple sensitivity measure that I have does this:

1) Set all variables except the one being tested to their average values. (this works because I have average values for them, otherwise, any fixed value could be used).

2) Set the test variable to 1, and get the result of the equation. This is the OneValue.

3) Set the test variable to 100, and get the result of the equation. This is the HundredValue.

Now, there are many ways to get a single sensitivity out of this:

a) HundredValue/OneValue
b) OneValue/HundredValue * 100
c) (HundredValue-OneValue)/100
d) 100/(HundredValue-OneValue)

Each of these produces a different range of results. I'm not sure that one is better than any other, but a, b, and d have the problems that they can be undefined for certain results. Therefore, I am using C.

In theory, an equation such as mX + b would have X being perfectly sensitive to fluctuations. In other words, X100 would be 100 * X1. This is shown best with test A. In test C, you get almost 1. Values less than 1 would be less sensitive, values greater than 1 would be excessively sensitive (for instance x^2), negative values would indicate variables with inverse fluctuations ( such as 1/x, as x gets bigger, 1/x gets smaller).

Does anybody have any thoughts or suggestions on better ways to do this?