# Thread: Sensitivity Analysis for Multivariable Problem

1. ## Sensitivity Analysis for Multivariable Problem

Hello all, first off I hope this is in the right forum and thanks for reading.

I am a practicing engineer and have run into a problem where I have (and can control) multiple input variables (5) into an equation and am given the solution. My task it to see which of these variables is the most influential on the final number. I have tried to decompose the equation, but it is extremely complex and does not simplify very well. Is there a method where I can hold 4 of the variables constant and vary the 5th (5 different times) and come to a conclusion? Would a sensitivity analysis be helpful here at all?

The end result I want is to use the most important variable as a basis to create a new equation only involving that variable, yet captures the majority of what the previous equation did but in a much easier to use form that can be distributed to my coworkers.

If you could point me in the right direction I would be extremely thankful thanks for reading and happy holidays!

------Clarifying example------
Suppose the problem is related to total pressure at the end of a pipe, my inputs could be:
1) Diameter of pipe
2) Friction of pipe
3) Number and type of bends
4) Viscosity of fluid
5) Input Pressure

Since many of these variable effect others would a sensitivity analysis capture the true dominant variable?

2. ## Re: Sensitivity Analysis for Multivariable Problem

This appears to be a "variable importance measure" problem to me. Try looking into that.

Also, do you know how many observations you have? A description of your data might allow us to help you more.

3. ## Re: Sensitivity Analysis for Multivariable Problem

Sorry for the delay, I was on vacation during the holiday.

The data is not actually coming from observations. Bear with me for a second:

we have a equation that accurately models the response of the our system (over a certain range), but it is far too complicated for everyday use. I can create as many cases or observations as I want by altering the input variables. The problem with this formula is that it is impractical and unnecessarily complicated for the purpose it serves. My hope is to create a simpler equation that only uses 1 or 2 of the variables with some sort of constant added (subtracted, multiplied, etc.) that captures the other less important variables

original equation:
x=(3a+2b-c)*d/4

modified simpler equation:
x=(a+b)*(constant)>=original x

Obviously this is a very simplified explanation, but as long as the modified x is within 1 or 2 standard deviations (above) the actual x it will serve our purposes.

Thanks.

Let me know if there is anything else I can explain better or more clearly.

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