topic Re: Integral of a Desirability Function in Discussions

Integral of a Desirability Function

Marco_ — Fri, 23 Feb 2024 18:21:05 GMT

Hi everyone,

I try to perform an optimization in the profiler, but instead of just searching for the highest desirability in the design space I'm actually looking for the maximal surface under the desirability curve. The desirability is a function of x, y and z, and these 3 parameters are also interacting with each other.

I found this post: https://community.jmp.com/t5/Discussions/How-can-I-calculate-area-under-the-curve-in-jmp-pro/td-p/314792

So I used in integrate function to get the area under the curve for x (I want to do the same for y and z)

Integrate( :Desirability 3, :"x"n, 35000, 95000 )

Afterwards I plotted both, the original desirability function and the integral function. However, both functions show the same profile in the profiler.

Does anyone have an idea, why this is the case? I'm also open for any other solutions, to get the integral as an interactive function.

Re: Integral of a Desirability Function

hogi — Sat, 24 Feb 2024 15:19:48 GMT

Integrate needs an expression as first argument.

So, instead of using the Desirability column, use the column formula of the desirability column.

The Desirability equation will looks like this:

here Disso is the predicted result Disso= f(x,y,z).

To get an equation depending on your input values f(x,y,z), you have to replace this Symbol with the prediction equation - i.e. the column formula of the Disso column.

Re: Integral of a Desirability Function

Marco_ — Mon, 26 Feb 2024 12:13:02 GMT

@hogi

Thanks a lot for your advice. However, it does not work.

I thought it might be easier to illustrate the problem with a real example. Therefore I have created a JMP file (attached) where I have a polynomial model y which is afunction of x1, x2 and x3. I have created a desirability function and replaced "y" with the model equation (analog to the comment)

@hogi wrote:
To get an equation depending on your input values f(x,y,z), you have to replace this Symbol with the prediction equation - i.e. the column formula of the Disso column.

From there I used the integrate function, to integrate x1 from -1 to +1.

I got the same result as before, the profile from the desirability function and the integral are identical.

Re: Integral of a Desirability Function

Marco_ — Thu, 29 Feb 2024 14:50:39 GMT

Does anyone have an idea what could cause the problem or any other solution?

Re: Integral of a Desirability Function

hogi — Sat, 02 Mar 2024 08:23:47 GMT

Hi @Marco_ , could you explain in more detail which values you want to vary and which values you want to integrate?
I wonder about the integral. Maybe better average?

Also - will the integral/average be over the whole range or just a small region around a central value x1c +/- sigma?

Regarding integral in general - according to the scripting index, the second argument should be a variable.
So I was wondering if it is at all possible to put a column name there:

Integrate(:x1, :x1, -1, 1)

Not really: Jmp first replaces x1 in the first argument with the entry of column :x1 - and then uses this constant numeric value for Integrate, so

Integrate(:x1,:x1,-1,1) = :x1 * Integrate(1,:x1,-1,1)= 2 :x1

[along this line: If there is no value in column :x1, the result is undefined.]

Same finding for the profiler:
- Jmp provides a slider for :x1 - despite the Integral.

- the result is not 0, but 2 x1

This fits to your findings: Integral = 2 x Expanded Desirability.

As a solution, let's follow the scripting index and use a variable (z):

If you generate a profiler plot for Integral, Jmp just displays sliders for x2 and x3 and calculates the integral over z (old :x1):