Using the Prediction Profiler to optimize for a certain range

[#1]

Hi everyone,

I'm trying to use the prediction profiler in JMP in combination with the desirability function in order to optimize several models simulatanously. 
There are several optimisation options in JMP implemented like maximizing, minimizing or matching a target. However, I need an option to match a range.

Since there are only 3 adjustable points in the desitability function and I need a desirability function where all values outside the target ranges are equal to 0 and within equal to 1, I need your help how I can achieve this ( the function should look similar to a rectangle)

Please note, I'm familiar with the option to set specification limits in order to perform simulations or to calculate defect rates. These static plots are unfortunately not a big help for me. What I need is the interactivity of the desirability plot.

I'm looking forward to your suggestions!

Thanks!

[#2 · Accepted solution]

Hi,

I think the solution here is to define a custom desirability function as a formula column.

In the attached example using the Tiretread data I created a custom desirability function for ELONG which is 1 for the range 450 to 550 and 0 outside of that range.

If( 450 < :Pred Formula ELONG < 550,
	1,
	0
)

Then we profile the prediction formula column for ELONG and the custom desirability function. Set the desirability function for ELONG to none and Maximise for the custom desirability function.

I think that should work. Let me know.

Phil

[#3]

That sounds super interesting. I will give it a try - thanks for your fast reply! 

[#4]

One thing you will need to careful of is that the custom desirability function that @Phil_Kay describes is flat over a range, so there are possibly many optimal solutions (with a maximum desirability).  To visualize factor regions where the desirability is constant and at the maximum, you could consider using the "Output Random Table" command under the Profiler and then make a scatterplot matrix of your factors, and filter that plot on the desirability. 

[#5]

Hi Phil,
in principal your idea works for my probleme. However, reality is sometimes more complex than expected...
For my approach, I have to consider also the uncertainity interval around my model. JMP only allows me to use CIs. However, with a simple trick where I save the PredSE Formula and add the MSE to that formula (see picture below with the example of 9.1816) I can also approximate the 95% prediction interval (PI).

So what I actually want to know is, where does my PI intersect with my specification limits in order to define an acceptable input-parameter range. 
I could do this with you approach by:

1. Create a new column where I have to multiply the "adjusted" PredSE column with the correct t value to consider the degrees of freedom of my model. Lets call this column "Interval"
2. Add the value from the Interval column to the :Pred Formula column and check whether the upper PI falls within the Specs
3. Substract from the :Pred Formula the value from the Interval column and check if also the lower PI falls within the specs.
4. If 2 and 3 are true => 1 and if not => 0

Since I have to perform this process on multiple outputs/models it is too much effort to this manually. Especially the degrees of freedom in each of my models are different and I would need to adapt the value manually.  Do you have any idea how I can automate this process or do you have a different idea how I can tackle this probleme?

[#6]

Interesting questions and challenge that you have there, @Marco. Unfortunately I don't think that I have time to fully explore the solution options at the moment. I think that @SamGardner 's suggestion of using Monte Carlo filtering might be a useful solution. I also think that the new design space capabilities that are currently being evaluated in the beta version of JMP 17 could be interesting for you. You might want to contact your JMP representative to ask about the Early Adopter program for JMP 17 in order to see if these capabilities can help in your situation and to provide useful feedback to the JMP Development team.

[#7]

@Phil_Kay well thats a pitty! Hopefully you have more time in the future, since I would really appreciate a solution option from you. 

By the way, I have already access to the JMP EA 17. However, you have to help me a bit where I can find your mentioned option "design space capabilities".

I have also investigated the solution from @SamGardner which is really interesting and might be handy for some other challenges I'm facing. However, it does not really tackle my problem since I'm looking for an analytical solution instead of a simulation driven one. Especially because JMP does simply use the RMSE in the Random by Model option and not the correlation structure. Thus, the simulation results will only be correct in cases where the investigated design is completly orthogonal.  

[#8]

Great news that you already have the JMP17EA.

When you log in to the Early Adopter web page look under Videos > EA2 > Design Space Profiler. That is a video from the developer that is working on that capability (one of most experienced developers ;)).

I have a long train journey tomorrow so I might get chance to think about this. I can't make any promises though. (I have promised to do too many things this week!)

[#9]

@Phil_Kay 
Just watched the video and it was really interesting. However, at first glance it seems that the model uncertainty is only implemented in form of the RMSE. Thus, no correlation with respect to the input parameters is taken into account. I need to look into this more closely and will let you guys know how helpful this feature is for my problems. Is there any chanche for an exchange with @John_Sall ?

[#10]

He's quite busy! I think the best thing to do start with is to use jmpbeta@jmp.com to provide feedback and ask about how these capabilities might/might not address these needs.