Can we have Monte Carlo simulation in regression parameters

[#1]

Hello:

I was just wondering if there is a way to incorporate Monte-Carlo simulation in regression parameters.

I guess once I have the regression equation I can run a Monte-Carlo simulation by specifying a distribution for each parameter and get the distribution of the output parameter.

Q1) But while creating that regression equation will three data points (one at each LSL and USL of tolerance zone and one in the middle) for each parameter suffice?

I am guessing I will need two runs of DOE, one to find the significant factors. and than another run on significant factors varying in the tolerance zone.

My ultimate goal is to vary the tolerance limit of each parameter in the system created by regression equation and get the failure rates within the acceptable limit.

Q2) How many replicates should I do?

Please accept my apologies, if the question seems to be stupid and please explain where my understanding is flawed.

Best Regards,

VarunK

[#2]

Based on what you are trying to accomplish, which sounds to me like finding a distribution for a response variable based on a varying x value, Monte Carlo simulation on the parameter estimates isn't the best way to go. It sure sounds to me like you should be using the Prediction Profiler to simulate the response distribution. Or maybe I'm just missing your goal?

[#3]

Thank you P_Bartell for your response:

Below I have tried to be more specific.

Say I got A and B as significant factor to get C as response variable.

A can be from 9-11, with nominal as 10

B can be 19-21, with nominal as 20

So I will run one more DOE with A having three levels 8,10 and 12 (intentionally kept it 1 additional on both sides)

B will also have three levels 18,20 and 22 (again intentionally increased it be 1 on both sides)

Now, I may get a more precise regression equation for A and B modeling the outcome C.

Now if my scrap rate is say 3%, I will vary the mean and tolerance zone of A and B such that the output values for C are within the 3% scrap rate.

This way I can have the maximum tolerance on the expensive part (say machining) A while B can be reduced to a possible limit.

This is for when we are still in the prototype phase of the component and we don't have much production data available with us.

This will give us a good ball park, doing changes later on is very expensive.

Prototype vs Production correlation will be another challenge, but at least it will give us some data point about the possible changes for next project.

Do we have any other better way to decide on the tolerances?

[#4]

Still sounds like a task well suited for the Simulation capabilities within the Prediction Profiler.

[#5]

Thank you P_Bartell

[#6]

Hi @VarunK,

As @P_Bartell, the simulation tool built into the prediction profiler is your best bet - if you know the expected variability of your process settings (A and B in your example) you can simulate to find the defect rate. If you want to explore how you can set the upper and lower limits for these settings, the Design Space Profiler will work well.

Thanks,

Ben

[#7]

Thank you Ben_Ingham