Power analysis for Mutiple response DOE

[#1]

Hi all, 

I have a custom design with 4 responses, and 3 factors that plan to run. 

Justin_Bui_0-1681290076999.png

I want to do a Power analysis. What I understand is I need to: 

- Estimate RMSE: Or noise in response when repeating many runs with the same factors setting 

- Define delta (or signal/ 2* Anticipated coefficient). The minimum change in the response that critical to detect. 

Justin_Bui_2-1681290297233.png

But I have 4 responses. Which one should I put in the Power analysis? 

is that correct if I use the most critical response in this? 

Hope that anyone can give your advice.
Thank you so much

[#2 · Accepted solution]

You are on the right track. One way to think of power analysis is as a risk associated with the hypothesis tests you'll be doing in the analysis. Hence JMP is 'wired' to allow you to estimate power based on an individual response because the RMSE will in all likelihood be different for each response. And the responses will almost certainly be in different units of measure. So the delta value is only meaningful for responses of consistent units of measure AND the delta value itself. So one way of thinking of which response is as you suggest most critical. But why not put all the responses in one at a time? That way you'll have a much more complete picture of how power covers ALL the responses, allowing you to make adjustments to the experimental design as needed.

[#3]

Thanks for the insight. 
I think I will do power analysis for all responses. & base on the level of risk I could take. I can decide the proper action for next step (like add more run or adjust the delta)