Using response surface equationsHello everyone,
I obtained response surface curves from an experimental design.
I would like to use these response surfaces to perform calculations; I would like to obtain the equation of these response surfaces. To obtain these equations, I took the results obtained in the table "parameter estimates". On the other hand, taking these results and drawing the curves on another software, I do not get the same curves.
Is there anything special about knowing how to write these response surface equations?
Thank you in advance.
Laura
Re: Utilisation des équations de surfaces de réponseYou are not providing many details here, so I will be making a guess on what is going on.
The coefficients that JMP reports on the parameter estimates table are often in terms of the coded units for the factors, not the natural units. There are many reasons for this, but that is beyond the scope of this post. A quick way to tell if this is the case, look at the label for the factors. Does it list something like A(x, y) where x and y are specific numbers? If so, then the parameter estimates are in terms of coded values. From the red popup menu you can ask for the prediction equation which lists everything explicitly. You could also save the prediction formula to ensure that you are getting the proper formula. If this is NOT what is going on, please post some details (what your formula is, ranges for the factors, what you see from the other package, etc.)
And finally, one more question: why not just get the graph you need from JMP? I would be curious to know what graph you desire that JMP does not offer.
Re: Using response surface equationsThank you for your reply.
From the red contextual menu (estimates -> display the expression of the forecast), I get an equation.
In my case, I get
-16,25164+ 0,1232075 * T -0,002904 * t -0,063439 * ((T-191,357) * (T (-191,357)) -0,001744 * ((T-191,357) * (t- 416,629) -7,258e-5 * ((t-416,629) * (t-416,629))
This is the concentration of a compound as a function of time (t) and temperature (T), which varies from my experience of about 300 to 500 seconds, and from 185 to 200 ° C.
I would like to find the values of temperature and time that I can apply to not exceed a threshold of concentration.
Re: Utilisation des équations de surfaces de réponseI would guess that this design was not created in JMP since the coding property is not being used. However, in order to protect you and provide more meaningful analyses, JMP will automatically center the interaction and quadratic terms. That is why you see (t-416.629) and (T-191.357) and is likely what led to your issue.
In order to determine values of t and T that will lead to lower concentrations, you have a few options to explore this. Keep in mind that the proper region with low concentrations is likely not rectangular, so you can't just say t < X value and T < Y value.
One approach is to use the contour profiler.
From the red triangle choose Factor Profiling > Contour Profiler. You will see a contour plot of time versus temperature and a single contour drawn for your concentration. Put your upper limit for concentration in the "Hi Limit" field. The areas above that upper limit will be shaded out. Anything in the white space is a predicted good combination of time and temperature.
There could be other approaches, but I think this is probably the quickest and easiest way to see the acceptable region for t and T.
Re: Using response surface equationsThank you !
