Resistance as a function of temperatureI have a customer who would like to reduce the number of measurements needed to calibrate temperature probes that they make. The have lots of historical data and they have a process that results in variable curves for resistance as a function of temperature. I am wondering if anyone has experience with this type of problem and how JMP can help. Thanks, Andrea
Re: Resistance as a function of temperatureWhat is their current calibration method or process? What does a calibration curve look like? Do they currently have a parametric model for the curve? Do they have calibration problems besides excess testing? Can they provide a sample of curves?
Re: Resistance as a function of temperatureAll we know so far is that they have tried lots of models that haven't worked. We are talking with them again on Wednesday after our NDA is in place and they are going to show us curves and what they've tried. I can provide more information then.
Re: Resistance as a function of temperatureHey Andrea,
Resistance as a function of temperature is a non-linear relationship.It is highest at lower temps and is low at higher temps. There are two approaches I have used to model data like this...
Start with a theoretical model from the literature for the material of interest. You can fit custom non-linear models in the nonlinear regression platform. The procedure for doing this is in the help documentation.
https://www.jmp.com/support/help/en/15.1/#page/jmp/nonlinear-regression.shtml#
The other approach is when a model from theory is not available. In this case use the fit curve platform to explore candidate models. If one is found then save the parametric prediction formula to the data table then use the formula in the non-linear platform to fit other candidate curves.
Either method you want a predictor formula. You can then use the predictor formula as X and response from one of the curves in DOE > Special Purpose > Nonlinear Design to come up a plan that requires fewer measurements to fit their curves.
https://www.jmp.com/support/help/en/15.1/?os=win&source=application#page/jmp/augment-a-design-using-prior-data.shtml#ww89885
Happy to talk it over with you if it seems like either approach could be helpful.
Enjoy!
Re: Resistance as a function of temperatureFDE might offer some advantages of JMP Pro for this application as well.
Re: Resistance as a function of temperatureThank you so much for your questions and background info - it was helpful before meeting with the customer. The customer is calibrating their temperature probes (which are ~ 2 inch wafers) between 0 and 350 kelvin!!! (As it turns out, Columbus, OH is one of the coldest places in the universe.) They are currently testing 86 temperatures points and feel like they can be more in the range of 10 points. The calibration data is difficult to get at so they were just looking at one calibration curve as a proof of concept. They were starting with "reduced" curves of 6, 8, 10, 12 points and fitting a model (polynomials in Fit Y by X) then plotting residuals when using each of those models with the "full" 86 points. They have a low tolerance and want the residuals within a .01% of actual. We had other things to talk about but before moving on I told them about the nonlinear and fit curve platforms and suggested that they 1) start with the "full", 86 points to define the model either using one available in JMP or a theoretical one they knew about 2) then use that model to fit a series of "reduced" curves 3) compare each "reduced" curve to the full 86 point curve 4) choose the reduced curve and test is out with additional calibration curves. Let me know what you think of this approach. We didn't speak about specific details here. For example, when they fit each of the "reduced" curves they should probably adjust the parameters to reflect each data set. Also, I did look at DOE and I'm not sure how that can help them define the correct number data points.
Re: Resistance as a function of temperatureWhen working with resistance temperature readings in the past I have used the Steinhart-Hart equation to calibrate thermistors (you mentioned resistance sensors, not sure if they are using thermistors). The Steinhart-Hart equation allows the user to develop a calibration curve with only a few readings using a three coefficients (A, B, and C) derived from 3 or more readings. Perhaps they can use this method, using 3 (or more) measurements to develop the calibration curve and current or historical data to estimate uncertainty. This might be a more advantageous route for them if they are using thermistors (though given the min temp of 0 K, perhaps not). https://en.wikipedia.org/wiki/Steinhart%E2%80%93Hart_equation
Re: Resistance as a function of temperatureHey Andrea,
The Nonlinear DOE will identify how many and where measurements should be taken to get accurate model parameter estimates and predictions. For resistance vs. temperature, I expect that the recommended measurements will be more frequent and closer together in non-linear or curved regions where measurements will be more sparse and spread in linear regions. The measurement plan you get from Nonlinear DOE will likely require fewer measurements than they are doing now.
