FDE to assess run-to-run variability: works with B/P-spline but not Wavelet (?)Hello,
Background : I have been working on using FDE to assess run-to-run variability for each Sensor on the example provided here, it works when using B-spline but not Wavelet. In the jmp file "1 - Furnace_10_Sensors_5_Runs.jmp", running the script "FDE by Sensor" (to assess run-to-run Variability)", I run FDE by "Sensor" without ID. For each Sensor I then save the summaries. From each Summary table ( e.g. "S1_B-Spline Model Summaries (Degree=3, Knots=9).jmp" ) I copy/paste the formula located in column :"Temperature (°C) Mean Function Formula"n back to the initial table in column 9 (i.e.: "Temp by sensor "n) which contain a Match() function to align correctly formula for each Sensor. I calculate in column 10 ("Residuals (by sensor) "n) the difference between the observed Temperature and the previous formula in order to assess run-to-run variability (see script "Residuals vs. Time (min)"). I'm happy with that.
Problem : For another example I'm using Wavelet rather than B-spline (because Diagnostic plots is much better when using Wavelet on this other example not provided here) and I'm stuck. For sake of demonstration if I run Model=Wavelet rather than B-spline on "1 - Furnace_10_Sensors_5_Runs.jmp", when saving Summaries ("S1_Wavelets Model Summaries (Wavelet=Symlet 6.jmp") I don't have the column :"Temperature (°C) Mean Function Formula"n but only Father Wavelet column and additional columns but none of them contain a formula that I could copy/paste back to the initial table so I'm stuck.
Question 1: is there a workaround when using Wavelet ? or do I need to use B or P-spline ?
Question 2: does anyone developped a script for easing the step of getting formulas from the various Summary tables and copy/paste back to the initial table in a single column where it Match() each formula to the appropriate condition ?
Note: analysis inspired by Colleen McKendry (2023-EU-30MP-1316)
Re: FDE to assess run-to-run variability: works with B/P-spline but not Wavelet (?)Hi @Emmanuel_Romeu ,
great example first of all, thanks for sharing.
You should be able to get those formulae in general, but I have encountered something similar once. I believe it was du to the number of individual curves, if I remember correct.
I just tried to save out summaries from your example table, by setting up FDE with "Sensor_Run" as ID variable:
In that case I was able to get the formulae you asked for.
So not the perfect answer or solution, but maybe it guides you towards an answer.
Would be happy to hear what your solution looks like 
BEst
Florian
Re: FDE to assess run-to-run variability: works with B/P-spline but not Wavelet (?)Hello,
After talking to Peter Hersh, I think we have found a solution.
Problem: when running without "ID" and saving the summaries, there are no formulas when using the wavelet, whereas there are when using the B/P splines models. Let's do it differently.
Workaround: When running with "ID = Sensor", we get 10 functions, one for each sensor, each containing the data from 5 curves/runs. However, the average curve is across all sensors, so I can't directly assess the run-to-run variability for each sensor.
By selecting a sensor in the score plot, for example S1, the FPCs are filled in the FPC Profiler. Using the simulator, we can simulate the result for the mean curve. Keep the FPCs fixed, set the time as random and cover the range from 1 to 60 minutes. I recommend using an external table in this example to target integers perfectly. Because of the random function, there are missing time points and duplicates, so make more runs than necessary and remove duplicates. From the simulated table, copy/paste into the original table, in a new column, the temperature values corresponding to the average curve opposite the appropriate rows (here, rows 1 to 300 corresponding to the 5 runs of 60 minutes for S1). Then calculate Residuals.
Note: I’ve added 2 columns ate the end of the table and a script at the end of the scripts for illustration. I did it for S1 only, not the remaining Sensors, as this table is provided only as an example. This process will be applied on other datasets where Wavelet is necessary (on this one B-spline works well).
Thanks Peter for the help.
