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Hi… I am working on an unconventional method to measure electrical resistivity of a material over time… There are three controllable variables (frequency, voltage, wave form) and I have chosen 3 levels for each (for example voltage could be 2V,5V, or 8V)…You can see an example of measurements (repeated 3 times with same test conditions) during 48 hours (attached pic)… I want to use Taguchi method to find the test conditions which leads to the minimum variations in resistivity readings(the resistivity value itself is not that important as the device will be calibrated, but I need to reach the highest repeatability) ….So now the question is that what should I choose as response variable (since readings are continuous)? I need a measure to show the variations over 48-hour time so I cannot use the resistivity in a single time point…thanks in advance!

The issue you are dealing with is one of repeated measures. The Y variable is resistivity. If your design allows you to test for main effects, curvilinear effects and two way interactions then, in addition to all of these terms you will have to investigate time, curvilinear time, and the interactions of the time terms with all of the terms from the design.

If your example plot is typical you will have to accept the fact that your variability is not constant over time. This means your definition of minimum variance will be time dependent.To address all of this you will need to have access to a statistics package that can handle repeated measures and that will allow you to specify the covariance structure of the repeated measures. If we express this in SAS (the program I use) the code would be

proc mixed data = datasetname;

class experimentno tval;

model resistance = x1 x2 x3 x1x2 x1x3 x2x3 x1sq x2sq x3sq x1*time x2*time x3*time …etc./s ddfm = bw;

repeated tval/type = ar(1) subject = experimentno;

run;Once you have this set up you will have to run backward elimination to identify the significant terms in the reduced model.

In the data set you would have to set the tval = time and define it as a class variable along with experimentno. You need to do this so that the program knows how to align the responses between the experiments across time. Based on your graph the choice of first order autoregressive for the covariance structure of the repeated measures would make sense. The subject containing all of those repeated measures are the individual experiments.

Given the complexity of the curves and the fact that the variance does not appear to be constant across time the simplest way to identify the settings for minimum variance would be graphical. There is probably a way run a Box-Meyer’s analysis (the method for identifying the combination of terms and levels providing minimum variance) but, offhand I can’t think of how to do that with this kind of data. As for Taguchi – it won’t do much of anything for you in this instance.

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