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After reading and applying many examples of DoE I have a question that has been bugging me and haven't found an answer so far.

Usually what we see in an example or publication is the design table with one response value for each run. But I assume this response is actually an average measurement from the variable of interest, and there is therefore an associated error with the measurement. Is the measurement error completely irrelevant because of the replicate runs? It seems to me that this might provide valuable information, to take into account the error given by the measurement device itself, but I haven't been able to find any discussion about it.

I hope my questio is clear. Any pointers on how this is handled would be greatly appreciated.

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First one needs to define the purpose for the experiment. Is is to determine the most influential factors, optimize the process or understanding interactions between the different factors? Depending on the objective, the DOE is just the start of the process, with additional confirmations or refinements as a follow-up to the initial test.

The goal of a well designed DOE is to gather the most amount of information in the least number of experimental runs, thus avoiding repeating runs. Your concern of measurement error is valid one but there are ways to account for that error in a well designed experiment.

  • It is assumed the measurement error in uniformed across all measurements and is not controlled
  • In a well designed experiment the magnitude of the measured effect is much larger then the measurement error. For example if going from the low to high condition results in 1-2 degree difference and your thermometer is accurate to 1 degree, this was not well designed, and thus that factor is not significant.
  • In a balanced block design, every condition for each factor is measured an equal number of times. For a basic 2x2 factorial design with "A" & "B" as factors, "A" at the high level and at the low level are each measured twice and the same goes for factor B, thus providing a level of replication.
  • Finally, the is the option of adding an additional center point to the experimental, and by replicating that measurement over the course of the experiment it provide an estimate of curvature and measurement repeatability.
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  • $\begingroup$ Thank you for the detailed answer Dave. $\endgroup$ – EG137 Jul 9 at 7:56

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