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This topic contains 4 replies, has 4 voices, and was last updated by Chris Seider 4 months, 2 weeks ago.

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hello professionals, i currently a student of TQM, i am working on DOE on a real time practical, but facing difficulty in execution, scenario is, there are 3-factors (continuous in %) and response Ys are 7 with a mean target value of each Y.

For each experimental condition you record the value of each of the 7 responses. When you are finished with the design you build a regression equation for each of the 7 responses. You group the 7 equations together in a computer program and run “what if” analysis for a matrix of the three X variables. You will have a matrix of 7 Y responses for each combination of the three X variables and you can take this output and sort it according to your Y responses with an eye to looking for the best grouping of the 7 Y responses of interest. When you find that “best group” of Y’s – look at the X settings and run confirmation experiments at the identified levels of the X’s and see if the resultant Y’s are within the prediction errors of each of the respective equations.

One thing that really helps in a situation like this is to scale each of your X’s from-1 to 1 before running the regression analysis (we are assuming here that you are NOT running a mixture design – if it is a mixture design then the scaling would have to be from 0 to 1 for each of the X’s). If you do this you can visually inspect the final reduced models for each of the Y’s and get a very good idea of where the trade-offs are going to be with respect to optimizing the 7 Y responses. With 7 responses it is unlikely that you will find a combination of X’s that will simultaneously optimize all 7 responses. What you will find are combinations of the X’s that identify the best trade-offs with respect to predicted Y responses.

If you don’t know how to scale the X’s – here’s how:

For each X find the ACTUAL minimum and maximum value used in the design. Take the individual minimums and maximums and compute the following:

A = (Xmax + Xmin)/2

B = (Xmax – Xmin)/2and compute

Xscaled = [(Xactual – A)/B]

then run the analysis on the scaled X’s

@rbutler – my guess is that you lost him at “For each experimental condition…” But that was a very good and concise description.

Greg ConnerDOE ultiple Responses are easily and very simply handled in the MINITAB MULITPLE RESPONSE OPTIMIZER. Check out MINITAB Website for information.

yes, you can analyze more than one at a time

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