Matlab function for the calculation of G-efficiency and D-efficiency coefficients of D-optimal DoE ?
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I have designed a fractional factorial DoE but I was not able to make the full test plan (1 experiment over the 16 is missing). But, due to the regulation constraints, I have 11 additional experimental conditions, that I would like to valorise for getting the best of this DoE. I would like to determine the D-optimal coeffcient in order to see if I can get a sufficiently good quality for my DoE. Is there a Matlab function that calculate this coefficient ? What about the G-efficiency coefficient ? Thanks by advance and best regards.
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Tom Lane
2012년 11월 7일
The D-optimal design maximizes the determinant of X'*X where X is the design matrix. If you have the Statistics Toolbox you could do things like this:
>> x = x2fx(fracfact('a b c d abcd'),'linear');
>> log(det(x'*x))
ans =
16.6355
>> log(det(x(2:end,:)'*x(2:end,:)))
ans =
16.1655
>> 2*sum(log(svd(x)))
ans =
16.6355
Notice the last one operates directly on x and would be okay even if det(x'*x) overflowed. You could append your other 11 rows to x to compute the value for your design. I don't think that would be an issue in your problem, though.
I'm less familiar with G-optimal designs, but my impression is that you'll want to compute things like
diag(x*((x'*x)\x'))
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Philippe
2012년 11월 20일
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Yangyang Liu
2020년 12월 10일
Thank you very much for your prompt reply.
I think I need to try as much as you do.
Thanks again.
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