The Good News—and Bad News—About DOE

Think of the principles in building a table

In my last column I explained how many situations have an inherent response surface, which is the “truth.” However, any experimental result represents this true response, which is unfortunately obscured by the process’s common-cause variation. Regardless of whether you are at a low state of knowledge (factorial) or a high state of knowledge, the same sound design principles apply.

The contour plot: a quadratic ‘French curve’

Response surface methodology’s objective is to model a situation by a power series truncated after the quadratic terms. In the case of three independent variables (x1, x2, x3), as in the tar scenario from my column, “90 Percent of DOE Is Half Planning,” in May 2016:

Y = B0 + (B1 x1) + (B2 x2) + (B3 x3) + (B12 x1 x2) + (B13 x1 x3) + (B23 x2 x3) + [B11 (x1**2)] + [B22 (x2**2)] + [B33 (x3** 2)]

Which designs give the best estimates of these B coefficients?

…

Want to continue?

By logging in you agree to receive communication from Quality Digest. Privacy Policy.

Create a FREE account

Forgot My Password

Comments

Bravo

I liked this article a lot...for too many reasons to list. Thanks!

Excellent Article

I picked up a few teaching things today - always a good day when you teach an old dog a new trick or two. My default is central composite designs for the simplicity and sequential nature that you can take when on the DOE journey. However, I've been faced with "gotta do it all in one design" and you've convinced me to look at BB designs instead. Also like the legs on the table analogy - I am definitely stealing that - I've seen that way too many times.

Steal away!

Thank you for your very kind feedback. I'm glad it will improve your teaching of DOE. We're all colleagues -- so by all means, steal the table top analogy!

Stay tuned: there are four more articles to follow in this series. When I said in my April Fool's day article that DOE was maybe the only thing salvagable from most statistical training, I thought I'd better weigh in with some vital basics that can easily get lost -- and there are quite a few!

Davis