TY - JOUR
AU - Draper, N. R.
AB -  Two of the basic approaches to choosing an n-point experimental design in many industrial situations are (i) to set down a simple factorial or fractional factorial design in the factors being studied, or (ii) to choose a design based on the well-known |X′X| criterion. Experimenters often prefer (i) due to its simplicity; our viewpoint here is that (ii) is much better. We first indicate some situations for which (when all the factors are restricted to a cuboidal region) the factorial approach is optimal, as judged by the |X′X| criterion, but the assumed models are often not sensible ones in practical work. We then examine what (similarly restricted) designs are optimal under the |X′X| criterion for the standard linear models of first and second order; because of the very rapid increase in computational difficulties, we consider only “cube plus star” type designs for k ≥ 3 (except for k = 3, n = 10). In spite of computational requirements, we recommend use of the |X′X| criterion in general rather than the indiscriminate use of factorials and we briefly discuss the reasons why, both for linear and nonlinear model situations. 
TI - Factorial Designs, the |X′X| Criterion, and Some Related Matters
JF - Technometrics
DO - 10.1080/00401706.1971.10488845
DA - 1971-11-01
UR - https://www.deepdyve.com/lp/taylor-francis/factorial-designs-the-x-x-criterion-and-some-related-matters-c3IYqnjFnw
SP - 731
EP - 742
VL - 13
IS - 4
DP - DeepDyve
ER -