Three-level screening designs

Vander Heyden, Y., Khots, M. S., and Massart, D. L., Three-Level Screening Designs for the Optimization or the Ruggedness Testing of Analytical Procedures, Analytica Chimica Acta 276, 1993, 189-195. 

Y. Vander Heyden, M.S. Khots, D.L. Massart, Three-level screening designs for the optimisation or the ruggedness testing of analytical procedures. Anal. Chim. Acta, 276 (1993) 189-195. 

If nonlinear effects are expected the variables must be varied at more than two levels. A screening plan comparable to the Plackett Burman design but on three levels is that of Box and Behnken [I960]. 

Xu, H., Cheng, S. W., and Wu, C. F. J. (2004). Optimal projective three-level designs for factor screening and interaction detection. Technometrics, 46, 280-292. 

As for full factorial designs the levels of the variables are situated at the borders of the experimental interval for that variable. It is possible that the response function of that variable is curved with an optimum at an intermediate factor level (see Fig. 6.11). The effect calculated from the design can then be small and the variable may be incorrectly considered as non-significant 45. When such intermediate optima are considered possible, a solution can be to perform the screening at three levels by reflecting a... 

Reflected FF and PB designs were applied during robustness testing of CE methods in References 66-71. To screen the factor(s) at three levels, three-... 

In contrast to the simultaneous factorial design study, experimentation by variation of one variable at a time is limited to the estimation of main effects, and no interactions, as are common in analytical chemistry, can be found. What cannot be evaluated with screening designs are curved dependences, that is, for more complicated relationships between responses and factors, designs at three or more factor levels are needed. 

Jones, B., Nachtsheim, C.J., 2011. A class of three-level designs for definitive screening in the presence of second-order effects. Journal of Quality Technology 43, 1—15. 

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