Experimental design with environmental variables

In this section it is supposed that the environmental variation is deliberately introduced into the experiment by including in the experimental design environmental variables that are controlled at predetermined settings during the experiment. Freeny and Nair [35] considered robust design experiments with uncontrollable, but measureable, environmental variables. Their approach will not be considered here in this chapter it will be assumed that environmental variables can be controlled during the experiment. 

the experimental designs advocated by Taguchi can require a prohibitively large number of runs. 

An alternative approach is to regard the enviroiunental variables as standard experimental variables and to apply the techniques associated with response surface methodology to the combined set of design and environmental variables (see Welch, Yu, Kang, and Sacks [36], Shoemaker, Tsui, and Wu [37], and Box and Jones [38]). This approach can result in considerably smaller and therefore cheaper experiments. 

As an example of the reduction in the size of the experiment, consider the tablet formulation study of Table 2.1 which had three quantitative design variables, x, x, x and two quantitative environmental variables, Zj, z. Suppose that all of the variables, both design and environmental, are to be studied at three settings (coded -1, 0, +1), and that each combination was to be run independently and the experiment fully randomized. 

TAGUCm-DESIGN FOR THREE DESIGN VARIABLES AND TWO ENVIRONMENTAL VARIABLES 

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Analysis of experimental designs with environmental variables... 

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