In the pre-computer age, for ease of analysis, design of experiments (DOEs) require certain balanced structure. Example of this type of DOEs are the well-known partially balanced incomplete block designs (PBIBDs) and balanced fractional factorial (BFF) designs. While these designs can be analyzed fairly easily by a hand-calculator, they are not necessarily good ones in terms of optimality. Plan T69 in Clatworthy (1973) for a 2-resolvable IBD of size (v,k,r)=(21,6,10), for example, is a very poor design in most situations as it does not make sense for certain pairs of treatments to appear together in five blocks while certain pairs never appear together in any of the blocks. An alternative computer-generated solution is in http://designcomputing.net/gendex/ibd/b10.html. For this solution, 105 pairs of treatments appear together in two blocks and 105 pairs of treatments appear together in three blocks.
As an additional example, the 210-BFF design in 76 runs of Chopra, et al. (1986) has A-efficiency E=28.2. The alternative computer-generated solution listed in Nguyen & Miller (1997) has A-efficiency E=86.3. The variances of the mean, each main effect and each 2-factor interaction of the former are 0.063903, 0.030147 and 0.049988 respectively. For the latter, the variance of the mean is 0.013731, the variances of the main effects range from 0.014736 to 0.015369, the variances of the 2-factor interactions range from 0.014736 to 0.019691. Clearly, the variances of the computer-generated solution particularly those of the main effects are within a very small range and uniformly smaller than those of the corresponding BFF design.
Recognizing the importance of computer-generate DOEs in research, Design Computing is set up to (i) promote a new philosophy of designing experiments, i.e. Design for the experiment, do not experiment for the design; (ii) to promote the use of computer-generated designs in industrial settings where it is difficult to adjust the experimental materials to published plans and in agricultural research stations in remote areas where it is easier to get access to a PC than to various catalogues and professional journals to find a usable plan; (iii) to foster research and research cooperation in computer-generated designs. The Gendex DOE toolkit has been used to achieve the first two objectives.
©2008 Design Computing