Sequentially Generated Second Order Quasi D-Optimal Designs for Experiments with Mixture and Process Variables

Balanced, Nearly Optimal Mixture Experiments for Models with Interactions with Process Variables

“…Vuchkov et al [18] and later Kowalski et al [9], extended Scheffé's quadratic model in (2) to include both mixture and process variables using the form…”

“…Vuchkov et al [18] considered nearly D-optimal designs for all cases with and produced tables of designs with a range of design sizes with max where p is the number of parameters in Model 1. These designs, which they called quasi D-optimal, were developed in a sequential manner using a three-stage procedure in which duplicate design points were allowed.…”

“…r which we shall refer to as KCV(3, 2, 17) and KCV(3, 2, 23) respectively, using sub-sets of the design points shown in Figure 2 and the notation KCV(q, r, n). When these designs are projected to the levels -1, 0 and 1 of the individual process variables, they have a complete replicate of the 7-point simplex-centroid mixture design at both the highest and lowest levels for both process variables, and either 3 design points or 9 design points (again involving a complete replicate of the mixture design) at the middle level, i for There is an intuitive appeal about the symmetry and balance achieved in these designs that is not present in the typical D-optimal designs with similar run sizes produced by the search algorithms (see Figures 4(a) and 4(b)), nor in the quasi D-optimal designs of Vuchkov et al [18]. Furthermore, if an estimate of the experimental error variance is available, a test for possible lack of fit for Model 1 could be made.…”

“…The D-, A-and G-criteria values for these designs are compared in Table 2 with the quasi D-optimal designs of Vuchkov et al [18] for and referred to as VDY (3,2,17) and VDY(3, 2, 23), and the D-optimal designs for Model 1 as derived by JMP [14]. The values given in Table 2 are for designs consisting of sub-sets of the complete replicate design in Figure 2 but with no repeated design points included.…”

“…The total design would involve some combination and compromise between the two types of design, that is, the mixture simplex and the conventional response surface design. M Vuchkov et al [18] proposed second-order designs for mixture and process variables, and gave tables of quasi D-optimal designs, sequentially generated using a three-stage procedure, for cases where the total number of mixture ingredients and of process variables was such that Cornell [2] considered combining different models for q r Downloaded by [George Mason University] at 16: 14 15 June 2016 mixture ingredients and process variables and made several suggestions for model-fitting strategies to improve the designs and model forms. Kowalski et al [9] considered a model with selected interaction terms between mixture and process variables, and proposed a new class of designs for this situation.…”