Sequentially Generated Designs

Abstract

Procedures for sequential generation of nearly D-optimal designs are described. Two kinds of des i p can be obtained: symmetrical block designs and nonsymmetrical onm. It is shown that in a special case when the number of the support points of a continuous D-optimal design equals to the number of regression coefficients the sequential designs can be constructed very easy without use of a computer. A Catalogue containing 135 designs has bean developed by use of these procedures. 34 of them can be used for experiments in cuboidal factor space and the remaining for experiments with mixture and process variables. Comparison with other designs is done. 7 8 9 10 11 12 13 14 15 Pesotchinsky D P [21] 42 0.97 0.98 50 0.98 0.98 66 0.99 0.97 Pesotchinsky DB [21] Optimalcomposite[18] 34 0.94 0.96 42 0.90 0.96 76 0.86 0.99 Optimal composite with j/2-replication [18] 26 0.87 0.91 44 0.87 0.93 78 0.85 0.96 Exact D-optimal [7] HARTLEY [11] 17 0.60 0.89 27 0.84 0.91 29 0.49 0.82 47 0.51 0.89 BOX-BEHKKEN [5] 27 0.52 0.97 46 0.33 0.97 54 0.45 0.96 62 0.40 0.93 RECHTSCI~APNER [23] 15 0.80 0.87 21 0.89 0.84 28 0.81 0.81 36 0.70 0.78 Rotatable [4] 31 0.16 0.99 52 0.09 0.98 Rotatable with i/2-replication [4] 32 0.13 0.93 53 0.07 0.95 92 0.04 0.98 Orthogonal central composite [4] 25 0.39 0.96 43 0.42 0.96 77 0.18 0.98 Orthogonal central composite with 1/2-replication [4] 27 0.28 0.91 45 0.29 0.93 79 0.14 0.96 HOKE D, [13] 19 0.84 0.91 26 0.90 0.91 34 0.82 0.88 43 0.71 0.88 BOX-DRAPER [6] 15 0.77 0.87 21 0.63 0.84 28 0.42 0.81 36 0.42 0.78 WESTLAKE [33] 23 0.52 0.89 41 0.46 0.85 34 0.90 0.99 15 0.88 0.87 569-575. 17-25.MOSCOW, 69-79.

Study of the molar mass of grafted polystyrene onto cellulose by the probability indices optimization

“…In Table 1, the D-optimal experimental design from the catalogue (Vuchkov et al, 1980) is presented in accordance with the number of variables and ranges of its variation. Two checking and two replicate experiments were done for the statistical analysis of the model adequacy and significance of the coefficients.…”

Simulation and optimization of cellulose and styrene graft copolymerization process

“…Considering that one of the mixture constituents (water) is present in large amounts, the other mixture variable can be studied using a factorial design by using the ratios of the mixture ingredients with water. Such a procedure will permit the simplification of the design matrix and allows us to use the least squares method combined with D-optimal design (Vuchkov et al, 1978). The fitted model will have the following form:…”

“…the combined influence of mixture and processing factors on the grafting may be estimated by the third block of terms. To obtain the fitted models coefficients (Mino and Kaizerman, 1958), the Doptimal design was chosen from Vuchkov's catalogue (Vuchkov et al, 1978). This design consists of 28 runs and is presented in Table 1.…”

“…To realize this procedure (Vuchkov et al, 1978), the modified "complex method" of Box (Voznesensky et al, 1989) is proposed. This method modification allows to find the decision X for non linear function with connected variables in such areas as cubes, simplex etc.. .…”