No abstract

No abstract

No abstract

No abstract

No abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. Miscellanea 147When the centre point is somewhat more heavily weighted than the other points in the design, the procedure generally followed in practice, the design will perform well by all criteria. Box & Behnken recommended three centre points to make the variance profile relatively flat near the centre of the design. This increases the E-and A-efficiencies and decreases the D-and G-efficiencies slightly. As additional centre points also allow an independent estimate of experimental error, their recommendation is a good one.The centre point weight giving the highest E-efficiency has the lowest efficiencies by the other criteria. E-optimality can be described as minimizing the variance of the linear combination of regression coefficients having maximum variance. For a second or higher order polynomial model, this optimization, which combines regression coefficients of different orders, is less intuitively pleasing than the other optimality criteria. The other optimality criteria illustrate Kiefer's (1975) point that finding a design optimum by one criterion often gives a design that performs well by other criteria. REFERENCES

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.

No abstract