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Blocking response surface designs. (English) Zbl 1157.62471
Summary: The design of experiments involving more than one blocking factor and quantitative explanatory variables is discussed, the focus being on two key aspects of blocked response surface designs: optimality and orthogonality. First, conditions for orthogonally blocked experiments are derived. Next, an algorithmic approach to compute \(D\)-optimal designs is presented. Finally, the relationships between design optimality and orthogonality in the context of response surface experiments are discussed in detail.

62K05 Optimal statistical designs
62K20 Response surface designs
Full Text: DOI
[1] Ankenman, B.E.; Avilés, A.I.; Pinheiro, J.C., Optimal designs for mixed effect models with two random nested factors, Statist. sin., 13, 385-401, (2003) · Zbl 1015.62078
[2] Atkinson, A.C.; Donev, A.N., The construction of exact D-optimum experimental designs with application to blocking response surface designs, Biometrika, 76, 515-526, (1989) · Zbl 0677.62066
[3] Atkinson, A.C.; Donev, A.N., Optimum experimental design, (1992), Clarendon Press Oxford · Zbl 0829.62070
[4] Box, G.E.P.; Hunter, J.S., Multi-factor experimental designs for exploring response surfaces, Ann. math. statist., 28, 195-241, (1957) · Zbl 0080.35901
[5] Cook, R.D.; Nachtsheim, C.J., Computer-aided blocking of factorial and response-surface designs, Technometrics, 31, 339-346, (1989) · Zbl 0705.62072
[6] Ganju, J., On choosing between fixed and random block effects in some no-interaction models, J. statist. plann. inference, 90, 323-334, (2000) · Zbl 0958.62069
[7] Ganju, J.; Lucas, J.M., Analysis of unbalanced data from an experiment with random block effects and unequally spaced factors, Amer. statist., 54, 5-11, (2000)
[8] Gilmour, S.G.; Trinca, L.A., Some practical advice on polynomial regression analysis from blocked response surface designs, Comm. statist.: theory methods, 29, 2157-2180, (2000) · Zbl 1061.62550
[9] Gilmour, S.G.; Trinca, L.A., Row-column response surface designs, J. qual. technol., 35, 184-193, (2003)
[10] Goos, P., The optimal design of blocked and split-plot experiments, (2002), Springer New York · Zbl 1008.62068
[11] Goos, P., Donev, A.N., 2006. The D-optimal design of blocked experiments with mixture components. J. Qual. Technol., to appear.
[12] Goos, P.; Tack, L.; Vandebroek, M., The optimal design of blocked experiments in industry, (), 247-279 · Zbl 1311.62116
[13] Goos, P.; Vandebroek, M., D-optimal response surface designs in the presence of random block effects, Comput. statist. data anal., 37, 433-453, (2001) · Zbl 1079.62532
[14] Goos, P.; Vandebroek, M., Estimating the intercept in an orthogonally blocked experiment when the block effects are random, Comm. statist.: theory methods, 33, 873-890, (2004) · Zbl 1066.62076
[15] Khuri, A.I., Response surface models with random block effects, Technometrics, 34, 26-37, (1992) · Zbl 0850.62618
[16] Khuri, A.I., Effect of blocking on the estimation of a response surface, J. appl. statist., 21, 305-316, (1994)
[17] Miller, A.J.; Nguyen, N.K., AS 295—A fedorov exchange algorithm for D-optimal design, Appl. statist., 43, 669-678, (1994)
[18] Trinca, L.A.; Gilmour, S.G., An algorithm for arranging response surface designs in small blocks, Comput. statist. data anal., 33, 25-43, (2000) · Zbl 1061.62551
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