zbMATH — the first resource for mathematics

An algorithm for arranging response surface designs in small blocks. (English) Zbl 1061.62551
Summary: We consider the problem of blocking response surface designs when the block sizes are prespecified to control variation efficiently and the treatment set is chosen independently of the block structure. We show how the loss of information due to blocking is related to scores and present an interchange algorithm based on scores to improve a given blocked design. Examples illustrating the performance of the algorithm are given and some comparisons with other designs are made.

62K20 Response surface designs
62K10 Statistical block designs
Full Text: DOI
[1] Atkinson, A.C., 1996. The usefulness of optimum experimental designs (with discussion). J. Roy. Statist. Soc. Ser. B 57(1), 59–76; discussion 95–111. · Zbl 0850.62602
[2] Atkinson, A. C.; Donev, A. N.: The construction of exact D-optimum experimental designs with application to blocking response surface designs. Biometrika 76, No. 3, 515-526 (1989) · Zbl 0677.62066
[3] Atkinson, A.C., Donev, A.N., 1992. Optimum Experimental Designs. Oxford University Press, Oxford. · Zbl 0829.62070
[4] Box, G. E. P.: Choice of response surface design and alphabetic optimality. Utilitas math. 21, No. B, 11-55 (1982) · Zbl 0524.62073
[5] Box, G.E.P., Draper, N.R., 1987. Empirical Model-Building and Response Surfaces. Wiley, New York. · Zbl 0614.62104
[6] Cook, R. D.; Nachtsheim, C. J.: Computer-aided blocking of factorial and response surface designs. Technometrics 31, No. 3, 339-346 (1989) · Zbl 0705.62072
[7] Edmondson, R. N.: Agricultural response surface experiments based on four-level factorial designs. Biometrics 47, No. 4, 1435-1448 (1991)
[8] Edmondson, R. N.: Fractional factorial designs for factors with a prime number of quantitative levels. J. roy. Statist. soc. Ser. B 56, No. 4, 611-622 (1994) · Zbl 0800.62490
[9] John, J.A., Williams, E.R., 1995. Cyclic and Computer Generated Designs. Chapman & Hall, London. · Zbl 0865.05010
[10] Khuri, A. I.: Effect of blocking on the estimation of a response surface. J. appl. Statist. 21, No. 4, 305-316 (1994)
[11] Khuri, A.I., Cornell, J.A., 1996. Response Surfaces, 2nd Edition. Marcell Dekker, New York. · Zbl 0953.62073
[12] Mead, R., 1988. The Design of Experiments. Cambridge University Press, Cambridge.
[13] Mead, R.: The non-orthogonal design of experiments (with discussion). J. roy. Statist. soc. Ser. A 153, No. 2, 151-201 (1990) · Zbl 1002.62508
[14] Mead, R., Jayawardena, D.S., Fletcher, D.J., 1995. The use of contrast scores to develop appropriate block-treatment designs. Applied Statistics Technical Report 95/3, The University of Reading, Reading.
[15] Myers, R.H., Montgomery, D.C., 1995. Response Surface Methodology. Wiley, New York. · Zbl 1161.62392
[16] Nguyen, N.-K., 1997. CUT: A program for blocking fractional factorial and response surface designs. User’s note, CSIRO, Sydney.
[17] Pearce, S. C.: Row-and-column designs. Appl. statist. 24, No. 1, 60-74 (1975)
[18] SAS Institute, 1995. SAS/QC Software, Version 6. SAS Institute Inc., Cary.
[19] Searle, S.R., 1982. Matrix Algebra Useful for Statistics. Wiley, New York. · Zbl 0555.62002
[20] Trinca, L. A.; Gilmour, S. G.: Variance dispersion graphs for comparing blocked response surface designs. J. qual. Technol. 30, No. 4, 314-327 (1998)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.