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Designing fractional factorial split-plot experiments with few whole-plot factors. (English) Zbl 1111.62316
Summary: When it is impractical to perform the experimental runs of a fractional factorial design in a completely random order, restrictions on the randomization can be imposed. The resulting design is said to have a split-plot, or nested, error structure. Similarly to fractional factorials, fractional factorial split-plot designs can be ranked by using the aberration criterion. Techniques that generate the required designs systematically presuppose unreplicated settings of the whole-plot factors. We use a cheese-making experiment to demonstrate the practical relevance of designs with replicated settings of these factors. We create such designs by splitting the whole plots according to one or more subplot effects. We develop a systematic method to generate the required designs and we use the method to create a table of designs that is likely to be useful in practice.

MSC:
62K15 Factorial statistical designs
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[1] Addelman S., Technometrics 6 pp 253– (1964)
[2] Bingham D., Technometrics 41 pp 62– (1999)
[3] Bingham D., Proc. Phys. Engng Sci. Sect. Am. Statist. Ass. (2000)
[4] Bingham D., J. Qual. Technol. 32 pp 2– (2001)
[5] Bingham D., Technometrics 45 pp 80– (2003)
[6] Bisgaard S., Technometrics 36 pp 308– (1994)
[7] Bisgaard S., J. Qual. Technol. 32 pp 39– (2000)
[8] Box G. E. P., J. Appl. Statist. 19 pp 3– (1992)
[9] Chen J., Int. Statist. Rev. 61 pp 131– (1993)
[10] Daniel C., Technometrics 1 pp 311– (1959)
[11] Finney D. J., Ann. Eugen. 12 pp 291– (1943) · doi:10.1111/j.1469-1809.1943.tb02333.x
[12] Fisher R. A., Ann. Eugen. 11 pp 341– (1942) · doi:10.1111/j.1469-1809.1941.tb02298.x
[13] Fries A., Technometrics 22 pp 601– (1980)
[14] Goos P., J. Qual. Technol. 33 pp 436– (2001)
[15] Huang P., Technometrics 40 pp 314– (1998)
[16] Kempthorne O., The Design and Analysis of Experiments (1952) · Zbl 0049.09901
[17] Letsinger J. D., J. Qual. Technol. 28 pp 381– (1996)
[18] Loeppky J. L., J. Qual. Technol. 34 pp 229– (2002)
[19] DOI: 10.1080/02664769922377 · Zbl 0939.62081 · doi:10.1080/02664769922377
[20] Schoen E. D., J. Qual. Technol. 32 pp 276– (2000)
[21] Sitter R. R., Technometrics 39 pp 382– (1997)
[22] Wu C. F. J., Experiments: Planning, Analysis, and Parameter Design Optimization (2000) · Zbl 0964.62065
[23] Yates F., Technical Communication 35 (1937)
[24] Y. Zhu (2000 ) A theory of experimental design for multiple groups of factors .PhD Thesis. Department of Statistics, University of Michigan, Ann Arbor.
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.