×

Algorithm for determining whether various two-level fractional factorial split-plot row-column designs are non-isomorphic. (English) Zbl 1184.62136

Summary: The confounding and aliasing scheme for fractional factorial split-plot designs with the units within each wholeplot arranged in rows and columns is described and illustrated. Isomorphisms for this design type are described, together with a procedure which considers extensions of the concepts of wordlength patterns and letter patterns that can be used to test isomorphism between designs. Using in part this isomorphism testing procedure, a construction algorithm that may be used to obtain a complete set of such non-isomorphic two-level designs is described. Software based on this construction algorithm was used to obtain a complete set of non-isomorphic designs for up to five wholeplot factors, five subplot factors and up to 64 runs, which is presented as a table of designs. To aid the experimenter in distinguishing between competing designs, the estimation capacity sequence for each design is presented.

MSC:

62K15 Factorial statistical designs
62K10 Statistical block designs
65C60 Computational problems in statistics (MSC2010)
62Q05 Statistical tables
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.2307/2983638 · doi:10.2307/2983638
[2] Bartlett M. S., Suppl. J. Roy. Statist. Soc. 2 pp 224– (1935)
[3] DOI: 10.1080/02664769200000001 · doi:10.1080/02664769200000001
[4] DOI: 10.2307/1270995 · doi:10.2307/1270995
[5] Mukerjee R., Statist. Sinica 12 pp 885– (2002)
[6] DOI: 10.1198/004017004000000176 · doi:10.1198/004017004000000176
[7] DOI: 10.1360/04ys0069 · Zbl 1076.62080 · doi:10.1360/04ys0069
[8] R.D. Stapleton, S.M. Lewis, and A.M. Dean,Two level fractional factorial experiments in split-plot row–column designs(2008), accepted for publication
[9] DOI: 10.2307/2346973 · doi:10.2307/2346973
[10] DOI: 10.2307/1403599 · Zbl 0768.62058 · doi:10.2307/1403599
[11] Clark J. B., Statist. Sinica 11 pp 537– (2001)
[12] Sun, D. X. 1993. ”Estimation capacity and related topics in experimental designs”. University of Waterloo. Ph.D. Diss
[13] DOI: 10.1214/aos/1024691471 · Zbl 0927.62076 · doi:10.1214/aos/1024691471
[14] DOI: 10.1111/1467-9868.00164 · Zbl 0913.62072 · doi:10.1111/1467-9868.00164
[15] Chen H. H., Statist. Sinica 14 pp 203– (2004)
[16] DOI: 10.1214/aos/1009210551 · Zbl 1041.62064 · doi:10.1214/aos/1009210551
[17] DOI: 10.1016/S0378-3758(02)00459-7 · Zbl 1011.62077 · doi:10.1016/S0378-3758(02)00459-7
[18] DOI: 10.1214/aoms/1177706888 · Zbl 0081.36405 · doi:10.1214/aoms/1177706888
[19] DOI: 10.1214/aoms/1177698780 · Zbl 0158.37404 · doi:10.1214/aoms/1177698780
[20] DOI: 10.1214/aoms/1177696965 · Zbl 0227.62046 · doi:10.1214/aoms/1177696965
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.