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Inter-class orthogonal main effect plans for asymmetrical experiments. (English) Zbl 1428.62362

Summary: In this paper we construct ‘inter-class orthogonal’ main effect plans (MEPs) for asymmetrical experiments. In such a plan, the factors are partitioned into classes so that any two factors from different classes are orthogonal. We have also defined the concept of “partial orthogonality” between a pair of factors. In many of our plans, partial orthogonality has been achieved when (total) orthogonality is not possible due to divisibility or any other restriction. We present a method of obtaining inter-class orthogonal MEPs. Using this method and also a method of ‘cut and paste’ we have obtained several series of inter-class orthogonal MEPs. One of them happens to be a series of orthogonal MEP (OMEPs) [see Theorem 3.6], which includes an OMEP for a \(3^{30}\) experiment on 64 runs. We have also obtained a series of MEPs which are almost orthogonal in the sense that every contrast is non-orthogonal to at most one more. A member of this series is an MEP for a \(3^{10}2^{10}\) experiment on 32 runs in which the only non-orthogonality is between the linear contrasts of pairs of three-level factors. Plans of small size \(( \leq 15\) runs) are also constructed by ad-hoc methods. Among these plans there are MEPs for a \(4^2.3^2.2\) and a \(3^5.2\) experiment on 12 runs and a \(5^2.3^2\) experiment on 15 runs.

MSC:

62K15 Factorial statistical designs
62K05 Optimal statistical designs
62K10 Statistical block designs
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References:

[1] Addelman, S. (1962). Orthogonal main effect plans for asymmetrical factorial experiments. Technometrics4, 21-46. · Zbl 0116.36704 · doi:10.1080/00401706.1962.10489985
[2] Bagchi, S. (2010). Main effect plans orthogonal through the block factor. Technometrics52, 243-249. · doi:10.1198/TECH.2010.07044
[3] Dey, A. (1985). Orthogonal fractional factorial designs. John wiley, New York. · Zbl 0626.62077
[4] Dey, A. and Mukherjee, R. (1999). Fractional factorial plans. Wiley Series in probability and Statistics. · Zbl 0930.62081
[5] Hedayat, A.S., Sloan, N.J.A. and Stufken, J. (1999). Orthogonal arrays, Theory and applications, Springer series in statistics. · Zbl 0935.05001
[6] Huang, L., Wu, C.F.J. and Yen, C.H. (2002). The idle column method : Design construction, properties and comparisons. Technometrics44, 347-368. · doi:10.1198/004017002188618545
[7] Jones, B. and Nachtsheim, C.J. (2013). Definitive screening designs with added two-level categorical factors. Jour Qual. Tech.45, 121-129. · doi:10.1080/00224065.2013.11917921
[8] Ma, C.X., Fang, K.T. and Liski, E. (2000). A new approach in constructing orthogonal and nearly orthogonal arrays. Metrika50, 255-268. · Zbl 1093.62563 · doi:10.1007/s001840050049
[9] Morgan, J.P. and Uddin, N. (1996). Optimal blocked main effect plans with nested rows and columns and related designs. Ann. Stat.24, 1185-1208. · Zbl 0862.62065 · doi:10.1214/aos/1032526963
[10] Nguyen, N. (1996). A note on the construction of near-orthogonal arrays with mixed levels and economic run size. Technometrics38, 279-283. · Zbl 0902.62089 · doi:10.1080/00401706.1996.10484508
[11] Starks, T.H. (1964). A note on small orthogonal main effect plans for factorial experiments. Technometrics8, P, 220-222. · doi:10.1080/00401706.1964.10490166
[12] Wang, J.C. and Wu, C.F.J. (1992). Nearly orthogonal arrays with mixed levels and small runs. Technometrics34, 409-422. · Zbl 0850.62623 · doi:10.1080/00401706.1992.10484952
[13] Xiao, L., Lin, D.K.J. and Fengshan, B. (2012). Constructing definitive screening designs using conference matrices. Jour. Qual. Tech.44, 1-7. · doi:10.1080/00224065.2012.11917876
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