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Inter-Class Orthogonal Main Effect Plans for Asymmetrical Experiments

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  • Sunanda Bagchi

    (Indian Statistical Institute)

Abstract

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 330 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 310210 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 (≤ 15 runs) are also constructed by ad-hoc methods. Among these plans there are MEPs for a 42.32.2 and a 35.2 experiment on 12 runs and a 52.32 experiment on 15 runs.

Suggested Citation

  • Sunanda Bagchi, 2019. "Inter-Class Orthogonal Main Effect Plans for Asymmetrical Experiments," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 93-122, June.
    • Handle: RePEc:spr:sankhb:v:81:y:2019:i:1:d:10.1007_s13571-018-0175-0
    DOI: 10.1007/s13571-018-0175-0
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