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Sankhya B

, Volume 81, Issue 1, pp 93–122 | Cite as

Inter-Class Orthogonal Main Effect Plans for Asymmetrical Experiments

  • Sunanda BagchiEmail author
Article
  • 7 Downloads

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.

Keywords

Main effect plans Inter-class orthogonality 

AMS (2000) subject classification

62k10 

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Notes

Acknowledgments

The author is extremely grateful to the reviewers for all the thoughtful suggestions which have improved the presentation of the paper considerably. The author also express her gratitude to Professor J.P. Morgan of Virginia Tech for many fruitful discussions.

References

  1. Addelman, S. (1962). Orthogonal main effect plans for asymmetrical factorial experiments. Technometrics4, 21–46.MathSciNetCrossRefGoogle Scholar
  2. Bagchi, S. (2010). Main effect plans orthogonal through the block factor. Technometrics52, 243–249.MathSciNetCrossRefGoogle Scholar
  3. Dey, A. (1985). Orthogonal fractional factorial designs. John wiley, New York.zbMATHGoogle Scholar
  4. Dey, A. and Mukherjee, R. (1999). Fractional factorial plans. Wiley Series in probability and Statistics.Google Scholar
  5. Hedayat, A.S., Sloan, N.J.A. and Stufken, J. (1999). Orthogonal arrays, Theory and applications, Springer series in statistics.Google Scholar
  6. Huang, L., Wu, C.F.J. and Yen, C.H. (2002). The idle column method : Design construction, properties and comparisons. Technometrics44, 347–368.MathSciNetCrossRefGoogle Scholar
  7. Jones, B. and Nachtsheim, C.J. (2013). Definitive screening designs with added two-level categorical factors. Jour Qual. Tech.45, 121–129.CrossRefGoogle Scholar
  8. Ma, C.X., Fang, K.T. and Liski, E. (2000). A new approach in constructing orthogonal and nearly orthogonal arrays. Metrika50, 255–268.MathSciNetCrossRefGoogle Scholar
  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.MathSciNetCrossRefGoogle Scholar
  10. Nguyen, N. (1996). A note on the construction of near-orthogonal arrays with mixed levels and economic run size. Technometrics38, 279–283.MathSciNetCrossRefGoogle Scholar
  11. Starks, T.H. (1964). A note on small orthogonal main effect plans for factorial experiments. Technometrics8, P, 220–222.CrossRefGoogle Scholar
  12. Wang, J.C. and Wu, C.F.J. (1992). Nearly orthogonal arrays with mixed levels and small runs. Technometrics34, 409–422.CrossRefGoogle Scholar
  13. Xiao, L., Lin, D.K.J. and Fengshan, B. (2012). Constructing definitive screening designs using conference matrices. Jour. Qual. Tech.44, 1–7.CrossRefGoogle Scholar

Copyright information

© Indian Statistical Institute 2019

Authors and Affiliations

  1. 1.Theoretical Statistics and Mathematics UnitIndian Statistical InstituteBangaloreIndia

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