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Journal of Statistical Theory and Practice

, Volume 7, Issue 4, pp 774–782 | Cite as

Construction of Search Designs From Orthogonal Arrays

  • P. Angelopoulos
  • K. Chatterjee
  • C. Koukouvinos
Article

Abstract

Search designs form an important class of experimental designs that allow the identifying of the true model, consisting of a set of factorial effects, among many. Most of the work in this field has been made in the cases where there are at most one or two two-factor interaction effects considered nonnegligible. This article focuses on model identification through the use of search linear models containing, apart from the general mean and the main effects, up to five nonnegligible two-factor interaction effects. The new search designs are based exclusively on orthogonal arrays.

Keywords

Orthogonal arrays Search designs Probability of correct searching 

AMS Subject Classification

Primary 62K15 Secondary 05B20 

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References

  1. Deng, L.-Y., and B. Tang. 2002. Design selection and classification for Hadamard matrices using generalized minimum abberation criteria. Technometrics, 44, 173–184.MathSciNetCrossRefGoogle Scholar
  2. Ghosh, S. 1980. On main effect plus one plans for 2m factorials. Ann. Stat., 8, 922–930.CrossRefGoogle Scholar
  3. Ghosh, S., T. Shirakura, and J.N. Srivastava. 2007. Model identification using search linear models and search designs. Bolyai Soc. Math. Stud., Entropy Search Complexity, 16, 85–112.MathSciNetCrossRefGoogle Scholar
  4. Ghosh, S., and L. Teschmacher. 2002. Comparison of search designs using search probabilities. J. Stati. Plan. Inference, 104, 439–458.MathSciNetCrossRefGoogle Scholar
  5. Hedayat, A. S., N. J. A. Sloane, and J. Stufken. 1999. Orthogonal arrays: Theory and application. New York, NY: Springer-Verlag.CrossRefGoogle Scholar
  6. Ohinishi, T., and T. Shirakura. 1985. Search designs for 2m factorial experiments. J. Stat. Plan. Inference, 11, 241–245.CrossRefGoogle Scholar
  7. Sarkar, A., and K. Chatterjee. 2010. An MEP.2 plan in 3n factorial experiment and its probability of correct identification. J. Stat. Plan. Inference, 140, 3531–3539.CrossRefGoogle Scholar
  8. Shirakura, T. 1991. Main effect plus one or two plans for 2m factorials. J. Stat. Plan. Inference, 27, 65–74.CrossRefGoogle Scholar
  9. Shirakura, T., T. Takahashi, and J. N. Srivastava. 1996. Searching probabilities for nonzero effects in search designs for the noisy case. Ann. Stat., 24, 2560–2568.MathSciNetCrossRefGoogle Scholar
  10. Shirakura, T. and S. Tazawa. 1991. Series of main effect plus one or two plans for 2m factorials when three-factor and higher order interactions are negligible. J. Jpn. Stat. Soc., 21, 211–219.MATHGoogle Scholar
  11. Srivastava, J. N. 1975. Designs for searching non-negligible effects. In A survey of statistical design and linear models, ed. J. N. Srivastava, 507–519. Amsterdam, The netherlands, North-Holland.Google Scholar
  12. Srivastava, J. N., and S. Ghosh. 1976. Series of 2m factorial designs of resolution V which allow search and estimation of one extra unknown effect. Sankhya, Ser. B, 38, 280–289.MathSciNetMATHGoogle Scholar
  13. Xu, H., F. K. H. Phoa, and W.K. Wong. 2009. Recent developments in nonregular fractional factorial designs. Stat. Surveys, 3, 18–46.MathSciNetCrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2013

Authors and Affiliations

  • P. Angelopoulos
    • 1
  • K. Chatterjee
    • 2
  • C. Koukouvinos
    • 1
  1. 1.Department of MathematicsNational Technical University of Athens, ZografouAthensGreece
  2. 2.Department of StatisticsVisva-Bharati UniversitySantiniketan, West BengalIndia

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