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Journal of Statistical Theory and Practice

, Volume 6, Issue 1, pp 169–177 | Cite as

Optimal Supersaturated Designs for sm Factorials in N ≢ 0 (mod s) Runs

  • Feng Shun Chai
  • Kashinath Chatterjee
  • Ashish Das
  • Chand Midha
Article
First Online:
Received:
Accepted:

Abstract

Supersaturated designs (SSDs) offer apotentially useful way to investigate many factors with only a few experiments during the preliminary stages of experimentation. A popular measure to assess multilevel SSDs is the E(χ2) criterion. The literature reports on SSDs have concentrated mainly on balanced designs. For s-level SSDs, the restriction of the number of runs N being only a multiple of s is really not required for the purpose of use of such designs. Just like when N is a multiple of s and the design ensures orthogonality of the factor effects with the mean effect, in the case of N not a multiple of s, we ensure near orthogonality of each of the factors with the mean. In this article we consider s-level E(χ2)-optimal designs for N ≡ n (mod s), 0 ≤ n ≤ s − 1. We give an explicit lower bound on E(χ2). We give the structures of design matrices that attain the lower bounds. Some combinatorial methods for constructing E(χ2)-optimal SSDs are provided.

AMS Subject Classification

62K15 

Keywords

Effect sparsity Lower bound Screening designs Supersaturated designs 
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Copyright information

© Grace Scientific Publishing 2012

Authors and Affiliations

  • Feng Shun Chai
    • 1
  • Kashinath Chatterjee
    • 2
  • Ashish Das
    • 3
  • Chand Midha
    • 4
  1. 1.Institute of Statistical ScienceAcademia SinicaTaipeiTaiwan, R.O.C.
  2. 2.Department of StatisticsVisva Bharati UniversitySantiniketanIndia
  3. 3.Department of MathematicsIndian Institute of Technology BombayMumbaiIndia
  4. 4.Department of StatisticsThe University of AkronAkronUSA

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