Journal of Statistical Theory and Practice

, Volume 12, Issue 1, pp 136–150 | Cite as

On the optimality of blocked main effects plans with even number of runs

  • Rita SahaRayEmail author
  • Ganesh Dutta


In this article, experimental situations are considered where a main effects plan is to be used to study m two-level factors using n runs, n≡2 (mod 4), which are partitioned into b blocks, with the ith block having size ki, where \(\sum _{i = 1}^b{k_i} = n\) and kis are not necessarily equal. Assuming the block sizes to be even for all blocks, optimal designs are identified with respect to type 1 optimality criteria in the class of designs providing estimation of all main effects orthogonal to the block effects. In practice, such orthogonal estimation of main effects is often a desirable condition. In some wider classes of m two-level blocked main effects plans, where the block sizes can be even or odd, D- and Ε-optimal designs are also characterized. Simple construction methods for these optimal designs, based on Hadamard matrices, Pn matrices, and Kronecker product, are also presented.


Design matrix Hadamard matrix Kronecker product type 1 criteria 

AMS Subject Classification



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© Grace Scientific Publishing, 20 Middlefield Ct, Greensboro, NC 27455 2018

Authors and Affiliations

  1. 1.Applied Statistics DivisionIndian Statistical InstituteKolkataIndia
  2. 2.Basanti Devi CollegeKolkataIndia

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