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

Article Type

Research Article

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Journal of Statistical Theory and Practice


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 ∑bi=1ki=n and ki ’s 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 E-optimal designs are also characterized. Simple construction methods for these optimal designs, based on Hadamard matrices, Pn matrices, and Kronecker product, are also presented.

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