On the optimality of blocked main effects plans with even number of runs
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.
SahaRay, Rita and Dutta, Ganesh, "On the optimality of blocked main effects plans with even number of runs" (2018). Journal Articles. 1521.