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

ABSTRACT

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, (mod 4), which are partitioned into b blocks, with the ith block having size , where and ’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, matrices, and Kronecker product, are also presented.

KEYWORDS:

• Design matrix
• Hadamard matrix
• Kronecker product
• type 1 criteria

AMS SUBJECT CLASSIFICATION:

• 62K05

Acknowledgment

The authors are thankful to the referees for their insightful comments, which led to an improved version of the original article.