Split-plot designs for multistage experimentation

ABSTRACT

Most of today’s complex systems and processes involve several stages through which input or the raw material has to go before the final product is obtained. Also in many cases factors at different stages interact. Therefore, a holistic approach for experimentation that considers all stages at the same time will be more efficient. However, there have been only a few attempts in the literature to provide an adequate and easy-to-use approach for this problem. In this paper, we present a novel methodology for constructing two-level split-plot and multistage experiments. The methodology is based on the Kronecker product representation of orthogonal designs and can be used for any number of stages, for various numbers of subplots and for different number of subplots for each stage. The procedure is demonstrated on both regular and nonregular designs and provides the maximum number of factors that can be accommodated in each stage. Furthermore, split-plot designs for multistage experiments with good projective properties are also provided.

KEYWORDS:

• Kronecker product
• mirror image pairs
• projectivity
• restrictions on randomization
• two-level designs

Acknowledgements

We would like to thank the reviewer of the original version of this paper for constructive remarks and comments that are incorporated in the latest version.

Disclosure statement

No potential conflict of interest was reported by the authors.