Constructing Optimal Baseline Designs from Regular Designs

This paper delves into the baseline design under the baseline parameterization model in experimental design, focusing on the relationship between the $K$ -aberration criterion and the word length pattern (WLP) of regular two-level designs. The paper provides a detailed analysis of the relationship between $K_5$ and the WLP for regular two-level designs with resolution $t=3$ , and proposes corresponding theoretical results. These results not only theoretically reveal the connection between the orthogonal parameterization model and the baseline parameterization model but also provide theoretical support for finding the $K$ -aberration optimal regular two-level baseline designs. It demonstrates how to apply these theories to evaluate and select the optimal experimental designs. In practical applications, experimental designers can utilize the theoretical results of this paper to quickly assess and select regular two-level baseline designs with minimal $K$ -aberration by analyzing the WLP of the experimental design. This allows for the identification of key factors that significantly affect the experimental outcomes without frequently changing the factor levels, thereby maximizing the benefits of the experiment.