A Theory on Optimal Factorial Designs presents a rigorous and unified treatment of factorial design theory, centered on the general minimum lower-order confounding (GMC) criterion.

It develops the theoretical foundations of the GMC criterion and demonstrates its wide-ranging applications to two-level, blocked, split-plot, compromise, robust parameter, and s-level designs, as well as to orthogonal arrays.

Experimental design and analysis is a cornerstone of mathematical statistics, with extensive applications in agriculture, engineering, medicine, and the social sciences. Among established methodologies, factorial designs remain one of the most powerful and efficient tools for investigating systems involving multiple factors.

The GMC criterion provides a principled framework for selecting optimal factorial designs by rigorously quantifying and minimizing confounding among factor effects. This work delivers both theoretical insights and practical methodological guidance, making it a valuable reference for researchers and graduate students in statistics and allied disciplines.