Circulant Matrix‐Based Box–Behnken Designs With Economic Run Sizes

We introduce Circulant Matrix‐Based Box–Behnken Designs (CBBDs), a new class of three‐level, second‐order response surface designs constructed using circulant matrix structures. These designs satisfy an enhanced orthogonal minimally aliased () property: they retain the classical OMA property—where main effects are orthogonal to each other and to all second‐order effects (i.e., quadratic effects and two‐factor interaction effects)—and further ensure orthogonality between quadratic and interaction effects. An efficient algorithm is developed for generating CBBDs, and a catalog of designs for up to 11 factors is provided. The resulting designs exhibit high D ‐efficiency, support full estimation of second‐order models, and preserve most of the desirable properties of traditional Box–Behnken Designs, while requiring fewer experimental runs. These properties make CBBDs a practical and resource‐efficient alternative for complex experimental settings.