A Class of Three-Level Experimental Designs for Response Surface Modeling

Abstract

Abstract Most empirically constructed response surface models are based on polynomials containing terms of order 2 or less. Experimental designs involving three equally spaced levels of each factor are popular choices for collecting data to tit such models. Because complete three-level factorial plans require more experimental runs than can usually be accommodated in practice, smaller designs are typically used. The families of three-level designs most often used in this context are the Box–Behnken plans and various forms of the central composite designs. This article introduces a different method for constructing composite designs, motivated by notions of sequential experimentation and the minimax and maximin distance criteria used in spatial modeling. Operational and performance characteristics of some designs constructed by the method are compared to those of competing Box–Behnken and central composite plans. KEY WORDS: Augmented pairs designBox–Behnken designCentral composite designMaximin distance criterionMinimax distance criterionResponse surface analysisSequential experimentSmall composite design