Choice of Response Surface Design and Alphabetic Optimality

Abstract

Abstract : It is argued that the specification of problem of experimental design (and in particular, of response surface design) should depend on scientific context. The specification for a widely developed theory of 'alphabetic optimality' for response surface applications is analyzed and found to be unduly limiting. Ways in which designs might be chosen to satisfy a set of criteria of greater scientific relevance are suggested. Detailed consideration is given to regions of operability and interest, to the design information function, to sensitivity of criteria to size and shape of the region, and to the effect of bias. Problems are discussed of checking for lack of fit, sequential assembly, orthogonal blocking, estimation of error, estimation of transformations, robustness to bad values, using minimum numbers of points, and employing simple data patterns. (author)