All-Bias Designs for Spline Functions Joined at the Axes

Abstract

Often, a sensible approach to a general design problem is to slightly expand the appropriate all-bias designs. This idea is applied to situations involving polynomial spline models in which it is necessary to (i) guard against second-degree models in some part, or all, of a cuboidal region of interest, while fitting first-degree models; (ii) guard against third-degree models, while fitting second-degree models. All joins are made on the axes. For (i), suitable designs include 2 _IV ^k—p factorial designs in each 2 ^k -tant. For (ii), consideration of symmetrical designs leads to cuboidal designs of the type previously considered in Draper and Lawrence (1965).

Key Words:

• Response surface designs
• First-order designs
• Second-order designs