D-optimum designs for the linear logistic model when restrictions exist on p

Abstract Suppose that the linear logistic model describes the relationship between a proportion p and some quantitative variable x and that p varies within the range [p01,p02]⊂[0,1]. Using the Karush-Kuhn-Tucker theorem, the D-optimum design for this model is a balanced 2-point design with the location of the design points determined by p01,p02. A step-by-step procedure is presented for obtaining the D-optimum design points for any values p01,p02. In addition, the efficiencies of these designs are discussed in the context of quality assurance experiments.