The Design and Analysis of 2^<i>k–p</i>× 2^<i>q–r</i>Split Plot Experiments

Abstract

AbstractSplit plot designs play a key role in the industrial application of factorial experiments. They have lately been used in connection with the development of robust products and other prototype testing where they are typically called inner and outer array designs. In this article, we will provide a discussion of their design and analysis from a classical factorial and fractional factorial design standpoint. We will show that the justification for the use of split plot designs is either because of physical constraints on the execution of the trials or for economic reasons. That we are dealing with design and environmental factors is not in itself necessarily a good reason for using inner and outer array designs, except when particular confounding structures are desired. We will focus on the special case of split plot designs composed of two-level fractional factorials. General expressions for finding the defining relations and confounding with and without split plot confounding for split plot designs will be discussed. We will also discuss the economics of split plot experiments and apply these concepts to show how savings in terms of runs or increased information sometimes can be achieved.KeywordsConfoundingCost of ExperimentationInner and Outer ArraysRobust DesignSplit Plot Confounding Additional informationNotes on contributorsSøren BisgaardDr. Bisgaard is a Professor and Director of the Institute for Technology Management. He is a Senior Member of ASQ. His email address is Soren.Bisgaard@unisg.ch.