Graphic-Aided Design of Experiments

In this talk I will outline some problems encountered in the planning of experiments that can benefit from the use of graphs. A primary example is the interaction assignment problem. In planning a factorial experiment prior knowledge may suggest that some interactions are potentially important and should therefore be assigned to columns free of the main effects. Each feasible assignment can be represented by a graph with the factors being the vertices and the 2-factor interactions being the edges. The collection of all the nonisomorphic graphs is called the solution set. For many 2-level designs of practical importance the solution set is not large and can be enumerated. The assignment can be solved by drawing a graph representing the designated interactions and “comparing” it with tne graphs in the solution set. This approach gives a substantial improvement over the method of linear graphs due to G. Taguchi. Other examples include the use of graphs for generating 4-level factors from2-level factors, assigning factors with a specified nonorthogonality structure represented by a graph, and the construction of nearly orthogonal arrays. Graphs can also be used to provide a simple representation of the confounding patterns among nonorthogonal factors The majority of results presented here are from Wu and Chen (1989).