Design and Analysis of Computer Experiments With Branching and Nested Factors

In many experiments, some of the factors exist only within the level of another factor. Such factors are often called nested factors. A factor within which other factors are nested is called a branching factor. For example, suppose we want to experiment with two processing methods. The factors involved in these two methods can be different. Thus, in this experiment the processing method is a branching factor and the other factors are nested within the branching factor. Design and analysis of experiments with branching and nested factors are challenging and have not received much attention in the literature. Motivated by a computer experiment in a machining process, we develop optimal Latin hypercube designs and kriging methods that can accommodate branching and nested factors. Through the application of the proposed methods, optimal machining conditions and tool edge geometry are attained, which resulted in a remarkable improvement in the machining process.