TABLE OF CONTENTS As is the case for other six sigma-related methods, practitioners of six sigma have demonstrated that it is possible to derive value from design of experiments (DOE) and regression with little or no knowledge of statistical theory. However, understanding the implications of probability theory can be intellectionally satisfying and enhance the chances of successful implementations.
Also, in some situations, theory can be practically necessary. For example, in cases involving mixture or categorical variables (Chapter 15), it is necessary to go beyond the standard methods and an understanding of theory is needed for planning experiments and analyzing results. This chapter focuses attention on three of the most valuable roles that theory can play in enhancing DOE and regression applications. For a review of basic probability theory, refer to Chapter 10.
First, applying t-testing theory can aid in decision-making about the numbers of samples and the ? level to use in analysis. Associated choices have implications about the chances that different types of errors will occur. Under potentially relevant assumptions, the chance of wrongly declaring significance (a Type I error) might not be the ? level used. Also, if the number of runs is not large enough, a lost opportunity for developing statistical evidence is likely (a Type II error).
Second, theory can aid in the many decisions associated with standard screening using fractional factorials. Decisions include which DOE array to use, which alpha level to use in analysis, and whether to use the individual error rate (IER)...
