TABLE OF CONTENTS In Chapters 2 and 3 we introduced two basic experimental designs for conducting gauge R&R studies. These designs are the single-factor design and the two-factor crossed (factorial) design. The objective for this chapter is to review some of the basic principles of designing experiments and to discuss how those principles apply to gauge R&R studies.
Montgomery [51] lists three basic principles of designing experiments: randomization, replication, and blocking. While these are very general principles that have application to all experiments, they can be particularly important in gauge R&R studies as well as other more general types of measurement systems capability studies.
Replication is a repetition of the basic experiment. In the gauge R&R experiment described in Chapter 3 (Table 3.1), replication consists of an operator making a measurement on a part. Two measurements are made by each operator on a part, and replication assumes that these measurements are made independently of each other with unique setup of any tool or fixture that is required. Replication has two important properties. First, it allows the experimenter to obtain an estimate of the experimental error ( 
in Chapter 3). This estimate of error is the repeatability of the measuring device. It also defines the scale that we use for determining whether observed differences in the data are really statistically different. Second, replication improves the precision with which model parameters are estimated. For example, suppose the repeatability variance component is of interest. Replication permits the experimenter to obtain a more...
