6.1 Introduction

In Chapters 3 and 5 we presented two-factor models where both factors are assumed to be random effects. Although this has traditionally been the assumption in gauge R&R studies, it is often more appropriate to treat operators as fixed effects. Consider the situation described by Dolezal, Burdick, and Birch [18], in which three mechanical testers (operators) are used to monitor a process that manufactures tape drive heads (parts). A random sample of 18 heads is obtained from the process output, and the response variable reverse overwrite was measured for each head using the set of three testers. Reverse overwrite is a measure of residual frequency after a second frequency is placed on magnetic tape. The units of measurement are decibels and the specification limits are LSL = ?41 and USL = ?33. Each tester makes three replicate measurements on each head. The total data set consists of 162 measurements. A partial listing of the data is given in Table 6.1. The testers in this situation are each attached to one of three production lines and will always be part of the testing system. Since these are the only three testers that will ever be used to monitor the process, the inference concerns only these three testers and not the population from which they were selected. Thus, the operator factor is a fixed effect. (If you are not familiar with the terms random and fixed in this context, review the material in Appendix A.) The...