TABLE OF CONTENTS Our final example considers a model with both crossed and nested factors. Borror, Montgomery, and Runger [4] described a semiconductor manufacturing process in which measurements are recorded at each of four sites on a wafer during the manufacturing process. Data are collected over three shifts (operators) each day for a 7-day period. Since shifts of operators differ by day, operators are nested within day. Table 8.21 displays a listing of the data for the first day. The response variable has been coded for proprietary reasons.
| Operator | Site | Measurements |
|---|---|---|
| 1 | 1 | 308.1, 308.2, 308.6, 308.5 |
| 1 | 2 | 308.5, 308.8, 308.5, 308.8 |
| 1 | 3 | 308.5, 308.8, 308.8, 308.7 |
| 1 | 4 | 308.5, 308.6, 308.7, 308.5 |
| 2 | 1 | 308.0, 309.5, 308.8, 310.8 |
| 2 | 2 | 308.2, 308.8, 308.3, 308.6 |
| 2 | 3 | 308.3, 308.4, 308.4, 308.3 |
| 2 | 4 | 308.3, 308.2, 308.4, 308.4 |
| 3 | 1 | 308.9, 308.5, 308.4, 308.5 |
| 3 | 2 | 308.8, 308.3, 308.4, 308.5 |
| 3 | 3 | 308.8, 308.4, 308.2, 308.3 |
| 3 | 4 | 308.6, 308.3, 308.4, 308.4 |
The model used to represent the data in Table 8.21 is
where ? Y is a constant and D i, O j(i), S k, (OS) jk(i), and E
