Читать книгу Introduction to Linear Regression Analysis - Douglas C. Montgomery - Страница 17
Designed Experiment
ОглавлениеThe best data collection strategy for this problem uses a designed experiment where we would manipulate the two temperatures and the reflux ratio, which we would call the factors, according to a well-defined strategy, called the experimental design. This strategy must ensure that we can separate out the effects on the acetone concentration related to each factor. In the process, we eliminate any collinearity problems. The specified values of the factors used in the experiment are called the levels. Typically, we use a small number of levels for each factor, such as two or three. For the distillation column example, suppose we use a “high” or +1 and a “low” or −1 level for each of the factors. We thus would use two levels for each of the three factors. A treatment combination is a specific combination of the levels of each factor. Each time we carry out a treatment combination is an experimental run or setting. The experimental design or plan consists of a series of runs.
For the distillation example, a very reasonable experimental strategy uses every possible treatment combination to form a basic experiment with eight different settings for the process. Table 1.1 presents these combinations of high and low levels. This experimental arrangement is called a factorial design.
Figure 1.7 illustrates that this factorial design forms a cube in terms of these high and low levels. With each setting of the process conditions, we allow the column to reach equilibrium, take a sample of the product stream, and determine the acetone concentration. We then can draw specific inferences about the effect of these factors. Such an approach allows us to proactively study a population or process.
TABLE 1.1 Designed Experiment for the Distillation Column
| Reboil Temperature | Condensate Temperature | Reflux Rate |
| −1 | −1 | −1 |
| +1 | −1 | −1 |
| −1 | +1 | −1 |
| +1 | +1 | −1 |
| −1 | −1 | +1 |
| +1 | −1 | +1 |
| −1 | +1 | +1 |
| +1 | +1 | +1 |
Figure 1.7 The designed experiment for the distillation column.
