A soft drink bottler is interested in obtaining more uniform fill heights in the bottles produced by his manufacturing process.
The filling machine theoretically fills each bottle to the correct target height, but in practice, there is variation around this target,
and the bottler would like to understand better the sources of variability and eventually reduce it.The process engineer can control three variables during the filling process: the percent carbonation (A), the operating pressure in the filler (B), and the bottles produced per minute or the line speed (C). The engineer can control carbonation at three levels: 10, 12, and 14 percent. There are two levels for pressure (25 and 30 psi) and two levels for line speed (200 and 250 bpm). she decides to run two replicates of a factorial design in these three factors, with all 24 runs taken in random order. The response variable is the average deviation from the target fill height observed in a production run of bottles at each set of conditions. The resulting data are given in the following table. Positive deviations are fill heights above the target, whereas negative deviations are fill heights below the target.
| Operating Pressure (B) | ||||
| 25 psi | 30 psi | |||
| Percent | Line Speed (C) | Line Speed (C) | ||
| Carbonation (A) | 200 | 250 | 200 | 250 |
| 10 | -3, -1 | -1, 0 | -1, 0 | 1, 1 |
| 12 | 0, 1 | 2, 1 | 2, 3 | 6, 5 |
| 14 | 5, 4 | 7, 6 | 7, 9 | 10, 11 |
- Write a model relating the response to each of the factors.
- Give the ANOVA table for this design. Use SAS. Draw conclusions.
- Construct a profile plot of AB (carbonation-pressure) interaction.
What does this plot say about the effect of these two factors on the average fill deviation?- Use Tukey's W procedure at an alpha = 0.05 level to compare the three mean fill
deviations for the three carbonation levels.
- The company wants the average deviation from the fill target to be close to zero.
What should the engineer recommend in terms of the level settings of the three factors? Explain.