The Soft Drink Bottling Problem

A soft drink bottler is interested in obtaining more uniform fill heights in the bottles produced by his manufactured 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 the sources of the variability and eventually reduces 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 pressure and speed are easy to control, but the percent carbonation is more difficult to control during actual manufacturing because it varies with product temperature. However, for purposes of an experiment, the engineer can control carbonation at three levels: 10, 12, and 14 percent. He chooses two-levels for pressure (25 and 30 psi) and two levels for line speed 9200 and 250 bpm). He decides to run two replicates of a factorial design in these three factors, with all 24 runs taken in random order. The response variable observed is the average deviations from the target fill height observed in a production run of bottles at each set of conditions. The data that resulted from this experiment are shown below. Positive deviations are the fill heights above the target, whereas negative deviations are fill heights below the target. The circled numbers are the three-way cell totals.

 

Table 6.1        Fill Height Deviation Data

 

                                    Operating Pressure (B) 

                                                25 psi                                                  30 psi  

Percent                                                     Line Speed (C)                          Line Speed ©

 Carbonation (A)                                 200                  250                  200                  250

            10                                -3                     -1                     -1                     1

                                                -1                     0                      0                      1

 

            12                                0                      2                      2                      6

                                                1                      1                      3                      5

 

14                                5                      7                      7                      10

                                    4                      6                      9                      11

B X C Totals                    6                      15                    20                    34

                                                      21                                                        54

                        A x B Totals                            A x C Totals

                                                                        

                             B                                                           C

            A         25        30                                A         200      250

            10        -5         1                                  10        -5         1

            12        4          16                                12        6          14

            14        22        37                                14        25        34