# (b) A soft-drinks bottler is interested in obtaining more

(b) A soft-drinks bottler is interested in obtaining more uniform fill heights in the boties the manufacturing process. The filling machine theoretically fills each bottle to the correct larget height but in practice there is variation around the target and the bottler would like tp beffer understand the sources of this variability and eventualy reduceit The Engineer can control three variables during the filling process (each at two leveis). These are Factor A: Carboriation with levels 10% and 20%, Factor B Operating Pressure in the filer with levels 1.7 and 2,0 Bar and Factor C: Line Speed with Levels 200 and 250 bottles per minutes. The response variable he chooses to measure is "Deviation (mm) from the target fill height". (0 Applying standard Yates Order in the sequence of A. B, & C. construct a full factorial design structure (array) for an experiment involving these three factors (A, B and C) each (2 marks) at two levels. Comment on what additional information is missing from the array and expand the array to include all this information (i) (2 marks) Table 4.0 lists the results for the response variable obtained on completion of the fuli-factorial experiment already described. The results are listed in standard Yates order sequerice. -4 -1 -1 3. 11 Table 4.0: Response Variable Results (in standard Yates order sequence) Draw the interaction tables for the AB and AC interactions and determine which (if any) is more significant (5 marks) (iv) Using the trade-off table on page 4 of the formulae pack, construct a suitable prthogonal array for an experiment involving the three factors (A. B. C) already described where we are limited to undertaking just four experimental runs (3 marks) (v) Explain the term "confounded" and show what factors are confounded with each other in the four factor experiment constructed in part (iv) above (4 marks) EMPAMEFA