In an article in Quality Engineering (“An Application of Fractional Factorial Experimental Designs,” 1988, Vol. 1, pp. 19–23), M. B. Kilgo describes an experiment to determine the effect of CO2 pressure (A), CO2 temperature (B), peanut moisture (C), CO2 flow rate (D), and peanut particle size (E)

on the total yield of oil per batch of peanuts (y). The levels that she used for these factors are shown in Table P8.11. She conducted the 16-run fractional factorial experiment shown in Table P8.12.

(a) What type of design has been used? Identify the defining relation and the alias relationships.

(b) Estimate the factor effects and use a normal probability plot to tentatively identify the important factors.

(c) Perform an appropriate statistical analysis to test the hypotheses that the factors identified in part

(b) have a significant effect on the yield of peanut oil.

(d) Fit a model that could be used to predict peanut oil yield in terms of the factors that you have identified as important.

(e) Analyze the residuals from this experiment and comment on model adequacy.