The article “An Application of Fractional Factorial

Chapter 9, Problem 12E

(choose chapter or problem)

The article “An Application of Fractional Factorial Designs” (M. Kilgo, Quality Engineering, 1988:19–23) describes a \(2^{5-1}\) design (half-replicate of a \(2^{5}\) design) involving the use of carbon dioxide \(\mathrm{(CO}_{2})\) at high pressure to extract oil from peanuts. The outcomes were the solubility of the peanut oil in the \(\mathrm{CO}_{2}\) (in mg oil/liter \(\mathrm{CO}_{2}\)), and the yield of peanut oil (in percent). The five factors were \(A: \mathrm{CO}_{2}\) pressure, \(B: \mathrm{CO}_{2}\) temperature, C: peanut moisture, \(D: \mathrm{CO}_{2}\) flow rate, and E: peanut particle size. The results are presented in the following table.

a. Assuming third- and higher-order interactions to be negligible, compute estimates of the main effects and inter- actions for the solubility outcome.  

b. Plot the estimates on a normal probability plot. Does the plot show that some of the factors influence the solubility? If so, which ones?  

c. Assuming third- and higher-order interactions to be negligible, compute estimates of the main effects and inter- actions for the yield outcome.  

d. Plot the estimates on a normal probability plot. Does the plot show that some of the factors influence the yield? If so, which ones?

Equation Transcription:

Text Transcription:

2^5-1

2^5

CO_2

CO_2

A:CO_2

B:CO_2

D:CO_2