Montgomery (2009a) describes a 241 fractional factorial design used to study four factors in a chemical process.

The factors are A temperature, B pressure, C concentration, and D stirring rate, and the response is filtration rate.

The design and the data are shown in Table 7-26 below.

(a) Write down the complete defining relation and the aliases from the design.

(b) Estimate the effects and prepare a normal probability plot of the effects. Which effects are active?

(c) Interpret the effects and develop an appropriate model for the response.

(d) Plot the residuals from your model against the fitted values. Also construct a normal probability plot of the residuals. Comment on the results.

7-35. An article in Industrial and Engineering Chemistry

(“More on Planning Experiments to Increase Research Efficiency,” Vol. 62, 1970, pp. 60–65) uses a 252 design to investigate the effect on process yield of A condensation temperature, B amount of material 1, C solvent volume, D condensation time, and E amount of material 2. The results obtained are as follows:

e 23.2 cd 23.8 ab 15.5 ace 23.4 ad 16.9 bde 16.8 bc 16.2 abcde 18.1

(a) Write down the complete defining relation and the aliases from the design. Verify that the design generators used were I ACE and I BDE.

(b) Estimate the effects and prepare a normal probability plot of the effects. Which effects are active? Verify that the AB and AD interactions are available to use as error.

(c) Interpret the effects and develop an appropriate model for the response.

(d) Plot the residuals from your model against the fitted values. Also construct a normal probability plot of the residuals. Comment on the results.

Transcribed Image Text:

Treatment Combination Filtration Rate = (1) 45 ad 100 bd 45 ab 65 cd 75 60 bc 80 abcd 96 ++++ Run B C D = ABC 1 2345678 +