In a process development study on yield, four factors were studied, each at two levels: time (A), concentration (B), pressure (C), and temperature (D). A single replicate of a 2⁴ design was run, and the resulting data are shown in the following table:

(a) Construct a normal probability plot of the effect estimates. Which factors appear to have large effects?

(b) Conduct an analysis of variance using the normal probability plot in part (a) for guidance in forming an error term. What are your conclusions?

(c) Write down a regression model relating yield to the important process variables.

(d) Analyze the residuals from this experiment. Does your analysis indicate any potential problems?

(e) Can this design be collapsed into a 2³ design with two replicates? If so, sketch the design with the average and range of yield shown at each point in the cube. Interpret the results.

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Actual Run Order Factor Levels Run Yield Number A B C D (lbs) Low (-) High (+) 1 5 12 A (h) 2.5 3 18 B (%) 14 18 C (psi) 60 D (C) 225 3 8 13 80 4 13 16 250 5 3 17 7 15 7 14 20 8 1 15 9 6. 10 10 11 25 11 2 13 12 15 + 24 13 4 19 14 16 21 15 10 17 16 12 23 + + + + + + + + + + + + +I + 1 + | + | +