5.31. An article in Quality Progress (May 2011, pp. 42–48)

describes the use of factorial experiments to improve a silver powder production process. This product is used in conductive pastes to manufacture a wide variety of products ranging from silicon wafers to elastic membrane switches. Powder density (g/cm2) and surface area (cm2/g) are the two critical characteristics of this product. The experiments involved three factors—reaction temperature, ammonium percent, and stirring rate. Each of these factors had two levels and the design was replicated twice. The design is shown below.

(a) Analyze the density response. Are any interactions significant?
Draw appropriate conclusions about the effects of the significant factors on the response.

(b) Prepare appropriate residual plots and comment on model adequacy.

(c) Construct contour plots to aid in practical interpretation of the density response.

(d) Analyze the surface area response. Are any interactions significant? Draw appropriate conclusions about the effects of the significant factors on the response.

(e) Prepare appropriate residual plots and comment on model adequacy.

(f) Construct contour plots to aid in practical interpretation of the surface area response.

Ammonium (%) Stir Rate (RPM) Temperature Surface (C) Density Area 2 100 8 14.68 0.40 2 100 8 15.18 0.43 30 100 30 100 8 8 15.12 0.42 17.48 0.41 2 150 2 150 0000 8 7.54 0.69 8 6.66 0.67 30 150 8. 12.46 0.52 30 150 2 100 2 100 30 100 30 100 2 150 2 150 30 150 30 150 * 4 4 4 4 4 4 4 8 12.62 0.36 40 10.95 0.58 40 17.68 0.43 40 12.65 0.57 40 15.96 0.54 40 8.03 0.68 40 8.84 0.75 40 14.96 0.41 40 14.96 0.41