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.

Ammonium

(%)

Stir Rate

(RPM)

Temperature

(∘C) Density Surface Area 2 100 8 14.68 0.40 2 100 8 15.18 0.43 30 100 8 15.12 0.42 30 100 8 17.48 0.41 2 150 8 7.54 0.69 2 150 8 6.66 0.67 30 150 8 12.46 0.52 30 150 8 12.62 0.36 2 100 40 10.95 0.58 2 100 40 17.68 0.43 30 100 40 12.65 0.57 30 100 40 15.96 0.54 2 150 40 8.03 0.68 2 150 40 8.84 0.75 30 150 40 14.96 0.41 30 150 40 14.96 0.41

(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.
5.37 Continuation of Problem 5.36. Suppose that the specifications require that surface area must be between 0.3 and 0.6 cm2∕g and that density must be less than 14 g∕cm3.
Find a set of operating conditions that will result in a product that meets these requirements.
5.38 An article in Biotechnology Progress (2001, Vol. 17, pp. 366–368) described an experiment to investigate nisin extraction in aqueous two-phase solutions. A twofactor factorial experiment was conducted using factors A = concentration of PEG and B = concentration of Na2SO4.
Data similar to that reported in the paper are shown below.
A B Extraction (%)
13 11 62.9 13 11 65.4 15 11 76.1 15 11 72.3 13 13 87.5 13 13 84.2 15 13 102.3 15 13 105.6

(a) Analyze the extraction response. 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.