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for studying a silver automobile basecoat. The response variable is distinctness of image (DOI). The variables used in the experiment are A Percentage of polyester by weight of polyester/melamine (low value 50%, high value 70%) B Percentage of cellulose acetate butyrate carboxylate (low value 15%, high value 30%) C Percentage of aluminum stearate (low value 1%, high value 3%) D Percentage of acid catalyst (low value 0.25%, high value 0.50%) The responses are (1) 63.8, a 77.6, b 68.8, ab 76.5, c 72.5, ac 77.2, bc 77.7, abc 84.5, d 60.6, ad 64.9, bd 72.7, abd 73.3, cd 68.0, acd 76.3, bcd 76.0, and abcd 75.9. (a) Estimate the factor effects. (b) From a normal probability plot of the effects, identify a tentative model for the data from this experiment. (c) Using the apparently negligible factors as an estimate of error, test for signi cance of the factors identi ed in part (b). Use 0.05. (d) What model would you use to describe the process, based on this experiment Interpret the model. (e) Analyze the residuals from the model in part (d) and comment on your ndings. 14-47. An article in the Journal of Manufacturing Systems (Vol. 10, 1991, pp. 32 40) describes an experiment to investigate the effect of four factors P waterjet pressure, F abrasive ow rate, G abrasive grain size, and V jet traverse speed on the surface roughness of a waterjet cutter. A 24 design follows.

Factors Surface V F P G Roughness Run (in/min) (lb/min) (kpsi) (Mesh No.) ( m) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 6 2 6 2 6 2 6 2 6 2 6 2 6 2 6 2 2.0 2.0 2.0 2.0 1.0 1.0 1.0 1.0 2.0 2.0 2.0 2.0 1.0 1.0 1.0 1.0 38 38 30 30 38 38 30 30 38 38 30 30 38 38 30 30 80 80 80 80 80 80 80 80 170 170 170 170 170 170 170 170 104 98 103 96 137 112 143 129 88 70 110 110 102 76 98 68

0 256. The destination image s red channel will be weighted by the remaining amount (256 redMultiplier). So 128 or 0x80 provides an even mix.

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(a) Estimate the factor effects. (b) Form a tentative model by examining a normal probability plot of the effects. (c) Is the model in part (b) a reasonable description of the process Is lack of t signi cant Use 0.05. (d) Interpret the results of this experiment. (e) Analyze the residuals from this experiment. 14-48. Construct a 24 1 design for the problem in Exercise IV 14-46. Select the data for the eight runs that would have been required for this design. Analyze these runs and compare your conclusions to those obtained in Exercise 14-46 for the full factorial. 14-49. Construct a 24 1 design for the problem in Exercise IV 14-47. Select the data for the eight runs that would have been required for this design, plus the center points. Analyze these data and compare your conclusions to those obtained in Exercise 14-47 for the full factorial. 14-50. Construct a 28 4 design in 16 runs. What are the IV alias relationships in this design 14-51. Construct a 25 2 design in eight runs. What are the III alias relationships in this design 14-52. 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 data are shown in the table below.

greenMultiplier The mix for the green channel; see redMultiplier. blueMultiplier The mix for the blue channel; see redMultiplier. alphaMultiplier The mix for the alpha channel; see redMultiplier.

(a) Plot the effect estimates on a normal probability scale. 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) Analyze the residuals from this experiment. Does your analysis indicate any potential problems (d) 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. 14-53. An article in the Journal of Quality Technology (Vol. 17, 1985, pp. 198 206) describes the use of a replicated fractional factorial to investigate the effect of ve factors on the free height of leaf springs used in an automotive application. The factors are A furnace temperature, B heating time, C transfer time, D hold down time, and E quench oil temperature. The data are shown in the following table. (a) What is the generator for this fraction Write out the alias structure. (b) Analyze the data. What factors in uence mean free height (c) Calculate the range of free height for each run. Is there any indication that any of these factors affect variability in free height (d) Analyze the residuals from this experiment and comment on your ndings.

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