Question

6.6.Reconsider the experiment described in Problem 6.1 Suppose that the experimenter only performed the eight trials from replicate I. In addition, he ran four center points and obtained the following response values: 36, 40, 43, 45 (a) Estimate the factor effects. Which effects are large? (b) Perform an analysis of variance, including a check for pure quadratic curvature. What are your conclusions? (c) Write down an appropriate model for predicting tool life, based on the results of this experiment. Does this model differ in any substantial way from the model in Problem 6.1, part (c)? (d) Analyze the residuals (e) What conclusions would you draw about the appropri- ate operating conditions for this process?

Answer 1

a) Normal plot DESIGN-EXPERT Plot Life A: Cutting Speed B: Tool Geometry C: Cutting Angle Effects B, C, and AC looks large 13.75 7.13 -0.50 612 12 75 E ffect "M (y,"X)' 8x4x(40.875-41.000),-0.4167 pare Quadratic Design Expert Output Response: Analysis of variance table Partial sum of squares Source Life in hours ANOVA for Selected Factorial Model Sum of Squares Mean Value 9.77 0.20 21.20 12.40 Prob>F 0.0439 0.6823 0.0193 0.0389 0.5722 0.0157 0.1542 0.0927 2.717E-003 0.9617 Model 1048.88 149.84 significant AB AC BC ABC Curvature Pure Emor Cor Total 3.13 325.13 190.12 6.13 378.12 55.12 91.12 32513 19012 6.13 378.12 55.12 91.12 24.66 3.60 5.94 0.042 0.042 not significant 46.00 15.33 1094.92 The Model F-value of 9.77 implies the model is significant. There is only a 4.39% chance that a "Model F-Value" this large could occur due to noise The "Curvature F-value" of 0.00 implies the curvature (as measured by difference between the average of the center points and the average of the factorial points) in the design space is not significant relative to the noise. There is a 96.17% chance that a "Curvature F-value"this large could occur due to noise

Design Expert Output Response Analysis of variance table Partial sum of squares Source Life in hours ANOVA for Selected Factorial Model Sun of Mean Square 224.13 3.13 325.12 190.12 378.12 28.35 38.10 15.33 Value 7.91 0.11 11.47 6.71 13.34 Prob F 0.0098 0.7496 0.0117 0.0360 0.0082 Squares 896.50 Model significant 3.13 AC Residual Lack of Fi Pure Error Cor Total 325.12 190.12 378.12 198.42 152.42 46.00 1094.92 2.49 0.2402 not significamt The Model F-value of 7.91 implies the model is significant. There is only a 0.98% chance that a "Model F-Value" this large could occur due to noise Effects B, C and AC are significant at 5%. There is no effect of curvature C) Based on the results of this experiment. The model shown in the Design Expert output below does not differ substantially from the model in problem 6.1 part C Design Expert Output factors Life +40.88 +0.62 +6.37 +4.87 -6.88

d) Normal Plot of Residu als Residuals vs. Predicted Reidual e To maximize life run with B at the high level, A at the low level and C at the high level Cube Graph Lifo 58.38 45 88 B 34.88 49.88 C: Cutting Angle B 22.13 37.13 C ACuing Speed