{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Assignment_Solution_Chp_6

# Assignment_Solution_Chp_6 - Chapter 6 Solutions 6.1 An...

This preview shows pages 1–4. Sign up to view the full content.

1 Chapter 6– Solutions 6.1. An engineer is interested in the effects of cutting speed ( A ), tool geometry ( B ), and cutting angle on the life (in hours) of a machine tool. Two levels of each factor are chosen, and three replicates of a 2 3 factorial design are run. The results are as follows: Treatment Replicate A B C Combination I II III - - - (1) 22 31 25 + - - a 32 43 29 - + - b 35 34 50 + + - ab 55 47 46 - - + c 44 45 38 + - + ac 40 37 36 - + + bc 60 50 54 + + + abc 39 41 47 (a) Estimate the factor effects. Which effects appear to be large? From the normal probability plot of effects below, factors B , C , and the AC interaction appear to be significant. (b) Use the analysis of variance to confirm your conclusions for part (a). The analysis of variance confirms the significance of factors B , C , and the AC interaction. Design Expert Output Response: Life in hours ANOVA for Selected Factorial Model Analysis of variance table [Partial sum of squares] Sum of Mean F Source Squares DF Square Value Prob > F Model 1612.67 7 230.38 7.64 0.0004 significant A 0.67 1 0.67 0.022 0.8837 B 770.67 1 770.67 25.55 0.0001 C 280.17 1 280.17 9.29 0.0077 AB 16.67 1 16.67 0.55 0.4681 AC 468.17 1 468.17 15.52 0.0012

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 BC 48.17 1 48.17 1.60 0.2245 ABC 28.17 1 28.17 0.93 0.3483 Pure Error 482.67 16 30.17 Cor Total 2095.33 23 The Model F-value of 7.64 implies the model is significant. There is only a 0.04% chance that a "Model F-Value" this large could occur due to noise. The reduced model ANOVA is shown below. Factor A was included to maintain hierarchy. Design Expert Output Response: Life in hours ANOVA for Selected Factorial Model Analysis of variance table [Partial sum of squares] Sum of Mean F Source Squares DF Square Value Prob > F Model 1519.67 4 379.92 12.54 < 0.0001 significant A 0.67 1 0.67 0.022 0.8836 B 770.67 1 770.67 25.44 < 0.0001 C 280.17 1 280.17 9.25 0.0067 AC 468.17 1 468.17 15.45 0.0009 Residual 575.67 19 30.30 Lack of Fit 93.00 3 31.00 1.03 0.4067 not significant Pure Error 482.67 16 30.17 Cor Total 2095.33 23 The Model F-value of 12.54 implies the model is significant. There is only a 0.01% chance that a "Model F-Value" this large could occur due to noise. Effects B, C and AC are significant at 1%. (c) Write down a regression model for predicting tool life (in hours) based on the results of this experiment. C A C B A ijk x x . x . x . x . . y 4167 4 4167 3 6667 5 1667 0 8333 40 + + + + = Design Expert Output Coefficient Standard 95% CI 95% CI Factor Estimate DF Error Low High VIF Intercept 40.83 1 1.12 38.48 43.19 A-Cutting Speed 0.17 1 1.12 -2.19 2.52 1.00 B-Tool Geometry 5.67 1 1.12 3.31 8.02 1.00 C-Cutting Angle 3.42 1 1.12 1.06 5.77 1.00 AC -4.42 1 1.12 -6.77 -2.06 1.00 Final Equation in Terms of Coded Factors: Life = +40.83 +0.17 * A +5.67 * B +3.42 * C -4.42 * A * C Final Equation in Terms of Actual Factors: Life = +40.83333 +0.16667 * Cutting Speed +5.66667 * Tool Geometry +3.41667 * Cutting Angle -4.41667 * Cutting Speed * Cutting Angle The equation in part (c) and in the given in the computer output form a “hierarchial” model, that is, if an interaction is included in the model, then all of the main effects referenced in the interaction are also included in the model.
3 (d) Analyze the residuals. Are there any obvious problems? Residual Norm al % probability Normal plot of residuals -7.33333 -2.625 2.08333 6.79167 11.5 1 5 10 20 30 50 70 80 90 95 99 Predicted Residuals Residuals vs. Predicted -7.33333 -2.625 2.08333 6.79167 11.5 27.17 33.92 40.67 47.42 54.17 There is nothing unusual about the residual plots.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern