- A 22 Experiment Was Run As Follows An Engineer Suspected That The Surface Finish Of A Metal Part Is Influenced By The F 1 (72.03 KiB) Viewed 36 times
- A 22 Experiment Was Run As Follows An Engineer Suspected That The Surface Finish Of A Metal Part Is Influenced By The F 2 (72.05 KiB) Viewed 36 times
- A 22 Experiment Was Run As Follows An Engineer Suspected That The Surface Finish Of A Metal Part Is Influenced By The F 3 (44.64 KiB) Viewed 36 times
A 22 experiment was run as follows. An engineer suspected that the surface finish of a metal part is influenced by the feed rate (A) and depth of cut (B). She selects feed rates of 0.20 and 0.30 inches/minute and 0.15 and 0.20 inches for depth of cut. She selects 20 parts and runs a completely randomized 22 design with (5 replications. The surface finish of each part was recorded in surface finish units (SFUs). The low and high levels of each factor were coded -1 and +1 respectively. Note that the -1, +1 coding is simply a linear transformation of the original variables (later called natural variables by Montgomery) if the variables (factors) are quantitative. If a variable is qualitative (categorical), then the assignment of -1, +1 is arbitrary. The table below summarizes the results by showing the mean and standard deviation of the five observations for each treatment. A B y S O B -1 - 1 90 10 0.214 +1 -1 105 9 -1 +1 115 7 0-30(+1) +1 +1 120 8 0.2014) Ot!) 1. Give the equation used to transform feed rate from its natural scale to the coded scale (A), i.e. A = f(feed rate) and show f(feed rate). 17 0.20(-1) +0-30C +1) 267 2. Calculate and interpret a 95% confidence interval for the mean response when A= -1 and B = -1, i.e. _.. (We did not do this in class but you should be able to do it.) 6.43 3. Calculate and interpret a 95% confidence interval for the mean response when A +1 and B = -1 minus the mean response when A= -1 and B = -1 i.e. H+----- (We did not do this in class but you should be able to do it.) 4. Draw the interaction plot. (a) Describe the effect of A when B= -1. 51
(b) Describe the effect of A when B = +1. (c) Based solely on the plot and your answers above, does it appear that there is an AB interaction effect? Why or why not? 5. Calculate the effects of A, B, and AB 6. Calculate and interpret a 95% confidence interval for the effect of A. 7. Give the ANOVA table for the model y = x+7+ 8+(B) + fixed effects, N (0,0%) tid. Include the columns Source, df, SS, MS, F, p-value 8. Based on this ANOVA table, and using a = .05, (a) Is there a significant AB interaction effect? (b) Regardless of your answer to the interaction question above, is there a significant effect of A? (e) Regardless of your answer to the interaction question above, is there a significant effect of B? 9. Give the fitted regression model with the -1, +1 coding that corresponds to this ANOVA table 10. Test for an effect of A in this regression model by providing Ho, H., t statistic, p-value, and conclusion 11. Convert the above fitted regression model to the regression model based on the natural units, 12. Predict the response when feed rate = 0.27 inches/minute and depth of cut = 0.17 inches (Just a point estimate is sufficient.) 13. Note that smaller SFU values are desirable and assume the four treatments are the only possible choices (a) Which treatment (A = B = .) do you recommend. Why? (b) Are you "confident that this choice is best? Answer statistically 14. Give the ANOVA table for the model yk = +74+B) + Euk, fixed effects, Eusk ~ N(0,0) lid. Include the columns Source, df, SS, MS, F, p-value.