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Analysis of Factorial Designs: Example: Design To Identify Factors That Effect Tool Life

This document summarizes the analysis of a factorial design experiment to identify factors that affect tool life. It finds that the cut speed (A) and cut angle (C) have the most significant effects on the tool life based on the fitted model. It recommends using a high cut speed and low cut angle to maximize tool life. Center points were added to the design to check for non-linear effects, but no evidence of curvature was found, validating the linear model.

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74 views7 pages

Analysis of Factorial Designs: Example: Design To Identify Factors That Effect Tool Life

This document summarizes the analysis of a factorial design experiment to identify factors that affect tool life. It finds that the cut speed (A) and cut angle (C) have the most significant effects on the tool life based on the fitted model. It recommends using a high cut speed and low cut angle to maximize tool life. Center points were added to the design to check for non-linear effects, but no evidence of curvature was found, validating the linear model.

Uploaded by

sainandha
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOC, PDF, TXT or read online on Scribd
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Analysis of

Example:
23

2k

Factorial Designs
(Problems 6 ! " 6 6#

Design to Identify Factors That Effect Tool Life

A $ %&t 'peed ( $ Tool )eometry % $ %&t Angle After entering the data found on page 254 of the text we begin our analysis by looking at a half normal plot of the estimated effects. Here we see that the variation in the response is probably driven by the main effect and the interaction between A ! ". #he " main effect also appears large$ but if it is involved in a significant interaction it will be included in the model along with the A effect which is currently not selected. %e will get a warning that our model is not hierarchical when we click on the A&'(A tab. )t is best to let the program add any necessary terms *A in this case+ to make the model hierarchical.

A&'(A table for the 2final3 model. #he A main effect is not significant but to keep the model hierarchical we include it.

ecause we have not entered upper and lower limits in the actual units we only need concern ourselves with the fitted model using the coded factors *- , . high$ / , . low+.
Tool Life = 4,.25 .25 A + 5.25 B + 3.11 C 4.11 A 0 C

&ormality seems suspect

#his plot looks fine.

Appears that their may be increased variation in the tool life when "ut Angle *"+ is at the low level. #hus it is possible that cut angle effects variation in the response. ecause we have three replicates we could use ln*4+ as the response to investigate this$ which yields p/value for " . .1456.

Plot of the A*% Interaction

Plot of the ( +ain Effect

#o maximi7e the tool life we definitely want to use at the high level. Also from the interaction plots we see that " at the high level and A at the low level results in the largest mean tool life. #his is also confirmed from the cube plot on the follow page. %,(E PL-T

. D /E'P-0'E ',/FA%E PL-T

8esponse surface viewed with at the high level. 9ou drag the slider to any position for and see the resulting changes in the level of the surface. %-0T-,/ PL-T -F /E'P-0'E ',/FA%E

Adding %enter Points to %hec1 for %&r2at&re (Problem 6 6#

Add center points to the existing design by selecting Design Tools 8 A&gment Design333 "hecking the options and editing the fields in the resulting dialog box as shown on the left will add four center points to the current design.

Adding %enter Points (see pgs3 456 47!# )n problem 5/5 of your text$ we asked to consider replicate , only *6 runs+ of the previous experiment and to add 4 center points to the design. #he addition of center points to design allows up to check whether the linearity of the effects is a reasonable assumption or whether :uadratic terms should be added to the model. "enter points are only applicable when the factors being studied are numeric. Pict&re:

)n ;esign <xpert select a full 2 3 factorial design with n = 1 replicates and then add 4 center points to check for curvature.

Add 4 center points to the design. #he test for curvature is given anytime center points are added to a 2 k factorial design. Here we see that there is no evidence of curvature so the assumption of linear effects is reasonable here. #he addition of center points also allows for lac1 of fit testing and we can see that the current model appears to be ade:uate for the given experimental data.

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