2.- An engineer suspects that the surface finish of a metal part is influenced b

Question

2.- An engineer suspects that the surface finish of a metal part is influenced by the depth of cut (factor A) and the feed rate (factor B). She selects four depths of cut and three feed rates. She then conducts a factorial experiment and obtains the following data: (i=1,2,3,4 for Depth = 0.15, 0.18, 0.20, and 0.25, respectively; j=1,2,3 for Feed-0.20, 0.25 and 0.30, respectively) Depth of Cut (in) Feed Rate 0.15 0.18 0.20 0.25 (in/min) 74 64 60 79 68 73 82 0.20 104 92 96 92 98 104 0.25 86 104 108 110 95 104 108 114 0.30 98 102 95 107

Explanation / Answer

b)

SSw= sum of squares within the means

SSb=sum of squares betwee the means

MSSw= Mean sum of squares within the means

MSSb=Mean sum of squares between the means

and

F= MSSw/MSSb

Using the ANOVA we get the

MSSw = 64.66= SSw/dof

dof= 6

MSSb=52.33= SSb/dof

dof= 36-8=28

F= 64.66/52.33

   =1.23562

tabulated F= 3.8082

e)

Since the calculated F falls well within the acceptance region defined by all values less than 3.8082

Being so it can be concluded that if:

H0: there is an association between the feed rate and depth of cut

H1: there is no association between the feed rate and depth of cut

H0 will be accepted

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