Question

Factorial Design (DOE)

An engineer is interested in the effects of cutting speed (A), tool geometry (B), and cutting angle (C) on the life (in hours) of a machine tool. Two levels of each factor are chosen, and three replicates of a 2³ factorial design are run. The results show the averages of the three replicates:

A	B	C	Mean
-	-	-	26.00
+	-	-	34.67
-	+	-	39.67
+	+	-	49.33
-	-	+	42.33
+	-	+	37.67
-	+	+	54.67
+	+	+	42.33

Please show steps

a) Estimate the factor effects.

b) Which effects appear to be large?

Answer 1

solution- Given Data is IA B sum of 3 oveplicates C Sum of Preplicates mean of 3 replicates 26.00 I 78(26+26+26) 104.01(84167+3467734 + 34.67 + + 119.01 I ' 39.67 49.33 147.99 ' + 126.99 42:33 + 113.01 37.67 + + 164.01 54.67 - + + + + 126.99 42-33 Average effect of factor A:- A = Yat - Y = (a+ab tact abc) _ (1)+ 6 + +6C - Thon (a+ab+ac+abc-7-6-6-6c) - ö (3-99) - 0.3325 Average effect of factoo B:- B: Yet - Y- btab+ bc tabc - (1)+a+c tac P = 1h (btab + bc tabc-l-a-c-ac) Average effect of factoare - = T (135.99) = 411-3325 a c: + -- : 1 + bc +bc+abc -|- a- -ab] - (81.99) - 16:8325

Two factoop interaction effecto Blw factay & :- ab tabe-a-ac - 6+bc-1-0 AB: in un = abc tabte ti-a-ac-b-bc Laig (2017) -F16725 A&C :- TWO factor interaction effect ofw factou AC = actabc-a-ab -ctocolit - Ct6c-1-6 4n ab-a-bc-c abct actbt eci TWO = (-105.99) = -8.8325 factour interaction effect Bllo tas efect Blu factor B BC = bctabc-b-ab - ctac-i-a 4n = Abc + bc +2 +1-ab-b-ac- ... un 47 - tz (-33-99) = -283a5 A,B,C Thoree factour interpolation et ABC = (abc-bc} -(ac-c) - (ab-b) -(0-1) un un = abcta+b+c-ab-ac-bc- sto (-26.01} = -2.1675 o effect on factar B appear to be large.