Question

Can I have the steps of minitab as well please

Question2) An engineer is interested in the effect of cutting speed (A), metal hardness (B), and cutting angle (C) on the life of a cutting tool. Two levels of each factor are chosen, and two replicates of a 2 factorial design are run. The tool life data (in hours) are shown in the following table. (a) Construct the design matrix with effect and all possible interactions Replicate (bManually calculate the main effects of A(ctting speed), B(hardness) and interactions AB and Treatment Combination BC only using contrasts. (c) II 311 435 354 348 472 440 453 406 377 500 2 19 Using the following ANOVA table, analyze the effects and make conclusions (alpha-0.05): 221 325 Analysis of Variance for life (coded units) Source DE MS ab 552 1332 1332 0.54 0.483 1 28392 28392 11.53 .009 1 20592 20592 8.36 0.020 506 506 0.21 0.662 1 56882 56882 23.10 0.001 2352 2352 0.96 0.357 4830 4830 1.96 0.199 be 605 A"B"C Error 19700 2463 Total 15 134588

Answer 1

a) Design matrix for a factorial design for 3 factors with two levels

I	A	B	A*B	C	A*C	B*C	A*B*C	Rep	Rep	Total
								1	2
1	-1	-1	1	-1	1	1	-1	-3	-1	-4
1	1	-1	-1	-1	-1	1	1	0	-1	-1
1	-1	1	-1	-1	1	-1	1	-1	0	-1
1	1	1	1	-1	-1	-1	-1	2	3	5
1	-1	-1	1	1	-1	-1	1	-1	0	-1
1	1	-1	-1	1	1	-1	-1	2	1	3
1	-1	1	-1	1	-1	1	-1	1	1	2
1	1	1	1	1	1	1	1	6	5	11

b) Main effects:

Effect= (½)^k-1*n(contrast of total)

A = m.e.(A)=¯y(A+) − y¯(A−) = 1 4 (¯y(−−−)+¯y(+ − −) − y¯(− + −)+¯y(+ + −) − y¯(− − +) +¯y(+ − +) − y¯(− + +) + ¯y(+ + +)) =3.00

The contrast is (-1,1,-1,1,-1,1,-1,1)

B : (−1, −1, 1, 1, −1, −1, 1, 1), B = 2.25

C : (−1, −1, −1, −1, 1, 1, 1, 1), C = 1.75

2-factor interactions:

AB: A × B component wise, AB=.75

BC: B × C component wise, BC=.50

c) From the ANOVA table, we can conclude that factor B (hardness), factor C (cutting angle), and the interaction of factor A (cutting speed) & factor C(cutting angle) has the significant effect on the life a cutting tool, because p value is less than 0.05(level of significance.

Steps in minitab

1-Go to Statà DOEà Factorial designàcreate factorial design

2- Select-2-leve factorial

Number of factors-3

3- Click onàDesign

Select- ½ fraction

No. of blocks-1

Click-OK

4- Go to options

Deselect the-randomised run

5- Click-OK- OK