Statistics Assignment

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Improve Phase Assignment

This phase is referred to as the proactive phase since the levels of input factors are changed to observe the effect on the output variable.

This phase will consider Analysis of Variance (ANOVA One Way and Two Way) and Design of Experiment (DOE)

Referred To:

Text Book: Implementing Six Sigma Smarter Solutions using Statistical Methods 2nd Edition By Forrest W Breyfogle III

a. Chapter 24

b. Chapter 25

Chapter 24

1. Exercise 7

2. Exercise 8

3. A manufacturer of steel wants to test the effect of the method of manufacture on the tensile strength of a particular type of steel. Four different methods have been tested and the data shown in Table 1. Test the significance of the effect at α = 0.05

Table 1

Methods Tensile Strength

1	2650	2765	2750	2600
2	2985	2975	2865	2890
3	2775	2620	2690	2700
4	2900	2885	2850	2950

Chapter 25

1. Exercise 2

2. A 2 Factor experiment was conducted to test whether the given factors affect the response variable. The data shown in Table 5 were collected for 3 levels for A and B respectively with 4 replicates.

i). Using α = 0.05, test for the significance of all possible effects.

Table 5

Factor A

Factor B 600 650 700

1	142, 113, 126, 130	115, 129, 109, 98	135, 120, 115, 110
2	122, 104, 118, 138	112, 104, 100, 119	144, 132, 120, 139
3	110, 126, 138, 120	122, 100, 118, 109	142, 130, 110, 125

3. A group of experimenters determine that 3 factors seem to have the most influence on a coating process. The measure the out come Y in terms of coating thickness in some consistent way.

		B - Catalyst
		0.1g/l	0.2g/l
	C- Temperature	C - Temperature
	15C	25C	15C	25C
A - Belt Rate	19	21	21	20
400 mm/min	17	20	19	18
Sum	36	41	40	38
	20	20	25	26
800 mm/min	19	23	22	24
Sum	39	43	47	50

· Which factors and interactions effects are significant?

4. In a 23 Full Factorial experiment to test the effects of cutting speed (A), Feed rate (B) and Hardness (C) on the surface finish. The data in Table 7 shows one observation per each of the 8 combinations.

i). Conduct ANOVA at α = 0.05 to test for the significance of all possible effects.

Table 7

Cutting Speed A

300RPM 350RPM

Hardness C

30 40 30 40

Feed Rate B

0.002 10 15 8 13

0.004 14 16 10 12

5. 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 follow:

			Treatment		Replicate
A	B	C	Combination	I	II	III
-	-	-	(1)	22	31	25
+	-	-	a	32	43	29
-	+	-	b	35	34	50
+	+	-	ab	55	47	46
-	-	+	c	44	45	38
+	-	+	ac	40	37	36
-	+	+	bc	60	50	54
+	+	+	abc	39	41	47

· Estimate the factor effects. Which effects appear to be large?