An experiment was conducted to determine the effect of three factors on warpage in an injection-molding process. The three factors of interest (each at two levels) are A = melt temperature, B = injection speed, and C = injection process. A complete factorial design experiment was conducted with two replicates and the results are given in the table below. Analyse the data from this experiment. Obtain the residuals, and test whether they are normally distributed. Also test whether the variance can be treated constant and whether the run order was satisfactory.
A
B
C
Replicate 1 (Run order)
Replicate 2 (Run order)
-1
-1
-1
1.35 (2)
1.40 (10)
1
-1
-1
2.15 (3)
2.20 (6)
-1
1
-1
1.50 (1)
1.50 (11)
1
1
-1
1.10 (5)
1.20 (14)
-1
-1
1
0.70 (12)
0.70 (15)
1
-1
1
1.40 (7)
1.35 (9)
-1
1
1
1.20 (4)
1.35 (13)
1
1
1
1.10 (8)
1.00 (16)
A single replicate of a 25 design was used to study the compressive strength of concrete. The factors are mix(A), time(B), laboratory(C), temperature(D), and drying time (E). Analyze the data assuming that three-factor and higher interactions are negligible. Use a normal probability plot to assess the effects. The results were: (1)=700, a=900, b=3400, ab=5500, c=600, ac=1000, bc=3000, abc=5300, d=1000, ad=1100, bd=3000, abd=6100,cd=800, acd=1100, bcd=3300, abcd=6000, e=800, ae=1200, be=3500, abe=6200, ce=600, ace=1200, bce=3006, abce=5500, de=1900, ade=1500, bde=4000, abde=6500, cde=1500, acde=2000, bcde=3400, abcde=6300. [Note on Montgomery's notation: In general, a treatment combination is represented by a series of lower case letters. If a letter is present, the corresponding factor is run at the high level in the treatment combination; if it is absent, the factor is run at its low level. For example, treatment combination bcd indicates that factors B, C and D are at the high level and the remaining factors (A and E in this case) are at the low level. The treatment combination with all factors at low level is called (1). Further, if there are n replications at each level, the value corresponding to bcd is the sum of the n observations or results at that treatment combination.]
An important property of electrical tape is the Percent Elongation at break. A quarter fraction of a 26 design is used to study the following factors and levels:
Factor
Low value (-)
High value (+)
X1=% of Plasticiser
20%
40%
X2=Time of Compounding
5min
15min
X3=Temp of Compounding
200F
350F
X4=Extruder Speed
200rpm
400rpm
X5=Thickness of tape
5mil
8mil
X6=Source of Plasticizer
A
B
The results were:
X1
X2
X3
X4
X5
X6
Percent elongation
Run Order
-
-
-
-
-
-
96
9
+
-
-
-
+
-
89
15
-
+
-
-
+
+
97
7
+
+
-
-
-
+
91
14
-
-
+
-
+
+
100
13
+
-
+
-
-
+
95
4
-
+
+
-
-
-
105
11
-
+
-
-
-
-
95
12
-
-
-
+
-
+
112
6
+
-
-
+
+
+
106
5
-
+
-
+
+
-
114
8
+
+
-
+
-
-
108
1
-
-
+
+
+
-
120
3
+
-
+
+
-
-
116
16
-
+
+
+
-
+
120
2
+
+
+
+
+
+
118
10
Analyze the experimental data and identify the significant factors. What operating conditions would give a maximum percent elongation?