American University of Armenia
Influence of Key Process Parameters on
Injection Blow Molding Quality
Design and Analysis of Experiments
College of Science and Engineering
Instructor: Alexan Simonyan
Students: Asdghig Ashekian, Avedis Keoshkerian
Fall 2015
Contents
Introduction .................................................................................................................................................. 3
The Response Variable .................................................................................................................................. 4
The Factors Which the Response Variable May Depend On and Their Levels ............................................. 5
Operations : .................................................................................................................................................. 5
Tests & Results .............................................................................................................................................. 6
Checking for normality (Kolmogorov-Smirov test): .................................................................................. 6
Performing Mann-Witney U test to compare mean value of percentage of defectives in the two types
of performs: .............................................................................................................................................. 7
Performing Mann-Witney U test to compare mean value of percentage of defectives in the two
machines: .................................................................................................................................................. 7
Chi Square test for independence (Machines and perform types): ......................................................... 8
Kruskal-Wallis test for 4 independent samples: ....................................................................................... 8
2 Independent sample test within the 4 groups:...................................................................................... 9
Machine A, virgin VS PCR ...................................................................................................................... 9
Virgin Machine A VS Machine B ............................................................................................................ 9
Machine A , virgin VS Machine B, PCR: ............................................................................................... 10
Machine A,PCR VS Machine B, virgin: ................................................................................................. 10
PCR Machine A VS Machine B: ............................................................................................................ 11
Machine B virgin VS PCR: .................................................................................................................... 12
Kruskal-Wallis test for color effect on percentage of defectives: .......................................................... 12
Regression Analysis: ................................................................................................................................ 13
Test for correlation between numerical variables:............................................................................. 13
Linear Regression: ............................................................................................................................... 14
Curve Estimation ................................................................................................................................. 15
OLAP Cubes ............................................................................................................................................. 16
Conclusions ................................................................................................................................................. 17
2
Introduction
Blow molding: is a manufacturing process by which hollow plastic parts are formed. In general, there
are three main types of blow molding: extrusion blow molding, injection blow molding, and injection
stretch blow molding.
Injection blow molding is used for the Production of hollow objects in large quantities. The main
applications are bottles, jars and other containers. The injection blow molding machine is based on an
extruder barrel and screw assembly which melts the polymer. The molten polymer is fed into a manifold
where it is injected through nozzles into a hollow, heated pre form mold. The pre form mould forms the
external shape and is clamped around a mandrel (the core rod) which forms the internal shape of the pre
form. The pre form consists of a fully formed bottle/jar neck with a thick tube of polymer attached, which
will form the body.
PET Preform
A hot pre form is clamped in a blow mold. A stretch rod is usually used to stretch the pre form to the
base of the mold, while low pressure compressed air is used to “pre-blow” the pre form into a bubble.
Then high pressure air is applied to push the PET bubble into all the details of the blow mold, and to cool
the newly-made bottle. Time is allotted in the cycle to depressurize the mold before opening it and
removing the bottle.
Blowing Process 1
Our study is focused on the blowing part of the process. Lebanese bottling company provided us with
their data that includes the following:
Number of used pre forms
3
Adequate produced bottles
Pre form color:
Pre form type
Pre form temperature
Blowing machine
Blowing pressure (pressure difference)
Preform type: The company purchases two types of performs;PCR (post consumer recycled), and virgin
(non recycled) .We think that the type of the preform affects the quality of the production.
Preform color: The Company produces 3 different colored bottles (clear, green, and blue).The color may
also has the its impact on the quality of the products.
Preform temperature: It is the temperature recorded by the sensor in the blow molding machine just
before blowing the perform.
Blowing machine: The Company has two machines from different manufacturers, both machines are set
to work on the same rate, pressure, and perform temperature.
Blowing pressure: he pressure of blowing can differ from the specification. This also can affect the
quality.
The Response Variable
We want to introduce the response variable as the percentage of defective produced bottles.
Defective% =
No. of used preform − No. of adequate botlles
∗ 100%
No. of used preform
4
The Factors Which the Response Variable May Depend On and Their
Levels
1. Preform type
a. PCR =1
b. Virgin =0
2. Preform color
a. Clear = 1
b. Green = 2
c. Blue =3
3. Preform temperature
4. Blowing machine
a. Machine A =0
b. Machine B=1
5. Blowing pressure Difference
Operations :
PCR vs Virgin: Determine whether there is significant difference between percentages of defectives
from the mentioned two types.
Machine 1 vs Machine 2: Determine whether there is significant difference between percentages of
defectives from the mentioned two machines.
Clear vs Blue vs Green: Determine whether there is significant difference between the percentage of
deffectives of the 3 colors.
Regression:We will search for the independent variables that our response variable mostly depend on,
and fit a regression model. (add dummy variables if needed).
Perform Olap cubes using preform types, colors, and blowing machines.
5
Tests & Results
Checking for normality (Kolmogorov-Smirov test):
Tests of Normality
Kolmogorov-Smirnova
Machine
percentage of defectives
Statistic
Df
Shapiro-Wilk
Sig.
Statistic
df
Sig.
machine A
.252
52
.000
.736
52
.000
machine B
.115
52
.083
.939
52
.010
a. Lilliefors Significance Correction
Tests of Normality
Kolmogorov-Smirnova
type
percentage of defectives
Statistic
df
Shapiro-Wilk
Sig.
Statistic
df
Sig.
virgin
.124
52
.045
.903
52
.000
PCR
.247
52
.000
.809
52
.000
a. Lilliefors Significance Correction
As it is shown in the tables above, according to Kolmogorov-Smirnov test 3 out of the 4 groups have non
normal distributions, therefore it’s more accurate to continue our tests with the assumption of non
normality.
Instead of doing ANOVAs we will perform non parametric 2 and K independent samples tests. Also
because the numbers of cases are equal in each group the mean ranks will hint us to determine which of
the groups have higher percentage of defectives in average.
6
Performing Mann-Witney U test to compare mean value of percentage of
defectives in the two types of performs:
Ranks
type
percentage of defectives
N
Mean Rank
Sum of Ranks
virgin
52
60.02
3121.00
PCR
52
44.98
2339.00
Total
104
Test Statisticsa
percentage of
defectives
Mann-Whitney U
961.000
Wilcoxon W
2339.000
Z
-2.542
Asymp. Sig. (2-tailed)
.011
a. Grouping Variable: type
Asymp. Sig. is less that 0.05 which means we reject the null hypothesis of the mean ranks equality, in
other words we can conclude that PCR performs has less defectives than virgin performs.
Performing Mann-Witney U test to compare mean value of percentage of
defectives in the two machines:
Ranks
Machine
percentage of defectives
N
Mean Rank
Sum of Ranks
machine A
52
41.07
2135.50
machine B
52
63.93
3324.50
Total
104
Test Statisticsa
percentage of
defectives
Mann-Whitney U
Wilcoxon W
Z
Asymp. Sig. (2-tailed)
757.500
2135.500
-3.865
.000
a. Grouping Variable: Machine
7
Asymp. Sig. value is 0, this means the mean ranks for the two groups are significantly different. Mean
ranks shows that in average machine A has lower percentage of defectives than machine B.
Chi Square test for independence (Machines and perform types):
Chi-Square Tests
Value
Asymp. Sig. (2-
Exact Sig. (2-
Exact Sig. (1-
sided)
sided)
sided)
df
.000a
1
1.000
Continuity Correctionb
.000
1
1.000
Likelihood Ratio
.000
1
1.000
Pearson Chi-Square
Fisher's Exact Test
1.000
Linear-by-Linear Association
.000
N of Valid Casesb
104
1
.578
1.000
a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 26.00.
b. Computed only for a 2x2 table
Since the Asymp. Sig. for Pearsons chi-square test is 1 this means that the two variables are fully
independent. Next we will compute a new categorical variable with 4 levels to test the four machines
and perform types combinations.
Kruskal-Wallis test for 4 independent samples:
Ranks
M_T
percentage of defectives
N
Mean Rank
machine A,virgin
26
50.02
machine A,PCR
26
32.12
machine B,virgin
26
70.02
machine B,PCR
26
57.85
Total
104
Test Statisticsa,b
percentage of
defectives
Chi-Square
Df
Asymp. Sig.
21.636
3 a. Kruskal Wallis Test
.000 b. Grouping Variable: M_T
Asymp. Sig. value is 0, which means that the mean ranks of at least 2 of the groups are not equal.
8
2 Independent sample test within the 4 groups:
Machine A, virgin VS PCR
Ranks
M_T
percentage of defectives
N
Mean Rank
Sum of Ranks
machine A,virgin
26
31.10
808.50
machine A,PCR
26
21.90
569.50
Total
52
Test Statisticsa
percentage of
defectives
Mann-Whitney U
218.500
Wilcoxon W
569.500
Z
-2.188
Asymp. Sig. (2-tailed)
.029
a. Grouping Variable: M_T
Asymp. Sig. is less than 0.05, H0 is rejected, which means the mean ranks are not equal, and the
ranks shows that PCR type has lower percentage of defectives than virgin in machine A.
Virgin Machine A VS Machine B
Ranks
M_T
percentage of defectives
N
Mean Rank
machine A,virgin
26
21.38
556.00
machine B,virgin
26
31.62
822.00
Total
52
Test Statisticsa
percentage of
defectives
Mann-Whitney U
205.000
Wilcoxon W
556.000
Z
Asymp. Sig. (2-tailed)
Sum of Ranks
-2.434
.015
a. Grouping Variable: M_T
9
Asymp. Sig. is less than 0.05, H0 is rejected, which means the mean ranks are not equal, and the
ranks shows that machine A has less percentage of defectives than machine B when it comes to
virgin performs.
Machine A , virgin VS Machine B, PCR:
Ranks
M_T
percentage of defectives
N
Mean Rank
Sum of Ranks
machine A,virgin
26
24.54
638.00
machine B,PCR
26
28.46
740.00
Total
52
Test Statisticsa
percentage of
defectives
Mann-Whitney U
287.000
Wilcoxon W
638.000
Z
-.933
Asymp. Sig. (2-tailed)
.351
a. Grouping Variable: M_T
The test shows that the null hypothesis cannot be rejected which means that there s no significant
difference between the percentage of defectives of the 1st and 4th groups.
Machine A,PCR VS Machine B, virgin:
Ranks
M_T
percentage of defectives
N
Mean Rank
Sum of Ranks
machine A,PCR
26
17.83
463.50
machine B,virgin
26
35.17
914.50
Total
52
10
Test Statisticsa
percentage of
defectives
Mann-Whitney U
112.500
Wilcoxon W
463.500
Z
-4.128
Asymp. Sig. (2-tailed)
.000
a. Grouping Variable: M_T
Asymp. Sig. is less than 0.05, H0 is rejected, which means the mean ranks are not equal, and the ranks
shows that the percentage of defectives are greater in machine B, virgin group than in machine A, PCR
group.
PCR Machine A VS Machine B:
Ranks
M_T
percentage of defectives
N
Mean Rank
Sum of Ranks
machine A,PCR
26
19.38
504.00
machine B,PCR
26
33.62
874.00
Total
52
Test Statisticsa
percentage of
defectives
Mann-Whitney U
153.000
Wilcoxon W
504.000
Z
Asymp. Sig. (2-tailed)
-3.387
.001
a. Grouping Variable: M_T
Asymp. Sig. is less than 0.05, H0 is rejected, which means the mean ranks are not equal, and the ranks
shows that machine A has less percentage of defectives than machine B when it comes to PCR performs.
11
Machine B virgin VS PCR:
Ranks
M_T
percentage of defectives
N
Mean Rank
Sum of Ranks
machine B,virgin
26
30.23
786.00
machine B,PCR
26
22.77
592.00
Total
52
Test Statisticsa
percentage of
defectives
Mann-Whitney U
241.000
Wilcoxon W
592.000
Z
-1.775
Asymp. Sig. (2-tailed)
.076
a. Grouping Variable: M_T
The test shows that the null hypothesis cannot be rejected which means that there s no significant
difference between the percentages of defectives of the machine B either for virgin or PCR performs.
Kruskal-Wallis test for color effect on percentage of defectives:
Ranks
Color
percentage of defectives
N
Mean Rank
Clear
36
57.31
Green
35
47.81
Blue
33
52.23
Total
104
12
Test Statisticsa,b
percentage of
defectives
Chi-Square
1.761
df
2
Asymp. Sig.
.415
a. Kruskal Wallis Test
b. Grouping Variable: Color
Because Asymp. Sig. is greater than 0.05, h0 cannot be rejected , in other words color don’t effect on the
percentage of defectives.
Regression Analysis:
Test for correlation between numerical variables:
Nonparametric Correlations
Correlations
percentage of
defectives
Spearman's rho
percentage of defectives
-.423**
.101
.
.000
.309
104
104
104
-.423**
1.000
.082
Sig. (2-tailed)
.000
.
.410
N
104
104
104
Correlation Coefficient
.101
.082
1.000
Sig. (2-tailed)
.309
.410
.
N
104
104
104
N
P
P
1.000
Correlation Coefficient
Sig. (2-tailed)
Temp
temp
Correlation Coefficient
**. Correlation is significant at the 0.01 level (2-tailed).
Since our response variable does not have normal distribution, we will us non
parametric(Spearman's) correlation result.
The test shows that our response variable is highly correlated with the temperature of performs
with negative coefficient, and pressure difference is not correlated with the other variables.
13
Linear Regression:
Model Summary
Model
R
Std. Error of the
Square
Estimate
R Square
.583a
1
Adjusted R
.340
.313
.2476434616
a. Predictors: (Constant), MachineB_PCR, temp, MachineA_Virgin,
MachineA_PCR
Coefficientsa
Standardized
Unstandardized Coefficients
Model
1
B
Std. Error
(Constant)
7.747
1.505
temp
-.074
.015
MachineA_Virgin
-.202
MachineA_PCR
MachineB_PCR
Coefficients
Beta
t
Sig.
5.146
.000
-.399
-4.820
.000
.069
-.294
-2.939
.004
-.311
.069
-.453
-4.484
.000
-.130
.069
-.189
-1.877
.064
a. Dependent Variable: percentage of defectives
In our linear regression model we used the most correlated numerical variable (temperature of
preforms) and added 3 dummy variables for the four level categorical variable (Machine*type)
Backward method was used , no variables was removed and the Adjusted R Square shows that the
model doesn’t fit linear regression , also the P value for MachineB_PCR is greater than 0.05 which means
B4=0
% of defectives = 7.747 - 0.074*temp - 020 2*MachineA_Virgin - 0.311* MachineA_PCR
14
Curve Estimation
We will split our file into 3 ( MachineA_Virgin , MachineA_PCR, MachineB)
Model Summary and Parameter Estimatesa
Dependent Variable:percentage of defectives
Model Summary
Equation
R Square
F
Parameter Estimates
df1
df2
Sig.
Constant
b1
b2
b3
Linear
.102
5.690
1
50
.021
5.944
-.057
Logarithmic
.103
5.771
1
50
.020
25.918
-5.566
Inverse
.105
5.851
1
50
.019
-5.187
547.414
Quadratic
.102
5.690
1
50
.021
5.944
-.057
.000
Cubic
.164
4.790
2
49
.013
176.989
-2.681
.000
Compound
.070
3.760
1
50
.058
5.154E8
.803
Power
.071
3.802
1
50
.057
2.013E42
-21.559
9.145E-5
The independent variable is temp.
a. splitgroups = 3.00
Model Summary and Parameter Estimatesa
Dependent Variable:percentage of defectives
Model Summary
Equation
R Square
F
Parameter Estimates
df1
df2
Sig.
Constant
b1
b2
b3
Linear
.110
2.967
1
24
.098
4.972
-.049
Logarithmic
.112
3.018
1
24
.095
22.414
-4.857
Inverse
.113
3.069
1
24
.093
-4.741
478.804
Quadratic
.110
2.967
1
24
.098
4.972
-.049
.000
Cubic
.230
3.442
2
23
.049
238.363
-3.627
.000
Compound
.130
3.585
1
24
.070
1.395E12
.731
Power
.132
3.658
1
24
.068
2.883E60
-30.969
The independent variable is temp.
a. splitgroups = 2.00
15
.000
Model Summary and Parameter Estimatesa
Dependent Variable:percentage of defectives
Model Summary
Equation
R Square
F
Parameter Estimates
df1
df2
Sig.
Constant
b1
b2
b3
Linear
.674
49.510
1
24
.000
15.175
-.152
Logarithmic
.676
50.075
1
24
.000
68.625
-14.917
Inverse
.678
50.630
1
24
.000
-14.658
1.459E3
Quadratic
.674
49.510
1
24
.000
15.175
-.152
.000
Cubic
.722
29.875
2
23
.000
204.829
-3.066
.000
Compound
.489
23.011
1
24
.000
3.440E25
.537
Power
.488
22.862
1
24
.000
6.806E119
-60.654
The independent variable is temp.
a. splitgroups = 1.00
The test shows that :




For Machine B (split group 3) the best fit curve is the cubic with R square = 0.164
For Machine A PCR type perform (split group 2) the best fit curve is the cubic with R square =
0.230
For Machine A virgin type perform (split group 1) the best fit curve is the cubic with R square =
0.722
Only the group one has enough R square value to say that it could fit the mentioned model
OLAP Cubes
Type
machine A
percentage of defectives
% of Total N
Median
Machine
Machine
machine B
Total
machine A
machine B
Total
Virgin
25.0%
25.0%
50.0%
0.165
0.421
0.318
PCR
25.0%
25.0%
50.0%
0.054
0.247
0.130
Total
50.0%
50.0%
100.0%
0.086
0.368
0.172
16
.000
Conclusions

The PCR has lower defectives percentage than the Virgin type performs.

The Machine A has lower defectives percentage than the Machine B.

The combination of Machine & Type has effect on the percentage of defectives.

Regression analysis shows that none of the tested models fit the response variable
except of the cubic model in the case of MachineA_Virgin group of samples.

To make this research more accurate , we suggest to increase the sample size ,
which may make the normality assumption valid and that may change some of
the observations.
17