influence of key process parameters on …ac.aua.am/.../public/final-spss-project-final.docx · web...

College of Science and EngineeringInstructor: Alexan SimonyanStudents: Asdghig Ashekian, Avedis Keoshkerian

American University of Armenia

Fall 2015

ContentsIntroduction.................................................................................................................................................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:

3

https://en.wikipedia.org/wiki/Plastic

Number of used pre forms

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 VariableWe want to introduce the response variable as the percentage of defective produced bottles.

Defective%= No .of used preform−No .of adequatebotllesNo. of used preform

∗100 %

4

The Factors Which the Response Variable May Depend On and Their Levels

1. Preform typea. PCR =1b. Virgin =0

2. Preform color a. Clear = 1b. Green = 2c. Blue =3

3. Preform temperature4. Blowing machine

a. Machine A =0b. 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

Machine

Kolmogorov-Smirnova Shapiro-Wilk

Statistic Df Sig. Statistic df Sig.

percentage of defectives machine A .252 52 .000 .736 52 .000

machine B .115 52 .083 .939 52 .010

a. Lilliefors Significance Correction

Tests of Normality

type

Kolmogorov-Smirnova Shapiro-Wilk

Statistic df Sig. Statistic df Sig.

percentage of defectives 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 N Mean Rank Sum of Ranks

percentage of defectives 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 N Mean Rank Sum of Ranks

percentage of defectives machine A 52 41.07 2135.50

machine B 52 63.93 3324.50

Total 104

Test Statisticsa

percentage of

defectives


7

Ranks

Machine N Mean Rank Sum of Ranks

percentage of defectives machine A 52 41.07 2135.50

machine B 52 63.93 3324.50

Wilcoxon W 2135.500

Z -3.865


a. Grouping Variable: Machine

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 df

Asymp. Sig. (2-

sided)

Exact Sig. (2-

sided)

Exact Sig. (1-

sided)

Pearson Chi-Square .000a 1 1.000

Continuity Correctionb .000 1 1.000

Likelihood Ratio .000 1 1.000

Fisher's Exact Test 1.000 .578

Linear-by-Linear Association .000 1 1.000

N of Valid Casesb 104

a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 26.00.

b. Computed only for a 2x2 tableSince 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.

8

Kruskal-Wallis test for 4 independent samples:

Ranks

M_T N Mean Rank

percentage of defectives 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 21.636

Df 3 a. Kruskal Wallis Test

Asymp. Sig. .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.

2 Independent sample test within the 4 groups:

Machine A, virgin VS PCR

Ranks

M_T N Mean Rank Sum of Ranks

percentage of defectives machine A,virgin 26 31.10 808.50

machine A,PCR 26 21.90 569.50

Total 52

Test Statisticsa

percentage of

defectives


Wilcoxon W 569.500

9

Ranks



machine A,PCR 26 21.90 569.50

Z -2.188


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



machine B,virgin 26 31.62 822.00

Total 52

Test Statisticsa

percentage of

defectives


Wilcoxon W 556.000

Z -2.434



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.

10

Machine A , virgin VS Machine B, PCR:

Ranks



machine B,PCR 26 28.46 740.00

Total 52

Test Statisticsa

percentage of

defectives


Wilcoxon W 638.000

Z -.933



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


percentage of defectives machine A,PCR 26 17.83 463.50

machine B,virgin 26 35.17 914.50

Total 52

11

Test Statisticsa

percentage of

defectives


Wilcoxon W 463.500

Z -4.128



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


percentage of defectives machine A,PCR 26 19.38 504.00

machine B,PCR 26 33.62 874.00

Total 52

Test Statisticsa

percentage of

defectives


Wilcoxon W 504.000

Z -3.387



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.

12

Machine B virgin VS PCR:

Ranks


percentage of defectives machine B,virgin 26 30.23 786.00

machine B,PCR 26 22.77 592.00

Total 52

Test Statisticsa

percentage of

defectives


Wilcoxon W 592.000

Z -1.775



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 N Mean Rank

percentage of defectives Clear 36 57.31

Green 35 47.81

Blue 33 52.23

Total 104

13

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 temp P

Spearman's rho percentage of defectives Correlation Coefficient 1.000 -.423** .101

Sig. (2-tailed) . .000 .309

N 104 104 104

Temp Correlation Coefficient -.423** 1.000 .082

Sig. (2-tailed) .000 . .410

N 104 104 104

P Correlation Coefficient .101 .082 1.000

Sig. (2-tailed) .309 .410 .

N 104 104 104

**. 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.

14

Linear Regression:

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .583a .340 .313 .2476434616

a. Predictors: (Constant), MachineB_PCR, temp, MachineA_Virgin,

MachineA_PCR

Coefficientsa

Model

Unstandardized Coefficients

Standardized

Coefficients

t Sig.B Std. Error Beta

1 (Constant) 7.747 1.505 5.146 .000

temp -.074 .015 -.399 -4.820 .000

MachineA_Virgin -.202 .069 -.294 -2.939 .004

MachineA_PCR -.311 .069 -.453 -4.484 .000

MachineB_PCR -.130 .069 -.189 -1.877 .064

a. Dependent Variable: percentage of defectivesIn 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

15

Curve Estimation

We will split our file into 3 ( MachineA_Virgin , MachineA_PCR, MachineB)

Model Summary and Parameter Estimatesa

Dependent Variable:percentage of defectives

Equation

Model Summary Parameter Estimates

R Square F 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 9.145E-5

Compound .070 3.760 1 50 .058 5.154E8 .803

Power .071 3.802 1 50 .057 2.013E42 -21.559

The independent variable is temp.

a. splitgroups = 3.00



Equation



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 .000

Compound .130 3.585 1 24 .070 1.395E12 .731

Power .132 3.658 1 24 .068 2.883E60 -30.969



16



Equation



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 .000

Compound .489 23.011 1 24 .000 3.440E25 .537

Power .488 22.862 1 24 .000 6.806E119 -60.654



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

% of Total N Median

Machine Machine

machine A machine B Total machine A machine B Total

percentage of defectives 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

17

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.

18

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