"PERFORMANCE OF DATA TRANSMISSION USING A USER AUTHENTICATION SYSTEM
FOR WIRELESS NETWORKS"
MATH 6301 PLANIFICATION ET ANALYSE STATISTIQUE D’EXPÉRIENCES
PROF. DR. BERNARD CLÉMENT PRESENTED BY CHRISTINA BRAZ
APRIL 21, 2004
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User Authentication System Overview
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Purpose of Experiment
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Experimental Design
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Results
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Conclusion
PRESENTATION PLAN
USER AUTHENTICATION SYSTEM OVERVIEW (1)
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To identify the optimal response time between ChipTag <-> Mobile Reader (Lower the better)
PURPOSE OF EXPERIMENT
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Statistical Plan: Screening
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Two-level fractional factorial design
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2 5-1 Fractional Factorial Design Plan :
– 5 factors in a total of 16 treatments
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Repetition number: n=2
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Resolution V (confounded effects)
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Analyse de la variance (ANOVA)
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Regression Analyses
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Residual Analyses
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Interaction Plots
EXPERIMENTAL DESIGN (1)
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Independent Variables (Factors):
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X1= Operating Frequency (100 – 500 kHz)
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X2= Operating Read Range (0.2 – 0.5 m)
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X3= Total Speed (30 – 100 Bps)
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X4= ChipTag Volume (159.76 cm3)
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X5= ChipTag Memory (64 – 128 bits) Dependent Variables (Responses)
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Y2 = Response Time (10 – 30 ms) Smaller the better
EXPERIMENTAL DESIGN (2)
Advantages
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Screening design (Many factors can be tested, few trial runs)
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Vary each factor with a small number of levels (2)
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A saving of factors just 5 (Savings $)
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Treatments savings (16 traitements is suffice)
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Repetition n=2 (Ø variation × sensitive to ≠s)
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Resolution V (E=ABCD)
EXPERIMENTAL DESIGN (3)
EXPERIMENTAL DESIGN (4)
1 2
2 2
2 30
16
1 1
2 2
2 21
15
1 2
1 2
2 30
14
1 1
1 2
2 19
13
1 2
2 1
2 30
12
1 1
2 1
2 18
11
1 2
1 1
2 28
10
1 1
1 1
2 16
9
1 2
2 2
1 27
8
1 1
2 2
1 15
7
1 2
1 2
1 25
6
1 1
1 2
1 13
5
1 2
2 1
1 24
4
1 1
2 1
1 12
3
1 2
1 1
1 22
2
1 1
1 1
1 10
1
X5
ChipTag Volume (cm3) X4
ChipTag Memory (Bits) X3
Total Speed (Bps) X2
Operating Read Range (M) X1
Operating Frequency (kHz) Y2
Response Time (Ms) Run
RESULTS (1)
RESULTS (2)
With Interaction
RESULTS (3)
Regression with Interaction Model Summary (b)
.000 3
12 580.124
1.000 .315
.998 1.000
1.000(a) 1
Sig. F Change df2
df1 F
Change R Square
Change
Change Statistics Std. Error
of the Estimate Adjusted
R Square R
Square R
Model
a) Predictors: (Constant), x1234, x4, x3, x2, x1, x234, x13, x34, x12, x23, x14, x24; b) Dependent Variable: y2
ANOVA (b)
.099 3
Residual .297
.000 (a) 580.124
57.512 12
690.140 Regression
1
Sig.
F Mean Square
df Sum of
Squares
Model
RESULTS (4)
a) Dependent Variable: y2
.059 -2.971
-.395 .238
-.707 x1234
.570 .636
.144 .724
.461 x234
.589 .603
.100 .996
.600 x34
.963 -.050
-.008 .996
-.050 x24
.589 .603
.100 .996
.600 x23
.378 1.032
.106 .621
.641 x14
.129 2.078
.214 .621
1.291 x13
.378 1.032
.106 .621
.641 x12
.009
6.061
.844 1.829
11.088 x4
.611 -.567
-.079 1.829
-1.037 x3
.337 1.142
.159 1.829
2.088 x2
.111 2.239
.308 1.810
4.052 x1
.079 -2.614
3.683 -9.628
(Constant) 1
Beta Std. Error
B
Sig.
t Standardized
Coefficients Unstandardized
Coefficients Model
Coefficients
RESULTS (5)
With Interaction
RESULTS (6)
RESULTS (7)
Regression without Interaction Variables Entered/Removed (b)
a All requested variables entered; b Dependent Variable: y2
a Predictors: (Constant), x4, x3, x2, x1; b Dependent Variable:
ANOVA (b)
1.849 .000
11 4
445.057 .994
.621 .992
.994 .997(a)
1
Sig. F Change df2
df1 F
Change R
Square Change
Durbin- Watson Change Statistics
Std. Error of the Estimate Adjuste
d R Square R
Square R
Mod el
Enter .
x4, x3, x2, x1(a) 1
Method Variables
Removed Variables Entered
Model
FINAL MODEL
RESULTS (8)
a) Dependent Variable: y2
Coefficients (a)
.000
37.127
.877 .310
11.525 x4
.001
4.349
.103 .310
1.350 x3
.000
8.134
.192 .310
2.525 x2
.000
17.798
.421 .310
5.525 x1
.000
-10.989
- .944 10.375 (Constant)
1
Beta Std.
Error B
Sig.
t Standardized
Coefficients Unstandardized
Coefficients Model
FINAL MODEL
RESULTS (9)
Without Interaction
RESULTS (10)
Without Interaction
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Even with interaction the R2 is almost the same
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Residual analysis: model is not good neither interaction plots
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Regression Analysis:
– The global F test (very significant effect)
– Individual regression coefficients (insignificant effect with interaction
– R2 is almost perfect (without interaction, very high R2 (99%))
– The plots also support the absence of interactions.
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The final model is without interaction (Error / Residual is
CONCLUSIONS
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Clément, B., MTH PLANIFICATION ET ANALYSE STATISTIQUE D'EXPÉRIENCES, Web site course, École Polytechnique de Montréal, Canada (2004)
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Utts, Jessica & Heckard, Robert, MIND ON STATISTICS, Duxbury Thomson Learning, CA – U.S. (2002)
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