IEE 572 DESIGN OF ENGINEERING EXPERIMENTS
FALL 2000
FINAL REPORT
TERM PROJECT
AN EXPERIMENTAL DESIGN FOR IMPROVING THE ACCURATE
CLASSIFICATION OF THE IMAGES OF PRESENT AND ABSENT
COMPONENTS IN PRINTED CIRCUIT BOARDS WHEN INSPECTED
BY AN AUTOMATED VISUAL INSPECTION SYSTEM
By
PRAVEEN BABU
SREENIVASULA REDDY KATHA
LUIS MAR
INTRODUCTION
The current miniaturization of the assembly surface mounted devices (SMD) in
Printed Circuit Boards (PCB) makes it a difficult task for human inspectors to
determine their correct positioning and even their presence in the board. This task
becomes even more difficult when the production cycle time for the PCBs is
small, leaving the inspectors with not enough time to accurately complete their
job.
Figure 1: Picture of a PCB. Note the size of
Components compared to a ten cents coin.
The typical solution to this problem is the introduction of an Automated Visual
Inspection (AVI) system to replace the human inspectors.
The imminent
advantage of these systems over human inspectors is their capability of reliably
inspecting a large number of small components at a fixed level of performance for
long periods of time [1]. Figure 2 describes a typical PCB assembly line:
1
Glue
Dispenser
Machine
Placement
Machine
2-D
Inspection
System
PCB
Feeder
Nozzle
(Pipette)
Figure 2. PCB Assembly Line
A bare PCB enters the glue dispenser where glue is placed to the positions in the
board where components will later be mounted.
The next operation is the
placement of the SMD to the board. This operation is performed by chip-shooters
which operate in tandem (placement machine). The components are fed to the
chip-shooter by a feeder, which is an array of rolls containing the components to
be placed in the PCB. Once the components have been fed to the chip-shooter it
places them on the board using vacuum nozzles. After the components have been
placed on the board the AVI machine inspects the presence and correct placement
of the components. [2]
The Electronics Assembly Laboratory (EAL) at Arizona State University is
developing an integrated quality environment for SMD assembly. This
environment consists of several modules that interact with each other to determine
in real time the quality of the assembly process for SMDs and hence the quality of
the product. These modules are:
2
 Inspection Allocation Module (IAM)
 Quality Monitoring Module (QMM)
 Inspection Module (IM)
The IAM instructs the different inspection systems as to which elements to inspect
considering the total available inspection time, the inspection time required by
each component and the needs of the QMM among others.
The QMM uses the information provided by the IM to determine if the SMD
assembly process is in state of statistical quality control.
The inspection module (Figure 3) is in charge of the acquisition, in real time, of
the process information. It consists of four Pulinix TM 440 monochromatic
cameras with a resolution of 510x480 pixels, two IAI actuators operated by
servomotors controlled by a Pentium II computer to move the cameras and an
illumination system composed of a set of eight rails of approximately sixty-six
LEDs each.
The inspection module receives from the IAM a list of components to inspect and
an algorithm to use to perform the inspection. Since one of the objectives of
inspection allocation is to get as much information as possible without increasing
the inspection cycle, the components to be inspected are only a fraction of the total
number of components of the board.
3
Set of cameras
Servo
motors
Set of LEDs
Conveyor
PCB
Figure 3: Side view of AVI system
PROBLEM DEFINITION AND FACTORS TO BE CONSIDERED
The images rendered by the inspection system are the basis for the decision
making of the entire quality control system. In order for these images to be useful
they must provide sufficient level of detail so that the location, inspection and
control chart plotting algorithms can make a decision. This decision consists of
determining whether the components are present or absent and if they are present,
determining their location and angle of rotation with respect to an ideal position
within the board. The quality of the image provided by the cameras in every
inspection routine depends greatly on three factors:
 Iris opening of lenses.
 Angle of illumination of the LEDs.
 Variation of current to manipulate the frontal illumination intensity.
4
The present set up of these factors is leading to an overlap of the populations of
present and absent components as rendered by a classification algorithm that uses
values such as energy, correlation and diffusion of the image captured by the
cameras. The algorithm generates statistical values for present and absent
populations, which can be plotted on histograms (Figure 4 & 5)[3]. When the
image is not accurate there is an overlapping of these histograms that leads to a
component classification error, that is, the value obtained from the algorithm falls
in the range of both the present and absent population (Figure 5).
Figure 4: Classification Algorithm
5
Overlapping
of
populations
2 50
2 00
1 50
P re s e n t
A b se nt
1 00
0
o
0
M
6
1
5
1
3
2
re
0
0
5
0
0
0
0
0
0
0
5
0
0
1
1
2 50
1
0
0
9
5
7
6
0
5
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
1
5
0
0
0
0
0
0
0
50
Overlapping
of
populations
2 00
1 50
P re s e n t
A b s e nt
1 00
M o re
25 0
2 30
2 10
1 90
17 0
15 0
1 30
1 10
90
70
50
30
10
0
-1 0
50
Figure 5: Histograms of present and absent populations of components
When a component cannot be classified none of the quality control techniques can
be applied to decide whether the process is in or out of statistical control. This
creates a general failure of the system.
SELECTION OF RESPONSE VARIABLE
The values obtained from the classification algorithm for present and absent
populations
are calculated using three different inputs, which are energy, correlation and
diffusion all of which are obtained from the image rendered by the inspection. For
6
the purpose of this experiment and in compliance with the request of the AVI
system administrator, we focused on the energy factor. After an inspection routine
is performed, a report file, which contains information regarding energy, is
generated. Tables 1 and 2 show a sample of such reports.
Table 1: Energy values for a
present component.
Component type Orientation Energy
805
V
1
805
V
2
805
V
40
805
V
125
805
V
125
805
V
29
805
V
84
805
V
69
805
V
81
805
V
54
805
V
157
805
V
157
805
V
157
805
V
39
805
V
68
805
V
45
805
V
42
Table 2: Energy values for an
absent component.
Component Type Orientation Energy
805
V
1
805
V
0
805
V
0
805
V
0
805
V
0
805
V
0
805
V
0
805
V
15
805
V
0
805
V
0
805
V
0
805
V
0
805
V
0
805
V
10
805
V
0
805
V
13
805
V
0
The component that was used as basis for the experiment was the most common
component in the PCB, which is the 805 vertical component. The code for this
component is used to identify capacitors, diodes and resistors that are placed in the
PCB in the vertical coordinate. The information of energy was then used to
calculate histograms to represent the energy distribution of the population of
present and absent components. The overlapping of these populations can be
estimated by subtracting the mean of each population. The response variable to be
monitored will then be :
7
Z=( Mean(P)-Mean(A))
Where:
Z= Mean distance of present and absent populations
P= Present Components.
A= Absent Components.
The desired response will be a large (positive) value of Z. To obtain the values of
energy for the present and absent populations the experiments will be performed
twice at each factor combination of the experiment, one over a board with present
components and one in a board without components.
FACTOR LEVELS AND RANGES
The factor levels and ranges will be as follows:
1. Iris Opening: (1.6 stop number x 2.8 stop number) 1.6 high level, 2.8 low
level
2. Angle of illumination (90  45) 90 high level, 45 low level
3. Variation of current to manipulate the intensity level of frontal illumination
(.6A  I  .3A) .6A high level, .3A low level.
The numbers given in the range and levels of factor #1 refer to stop numbers on
the 25mm focal distance TV lenses that are used by each of the cameras in the
vision system where the lower the stop number the grater the opening of the iris.
8
According to the AVI administrator the assumption of linearity in the factor
effects is not clear specially in the Iris opening factor because when going from
one stop number to the other the opening varies according to a constant (π/4)*D2 ,
in other words, not linear. The use of center points will allow us to check for this
nonlinearly effect. The values for the center points will than be: Iris opening: 2.2,
Angle: 67.5, Current: 0.45 A. Four center points are used.
DESIGN OF TEST MATRIX
The design of the experiment to find the appropriate settings of the parameters
described in the last section in order to obtain a optimum image from the
inspection machine require the development of a test matrix of the different factor
combinations. The design of this matrix involves the following main issues:
 Number of factors
 Levels of factors
 Number of replications
 Decision on Blocking
 Run order
 Power of the test (1-β )
Since the number of factors of interest for the experiment is 3, we have adopted 23
design, with 3 replications (refer to Table 4) and 4 center points.
9
The blocking technique was not considered to this experiment because none of the
factors (or the experiment itself) was affected by any nuisance source of variation.
The PCB boards belong to the same batch, no human interaction is related to the
inspection routine that renders the image of the population of components within
each PCB.
The run order was determined by Design Expert software, the complete test matrix
is shown in Table 3:
Std
27
22
4
17
14
8
12
1
21
26
19
9
6
16
3
2
11
7
24
23
18
5
25
10
20
13
15
28
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Block
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Factor 1
Factor 2
Factor 3
Response
A:Iris Opening B:Angle, Degrees C:Current, Amps Overlap, pixels
2.2
67.5
0.45
2.8
90
0.6
2.8
45
0.3
2.8
45
0.6
1.6
45
0.6
1.6
90
0.3
2.8
90
0.3
1.6
45
0.3
1.6
90
0.6
2.2
67.5
0.45
1.6
90
0.6
1.6
90
0.3
2.8
45
0.3
2.8
45
0.6
1.6
45
0.3
1.6
45
0.3
2.8
90
0.3
1.6
90
0.3
2.8
90
0.6
2.8
90
0.6
2.8
45
0.6
2.8
45
0.3
2.2
67.5
0.45
2.8
90
0.3
1.6
90
0.6
1.6
45
0.6
1.6
45
0.6
2.2
67.5
0.45
Table 3: Test Matrix
10
The results table for a number of replicates=3 is shown in Table 4:
Term StdErr**
A
0.2041
B
0.2041
C
0.2041
AB
0.2041
AC
0.2041
BC
0.2041
ABC 0.2041
VIF
1
1
1
1
1
1
1
Power at 5 % alpha level for effect of
Ri-Squared 1/2 Std. Dev.
1 Std. Dev.
2 Std. Dev.
0
21.1 %
63.3 %
99.6 %
0
21.1 %
63.3 %
99.6 %
0
21.1 %
63.3 %
99.6 %
0
21.1 %
63.3 %
99.6 %
0
21.1 %
63.3 %
99.6 %
0
21.1 %
63.3 %
99.6 %
0
21.1 %
63.3 %
99.6 %
Table 4: Results table
The result table shows 99.6 as the percentage alpha level of all effects at 2
standard deviations from the mean, which is sufficiently accurate in terms of this
experiment.
PERFORMING THE EXPERIMENT
The run order (random) and combination of factor levels provided by design
expert was followed and the results rendered are shown in Table 5 in the
Appendix. While running the experiment the most difficult factor to vary was the
current of the LED panels because of the lack of accessibility presented by the
layout of the machine. While changing the Iris opening an adjustment to the focus
of the camera was also required to provide a clear image in the monitor, this
adjustment (or the check for a proper image) was required each time the iris
opening was changed from one level to the next. The variation of the angle factor
was the one that did not present any major difficulty. The computation of the
11
response variable in each run was performed by the method described earlier in
this report.
STATISTICAL ANALYSIS OF THE DATA
The statistical analysis of the response variable and the interpretation of the results
derived form this analysis was performed by using the Design Expert® software.
Tables 5 to 8 as well as graphs 1 to 7 are presented in the Appendix. Table 5,
Table 6 show the Run matrix with responses and Design summary respectively.
The highest order interaction term was assumed as the error term. The half normal
plot (Graph1) clearly shows that A, C, AC are the significant factors. Taking the
significant terms as the main effects and the remaining terms as error terms refines
the model. The degrees of freedom for the model are 3, for curvature 1 and for the
error are 24.
The analysis of variance table (Table 7) provided by Design Expert ® shows the p
values, the F values, Degrees of freedom, Sum of squares and Mean square terms.
The high value of the model F-value is strong evidence that it is significant.
According to the Design Expert ® report, there is only a 0.01% chance that a
"Model F-Value" this large could occur due to noise. It is important to mention
that as shown by Graph 5 (plot of residuals Vs. current) the assumption of
homogeneity of variance seems not to hold. This happens even after data
transformation has been applied to the data (Square root transformation with
constant k=2 as suggested by Design Expert® when observations seem to follow a
12
Poisson distribution). However, due to the high value of the F ratio
MS Model
(2512.
MS E
23), the effects of non-constant variance will be very unlikely to alter the results
obtained by the experiment. More over, since the experiment was a balanced
fixed effects model the results are only slightly affected when the assumption of
constant variance is violated [4].
The analysis also found that there is evidence of significant second-order
curvature in the response as measured by difference between the average of the
center points and the average of the factorial points over the region of exploration.
Regression Equation obtained from Design Expert® is as shown below.
Final Equation in Terms of Coded Factors:
Sqrt(Overlap + 2.00)
3.671378879
-1.19246518
1.330008522
-0.367902103
=
*A
*C
*A*C
Final Equation in Terms of Actual Factors:
Sqrt(Overlap + 2.00)
=
0.006802504
-0.14793145
* Iris Opening
17.85988601
* Current
-4.087801148 * Iris Opening * Current
According to Design Expert® the lack of fit is not significant relative to the pure
error. This result suggests that this model is adequately fitted by the regression
equation.
13
Residuals and Model Adequacy:
The Graph 2 shows the plot of Normal probability vs studentized residuals .The
assumption of normality is satisfied after the square root transformation.We have
considered the square root transformation since the observations in this model
follows the poisson distribution as our response deals with counting the number of
components on the PCB board and this is also suggested by Design Expert®
BOXCOX plot. The Graphs 3 and 4 shows the plots of residuals vs. predicted
values and residuals vs. run order. These graphs show that the independence
assumption on the errors has not been violated and also shows that there is no nonconstant variance. Graphs 6 and 7 are the plots of response surfaces. These graphs
suggests that the response increases with the increase of the increase in Current
and Iris opening .The interaction between these significant factors can be seen
from the curvature of the response surface.
The R-Squared value of 0.9969 shows that the proportion of the variability in the
data is mostly explained by the model. Also, the "Pred R-Squared" and the"Adj
R-Squared" values of 0.9956 and 0.9966 respectively are in reasonable
aggreement with each other. Because the "Adeq Precision" ratio (which measures
the signal to noise ratio) is 116.000 this model can be used to navigate the design
space [4].The PRESS value of 0.36 suggests that the model for the experiment can
be used in a new experiment to predict the response confidently.
14
CONCLUSIONS AND RECOMMENDATIONS
The identification of the light intensity of the LED panels (current factor), the iris
opening of the lenses of the cameras and their interaction as the significant factors
in controlling the clarity of the image used by the AVI system, will lead to an
increase of accuracy and efficiency in the calibration process of the inspection
machine.
The maximum value obtained for the difference in mean energy value for present
and absent populations (42.8 pixels) was obtained when the Iris factor was in the
high level (1.6 step numbers) the Current factor was in the high level (0.6 Amps)
and the angle factor was in the low level (45°). It is then recommended to run the
inspection machine at these levels. The significance of the non-linearity between
the high and low levels of the factors (especially iris opening) needs to be taken
into account when adjusting the levels in future research to optimize the response
variable defined in this experiment and as suggested by Graphs 6 and 7.
15
REFERENCES
1. Muñoz, L., et al, Multivariate On-line Quality Monitoring of SMD Assembly,
Working Paper, The University of Texas At El Paso,1999
2. Villalobos, J. and Verduzco, A., Integration of Quality and Process Planning
Activities in SMD Assembly, Working Paper, The University of Texas at El
Paso,1997
3. Arellano, M. and Villalobos, J., Vector Classification of SMD Images,
Working Paper, Arizona State University,1999
4. Montgomery, D.C. (2000), Design and Analysis of Experiments,5th Edn, John
Wiley & Sons, New York.
16
Appendix
17
Table 5: Run matrix with response.
Std
27
22
4
17
14
8
12
1
21
26
19
9
6
16
3
2
11
7
24
23
18
5
25
10
20
13
15
28
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Block
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Block 1
Factor 1
Factor 2
Factor 3
Response
A:Iris Opening B:Angle, Degrees C:Current, Amps Overlap, pixels
2.2
67.5
0.45
17.904
2.8
90
0.6
9.33
2.8
45
0.3
0.367
2.8
45
0.6
9.64
1.6
45
0.6
40.77
1.6
90
0.3
8.37
2.8
90
0.3
0.321
1.6
45
0.3
8.351
1.6
90
0.6
39.82
2.2
67.5
0.45
18.79
1.6
90
0.6
37.77
1.6
90
0.3
7.585
2.8
45
0.3
0.279
2.8
45
0.6
11.38
1.6
45
0.3
7.73
1.6
45
0.3
8.36
2.8
90
0.3
0.262
1.6
90
0.3
7.76
2.8
90
0.6
9.9
2.8
90
0.6
9.08
2.8
45
0.6
9.78
2.8
45
0.3
0.282
2.2
67.5
0.45
16.64
2.8
90
0.3
0.294
1.6
90
0.6
43.27
1.6
45
0.6
42.035
1.6
45
0.6
42.8
2.2
67.5
0.45
17.09
Table 6: Design Summary
Study Type
Factorial
Initial Design 2 Level Factorial
Center Points
4
Design Model
3FI
Response
Name
Y1
Overlap
Factor
A
B
C
Name
Iris Opening
Angle
Current
Experiments
Blocks
28
No Blocks
Units
Pixels
Obs
28
Minimum
0.262
Units
Type
Numeric
Numeric
Numeric
Low Actual
1.6
45
0.3
Degrees
Amps
Maximum
43.27
Trans
Square root
High Actual Low Coded
2.8
-1
90
-1
0.6
-1
Model
R2FI
High Coded
1
1
1
18
Table 7: Analysis of Variance from Design Expert®
Response:
Overlap
Transform:
Square root
ANOVA for Selected Factorial Model
Analysis of variance table [Partial sum of squares]
Sum of
Mean
Source
Squares
DF
Square
Model
79.82994798
3
26.60998266
A
34.12735695
1
34.12735695
C
42.45414405
1
42.45414405
AC
3.248446983
1
3.248446983
Curvature
1.957086139
1
1.957086139
Residual
0.243620098
23
0.010592178
Lack of Fit 0.046068325
4
0.011517081
Pure Error
0.197551773
19
0.010397462
Cor Total
82.03065422
27
Std. Dev.
Mean
C.V.
PRESS
0.102918308
3.779310906
2.723203008
0.362336946
Coefficient
Factor
Estimate
Intercept
3.671378879
A- Iris Opening-1.19246518
C-Current
1.330008522
AC
-0.367902103
Center Point 0.755524183
DF
1
1
1
1
1
Constant:
2
F
Value
2512.229517
3221.939472
4008.065513
306.6835669
184.7671089
Prob > F
< 0.0001
< 0.0001
< 0.0001
< 0.0001
< 0.0001
1.107682007
0.3818
R-Squared
Adj R-Squared
Pred R-Squared
Adeq Precision
0.996957547
0.996560705
0.995582908
116.0000076
Standard
Error
0.021008112
0.021008112
0.021008112
0.021008112
0.055582239
95% CI
Low
3.627920289
-1.23592377
1.286549932
-0.411360693
0.640543561
95% CI
High
3.714837
-1.14901
1.373467
-0.32444
0.870505
significant
significant
not significant
VIF
1
1
1
1
Final Equation in Terms of Coded Factors:
Sqrt(Overlap + 2.00)
3.671378879
-1.19246518
1.330008522
-0.367902103
=
*A
*C
*A*C
Final Equation in Terms of Actual Factors:
Sqrt(Overlap + 2.00)
=
0.006802504
-0.14793145
* Iris Opening
17.85988601
* Current
-4.087801148 * Iris Opening * Current
19
Table 8: Diagnostics Case Statistics
Standard
Order
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Actual
Value
3.217297002
3.218695388
3.119294792
1.538505769
1.510629008
1.509635718
3.12409987
3.220248438
3.095965116
1.514595656
1.503994681
1.523482852
6.635887281
6.539877675
6.693280212
3.657868232
3.411744422
3.43220046
6.30634601
6.728298448
6.466838486
3.366006536
3.328663395
3.449637662
4.317406629
4.559605246
4.461389918
4.369210455
Predicted
Value
3.165933434
3.165933434
3.165933434
1.51680728
1.51680728
1.51680728
3.165933434
3.165933434
3.165933434
1.51680728
1.51680728
1.51680728
6.561754685
6.561754685
6.561754685
3.441020118
3.441020118
3.441020118
6.561754685
6.561754685
6.561754685
3.441020118
3.441020118
3.441020118
4.426903062
4.426903062
4.426903062
4.426903062
Residual
Leverage
0.05136357
0.05276195
-0.0466386
0.02169849
-0.0061783
-0.0071716
-0.0418336
0.054315
-0.0699683
-0.0022116
-0.0128126
0.00667557
0.0741326
-0.021877
0.13152553
0.21684811
-0.0292757
-0.0088197
-0.2554087
0.16654376
-0.0949162
-0.0750136
-0.1123567
0.00861754
-0.1094964
0.13270218
0.03448686
-0.0576926
0.16666667
0.16666667
0.16666667
0.16666667
0.16666667
0.16666667
0.16666667
0.16666667
0.16666667
0.16666667
0.16666667
0.16666667
0.16666667
0.16666667
0.16666667
0.16666667
0.16666667
0.16666667
0.16666667
0.16666667
0.16666667
0.16666667
0.16666667
0.16666667
0.25
0.25
0.25
0.25
DESIGN-EXPERT Plot
Sqrt(Overlap + 2.00)
A: Iris Opening
B: Angle
C: Current
Student
Residual
0.546705153
0.561589335
-0.49641384
0.230955048
-0.06576049
-0.0763329
-0.4452694
0.578119734
-0.74473098
-0.02354016
-0.13637515
0.071053657
0.789054842
-0.23285521
1.399935528
2.308094749
-0.31160557
-0.09387495
-2.71852686
1.772663718
-1.01027202
-0.79843191
-1.195906
0.091723688
-1.22850436
1.488863216
0.386928155
-0.64728701
Cook's
Distance
0.01195546
0.0126153
0.00985707
0.00213361
0.00017298
0.00023307
0.00793059
0.0133689
0.02218497
2.2166E-05
0.00074393
0.00020194
0.0249043
0.00216886
0.07839278
0.21309205
0.00388392
0.0003525
0.29561553
0.12569347
0.04082598
0.02549974
0.05720765
0.00033653
0.10061486
0.14778091
0.00998089
0.02793203
Outlier
Run
t
Order
0.5381966
8
0.5530501
16
-0.488124
15
0.2261409
3
-0.064321
22
-0.074665
13
-0.437371
18
0.5695657
6
-0.737305
12
-0.023023
24
-0.133431
17
0.0694995
7
0.7823729
26
-0.228006
5
1.4315109
27
2.5752153
14
-0.305402
4
-0.091829
21
-3.227371
11
1.8658367
25
-1.010746
9
-0.791934
2
-1.207773
20
0.0897239
19
-1.242974
23
1.5318246
10
0.3796609
1
-0.638905
28
Half Normal plot
99
C
97
95
Half
Normal
%
Probability
A
AC
90
85
80
70
60
40
20
0
0.00
0.67
1.33
2.00
2.66
|Effect|
Graph1: Half Normal Plot of the factor effects
20
DESIGN-EXPERT Plot
Sqrt(Overlap + 2.00)
Normal plot of residuals
99
95
Normal %probability
90
80
70
50
30
20
10
5
1
-2.72
-1.46
-0.21
1.05
2.31
Studentized Residuals
Graph 2: Normal Probability Plot of Residuals
DESIGN-EXPERT Plot
Sqrt(Overlap + 2.00)
Residuals vs. Predicted
3.00
Studentized Residuals
1.50
0.00
-1.50
-3.00
1.52
2.78
4.04
5.30
6.56
Predicted
Graph 3: Residuals vs. Predicted
21
DESIGN-EXPERT Plot
Sqrt(Overlap + 2.00)
Residuals vs. Run
3.00
Studentized Residuals
1.50
0.00
-1.50
-3.00
1
10
19
28
Run Number
Graph 4: Residuals vs. Run Number
DESIGN-EXPERT Plot
Sqrt(Overlap + 2.00)
Residuals vs. Current
3.00
Studentized Residuals
1.50
0.00
-1.50
-3.00
0.30
0.37
0.45
0.52
0.60
Current
Graph 5: Residuals vs. Current
22
DESIGN-EXPERT Plot
Sqrt(Overlap + 2.00)
0.60
Sqrt(Overlap + 2.00)
X = A: Iris Opening
Y = C: Current
5.72093
Design Points
4.88011
0.52
Actual Factor
B: Angle = 67.50
C: Current
4.03928
4
0.45
3.19846
0.37
2.35763
0.30
1.60
1.90
2.20
2.50
2.80
A: Iris Opening
Graph 6: Contour Plot with Iris Opening
DESIGN-EXPERT Plot
Sqrt(Overlap + 2.00)
X = A: Iris Opening
Y = C: Current
Actual Factor
6.56175
B: Angle = 67.50
5.30052
4.03928
Sqrt(Overlap 2.77804
+ 2.00)
1.51681
0.60
2.80
0.52
C: Current
2.50
0.45
2.20
0.37
1.90
0.30
A: Iris Opening
1.60
Graph 7: 3D Response Surface Plot
23