IEE 572
Design of Experiments
Experimental Design in Simulation of
Semiconductor Manufacturing
Dr. Douglas Montgomery
Date: February 12, 2016
Team:
Chanettre Rasmidatta
Ching I Tseng
Aditya Rastogi
Design of Experiments
Project Report
Executive Summary
Due to the competitive market today in the semiconductor industry, ABC Co. wants to
investigate the factors, which affect the average cycle time and throughput.
The
objective is to minimize the average cycle time and maximize throughput. Since the
model has eight factors and two levels each, we want to identify the factors that have
large effect. By doing this, 28-4 fractional factorial design is demonstrated and single
replication with 6 runs at the center is also used in this experiment. We have emphasized
the use of these designs in screening experiments to quickly and efficiently identify the
subset of factors that are active and to provide some information on interaction. HalfNormal plot is used in the ANOVA, residual analysis and model adequacy checking,
regression analysis and contour plots to help the engineer to have the better interpretation
of the experiment as well to examine the active factors in more details.
The results from the experiment suggest that only two out of eight factors were
significant, which are release rate and dispatching rule. The model passed the tests for
normality and independence assumptions. In additions, the validity of the model was
performed based on the regression models to verify the two responses, average cycle time
and throughput. The model was verified using the confirmation run and the error was less
than one percent. The predicted values were very close to the actual values and thus
supporting the design.
Based on the results, we recommend that SSU dispatching rule should be used at release
rate of 19.5K wafers per month is the best combination to yield a higher throughput and
lower average cycle time.
Ching-I Tseng, Chanettre Rasmidatta, Aditya Rastogi
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TABLE OF CONTENTS
1.
Experimental Design in Simulation of Semiconductor Mfg.
4
1.1 Problem Statement
1.2 Description of the Model
2.
Choice of Factors Levels and Range
6
3.
Selection Response Variable
8
4.
Choice of Experimental Design
9
5.
Performing the Experiment
10
6.
Statistical Analysis of the data
11
6.1 Analysis of Variances (ANOVA)
6.2 Model Adequacy Checking
6.2.1 Normality Assumption
6.2.2 Residual Analysis
6.2.3 Box-Cox Transformation
6.3 Regression Analysis
6.3.1 Average Cycle Time
6.3.2 Throughput
6.4 Interaction Graph of Factors A and G
6.5 Optimal Designs
7.
Conclusions
24
7.1 Confirmation Testing
7.2 Recommendations
APPENDIX
27
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Design of Experiments
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Experimental Design in Simulation of Semiconductor Manufacturing
1.1 Problem Statement
ABC Co. is a leading semiconductor manufacturing company. Lately they have
discovered that modeling the semiconductor manufacturing and simulating it for various
conditions would save lot of time and resources. The manager of the ABC Co. wants to
investigate the factors, which affect the average cycle time and throughput.
The
objective is to minimize the average cycle time and maximize throughput. The lesser the
cycle time, the lesser the work-in-process, which means lesser investment in inventory.
The shorter cycle time also provides market responsiveness. With this goal in mind he
wants to plan an experiment or sequence of experiments designed to take him in the
direction of that goal.
1.2 Description of the Model
The model represents a 300mm DRAM facility with approximately 450 process steps and
398 process tools providing 1709 total tool ports, WIP positions, handlers, etc. that are
grouped into 80 tool groups.
There are 15 operators in 8 different types and the
maximum designed capacity was 20,000 wafers/month. Only one type of DRAM part,
which processes through one routing, is released into the system. The flow is a highly reentrant, i.e. jobs feedback through sequences of the tool-groups many times. A lot of 25
parts is released at a fixed interval depending upon the maximum designed capacity.
Twenty-one types of reticles, generic resources, with a capacity of two each, are used.
Process tool downtimes for both preventative and unexpected maintenance are
incorporated, along with employee lunches and breaks. AutoSched AP, a commercial
simulation software package was used to model this system.
This model simulates the manual material handling system and the various assumptions
for this system are listed below:

There is no operator’s traveling time to the front of stocker when an inter-bay
movement was requested.

Gaining access to stockers in a bay is considered as resource contingent.

Load and unload times are 1 minute each.
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Design of Experiments

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The average operator’s traveling speed is assumed to be 2 miles/hr, which is a
reasonably slow walking speed, considering the weight of the AGV (Automate Guide
Vehicle).

To compensate for safety precautions and other human factors in the Fab, travel times
used are equal to [distance/speed]*, where  is equal to 1.5.
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Design of Experiments
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Choice of Factors Levels and Range
From the previous experiment and experience, the Potential Design Factors and the
Nuisance factors can be identified. The potential design factors are number of operators,
release rate, dispatching rule, stocker quantity, and number of reticles, of which number
of reticle is held-constant factor and the design factors are:
1) For operators, there are 5 factors and two levels each. The operator in this model
is responsible for loading and unloading the wafers on the machines and they are
also responsible for transportation of wafers within the Fab. Varying the number
of operators would possibly affect the performance of the system.
2) Release Rate, i.e. the rate at which the wafers are released into the factory, has
two levels. The release rate is measured by the number of wafers scheduled to
release into the Fab per month. The release rate affects the machine utilization,
specially the batching machine that in turn affects the system performance.
3) The dispatching rule for the bottleneck workstations has two levels. The
bottleneck machines were identified from the previous experiments. According to
the theory of constraints, the bottleneck machine determines the capacity of the
Fab that determines the throughput.
4) Stocker Quantity, which has two levels. In this model the stockers are treated as
stations and there is one stocker at each bay. The shortage of stockers can cause
blocking which can severely delay the manufacturing processes.
The details of the factors, level and range are given in the table below
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Table 1 Design Factors and their Levels
Factor
Levels
Range
Operator
OP_DIFF
2
2
4
OP_PHOTO
2
2
4
OP_ETCH
2
3
5
OP_WET
2
2
4
OP_MOVE
2
35
55
Release Rate
2
18K
19K
Dispatching Rules
2
FIFO
Stockers Qty.
2
2
Same
Setup
4
The Nuisance Factors are the various distributions for the processing time and the down
time, which are uncontrollable or the noise factors. The controllable nuisance factor that
can be identified is the random number stream that is to be used for the simulation. We
intend to keep the random number stream constant throughout the experiment.
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Selection Response Variable
The purpose of the study is to determine the time taken for a lot of wafers to be produced.
This factor is best represented by the average cycle time and thus the average cycle time
happens to be one of our response variables.
Various other parameters are necessary to determine the proper running of the factory,
one of which is the throughput. Thus the two-response variables for our project are:
1) Average cycle time and
2) Throughput
Cycle time is defined as total elapsed time from lot creation to lot completion that include
process time, move time, queue time, and hold time.
The average output of a production process (machine, workstation, line, and plant) per
unit time is defined as the system’s throughput.
These response variables can be obtained from the simulation output report. The
simulation would run for a period of time at steady state. The steady state would be
determined by a long initial run and the statistics collected during this warm-up period
would be eliminated from the simulation output.
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Choice of Experimental Design
Since the model has eight factors and two levels each, we need to identify the factors that
have large effects. To do so, screening experiments will be used at the initial stage of the
experiment. We will use the 2k Fractional Factorial Design for this screening experiment.
We choose 28-4 Fractional Factorial Design, single replication with 6 runs at the center
point as shown in Table 2. We determine the number of runs from the results of the
Design Expert software.
The alias for this design is a bit different for factor A. The possible reason for this could
be the use of center points and also that the factor A is a categorical factor. The defining
relation and the aliases is shown in Appendix 1.
Table 2: Design Matrix
R1:
AVG.
R2:
Factor1:
CYCLE THROU
DISPATC
Factor7: Factor8: TIME GHPUT
HING
Factor2: Factor3: Factor4: Factor5: Factor6: RELEASE STOCKER
Std Run Block
RULE
OP_DIFF OP_PHOTO OP_ETCH OP_WET OP_MOVE
RATE
S QTY.
Hours
Lots
1 21 Block 1
{-1}
-1
-1
-1
-1
-1
-1
-1
2
14
Block 1
{1}
-1
-1
-1
-1
1
1
1
3
17
Block 1
{-1}
1
-1
-1
1
-1
1
1
4
22
Block 1
{1}
1
-1
-1
1
1
-1
-1
5
3
Block 1
{-1}
-1
1
-1
1
1
1
-1
6
12
Block 1
{1}
-1
1
-1
1
-1
-1
1
7
9
Block 1
{-1}
1
1
-1
-1
1
-1
1
8
20
Block 1
{1}
1
1
-1
-1
-1
1
-1
9
10
Block 1
{-1}
-1
-1
1
1
1
-1
1
10
2
Block 1
{1}
-1
-1
1
1
-1
1
-1
11
8
Block 1
{-1}
1
-1
1
-1
1
1
-1
12
13
Block 1
{1}
1
-1
1
-1
-1
-1
1
13
11
Block 1
{-1}
-1
1
1
-1
-1
1
1
14
19
Block 1
{1}
-1
1
1
-1
1
-1
-1
15
6
Block 1
{-1}
1
1
1
1
-1
-1
-1
16
18
Block 1
{1}
1
1
1
1
1
1
1
17
16
Block 1
{-1}
0
0
0
0
0
0
0
18
1
Block 1
{1}
0
0
0
0
0
0
0
19
7
Block 1
{-1}
0
0
0
0
0
0
0
20
15
Block 1
{1}
0
0
0
0
0
0
0
21
4
Block 1
{-1}
0
0
0
0
0
0
0
22
5
Block 1
{1}
0
0
0
0
0
0
0
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Design of Experiments
5.
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Performing the Experiment
The experiments were performed using the AutoSched AP simulation software package.
In the initial stage, one long run was made to determine the warm-up period. The warmup period is the time taken by the simulation model to reach a steady state, where no
statistics is collected. Cycle time was plotted against time (in days) and the period was
determined to be 94 days as shown in Figure 1.
Warm-Up Period Determination
Cycle Time (Days)
35
30
25
20
15
10
5
477
449
421
393
365
337
309
281
253
225
197
169
141
113
85
57
29
1
0
Days
Fig.1 Warm-up Period Determination
The run length was determined to be 3 years and only single replication was made at each
run due to the limited resources. A single run took about two and half hours on a fast
machine (PIII, 800Mhz). Refers to Appendix 2 and see the Result Matrix.
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6.
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Statistical Analysis of the data
Upon completion of the runs, the results were fed to the Design Expert software and
the results were analyzed. As mentioned earlier, the design chosen was a resolution
IV, 28-4 fraction factorial design. The analysis includes ANOVA, residual analysis
and model adequacy checking, regression analysis, and contour plots. These analyses
are discussed in detail below.
6.1 Analysis of Variances (ANOVA)
Figure 2 below shows the half-normal plot, which shows the effects of various
factors. Based on this graph, where the response variable is average cycle time, the
factors that lie along the line are negligible and three factors seem to be significant.
The two main effects from this analysis are A and G and a two-factor interaction AG.
Fig.2 Half-Normal Plot of Average Cycle Time
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The similar analysis was performed for response variable, throughput, as shown in the
Figure 3 below.
Fig.3 Half-Normal Plot of Throughput
Table 3 shows the results of analysis of variance. Based on the response variable, average
cycle time, it shows that the factors that we chose are significant and their interaction is
significant, and that there is no evidence of second-order curvature in the response.
Table 3 ANOVA for Avg. Cycle Time
Source
Model
A
G
AG
Curvature
Residual
Lack of Fit
Pure Error
Cor Total
Sum of
Squares
3094696.40
2440544.15
510956.81
143195.44
852.64
7832.96
5791.66
2041.30
3103382
DF
3
1
1
1
1
17
13
4
21
Mean
Square
F Value
1031565.47
2238.82
2440544.15
5296.75
510956.81
1108.94
143195.44
310.78
852.64
1.85
460.76
445.51
0.872996454
510.33
Ching-I Tseng, Chanettre Rasmidatta, Aditya Rastogi
Prob > F
< 0.0001
< 0.0001
< 0.0001
< 0.0001
0.1915
not significant
0.6215
not significant
significant
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The Table 4 supplements ANOVA table. The high value of R-Squared indicates that the
major proportion of variability is included in the model.
Table 4 Supplementary Data of Avg. Cycle Time
Std. Dev.
Mean
C.V.
PRESS
R-Squared
Adj R-Squared
Pred R-Squared
Adeq Precision
21.4654
1288.3230
1.6661
12992.7900
0.9975
0.9970
0.9958
100.0214
The similar analysis was performed for response variable, throughput, as shown in the
Table5&6 below.
Table 5 ANOVA for Throughput
Source
Model
A
AG
Curvature
Residual
Lack of Fit
Pure Error
Cor Total
Sum of
Squares
14050525.55
13028404.55
1022121.00
560.48
27645.79
17847.12
9798.67
14078731.82
DF
2
1
1
1
18
14
4
21
Mean Square
7025262.77
13028404.55
1022121.00
560.48
1535.88
1274.79
2449.67
F Value
4574.10
8482.71
665.50
0.36
Prob > F
< 0.0001
< 0.0001
< 0.0001
0.5533
not significant
0.52
0.8373
not significant
significant
Table 6 Supplementary Data of Avg. Throughput
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6.2 Model Adequacy Checking
6.2.1
Normality Assumption
The adequacy of the underlying model should be checked before the conclusions from
the analysis of variance are adopted. Violation of the basic assumptions and model
adequacy can be easily investigated by the examination of residuals. For example, if the
model is adequate, the residuals should be structure less and that is, they should contain
no obvious patterns. In Figure 4, presents a normal probability plot of the residuals for
average cycle time. There is no severe indication of non-normality, nor is there any
evidence pointing to possible outliers and the equality of variance assumption does not
seem to be violated. Figure 5, Normal Plot of Residuals for Throughput shown below is
also normally distributed and it resembles a straight line.
Fig 4 Normal Plot of Residuals for Avg. Cycle Time
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Fig 5 Normal Plot of Residuals for Throughput
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6.2.2
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Residual Analysis
Various residual plots are shown in this section below. Figure 6-10 show diagnostic plots
of the model. The residuals are normally distributed and the equality of variance does not
seem to be violated.
Fig 6 Residual vs. Predicted Plot for Cycle Time
Fig.7 Residual vs. Predicted Plot for Throughput
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Fig.8 Residual vs. Run Number for Avg. Cycle Time
Fig.9 Residual vs. Run Number for Throughput
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Fig.10 Residuals vs. Significant Factor
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6.2.3
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Box-Cox Transformation
The model was tested for any transformations that could have been applied, but the BoxCox Plot did not suggest any new transformations for both response variables, namely
Average Cycle Time and Throughput as shown in Figure 11 and 12.
Fig.11 Box Cox Plot for Cycle Time
Fig.12 Box Cox Plot for Throughput
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6.3 Regression Analysis
The equations below are fitted regression model representations of the two-factor
factorial experiments for both responses.
6.3.1
Average Cycle Time
Final Equation in Terms of Coded Factors:
Avg Cycle Time = 1292.14 - 333.07 * A +178.70 * G - 94.60 * A * G
Final Equation in Terms of Actual Factors:
Dispatching Rule
FIFO
Avg Cycle Time = -5207.44845 + 0.36441 * RELEASE RATE
Dispatching Rule
SSU
Avg Cycle Time = -1143.43634 + 0.11213 * RELEASE RATE
6.3.2
Throughput
Final Equation in Terms of Coded Factors:
Throughput = 8004.00 + 769.55 * A + 14.62 * G + 252.75 * A * G
Final Equation in Terms of Actual Factors:
Dispatching Rule
FIFO
Throughput = 13187.57955 - 0.31750 * RELEASE RATE
Dispatching Rule
SSU
Throughput = 2089.17045 + 0.35650 * RELEASE RATE
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6.4 Interaction Graph of Factors A and G
Figure 13 shows the interaction effect of factors A and G. The average cycle time
decreases when changing from FIFO to SSU and from 19.5K wafers per month to 18K
wafers per month. The other factors do not have significant effect on the responses. The
contour plot was constructed by converting the type of factors from categorical to
numeric as shown in Appendix 3.
Fig.13 Interaction Graph of Avg. Cycle Time
Figure 14 below shows the interaction effect of factors A and G. Using the dispatching
rule FIFO, throughput is higher at 18K release rate than at 19.5K release rate compared to
the dispatching rule SSU where the throughput is higher at 19.5K than 18K release rate.
The other factors do not have significant effect on the responses. The contour plot was
constructed by converting the type of factors from categorical to numeric as shown in
Appendix 3
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Fig.14 Interaction Graph of Throughput
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6.5 Optimal Designs
The Design Expert provides optimal designs with the desirability factor of 0.852, which
determines the optimal level for each factor as shown in the Figure 15. The “circle” mark
and two ends on the line represent the current operating condition and its ranges. The last
two boxes show the ranges of two responses.
Cycle time follows the hierarchical
principle, while throughput follows the linear relationship. The alternative solutions are
shown in the Appendix 4. The constraints used are the high and the low level of each
factor, where the objective used is to maximize the Throughput and minimize the Avg.
Cycle Time.
Fig. 15 Ramps for various factors
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Conclusions
The 28-4 fractional factorial designs were run and analyzed to determine the effect of
various factors on average cycle time and throughput. The following conclusions were
made:

Only two factors and their interaction were significant: release rate and
dispatching rule

The model was tested for its adequacy and found that the assumption of normality
and independency are not violated

R2 value was very high, that suggesting that model accounted for most of the
variability

Box-Cox Plot did not suggest any transformation

The graphs for the significant factors were analyzed and the best value is obtained
at high value of release rate and using dispatching rule as SSU, which is in
conjunction with our intuition.

The optimal value with specified desirability was calculated using the software.

Since only two factors have been identified as significant, more detailed
experiment can be designed to study the effects are various levels of these factors.
7.1 Confirmation Testing
Based on the regression models, runs were made to verify the results obtained for both
responses, average cycle time and throughput. Table 7 shows the predicted and actual
results.
Table 7 Confirmation Testing values
The table indicates that the predicted values are very close to the actual values and thus
supporting the design.
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7.2 Recommendations
Based on the conclusions and the validity of the model, we recommend:

To use SSU as a dispatching policy

To operate at a release rate of 19.5K to yield a higher throughput and lower
average cycle time.

To design a new experiment to take into consideration more levels of these
significant factors, such as 32 or higher
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APPENDIX 1
Defining Relation and Aliases
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APPENDIX 2
Result Matrix
Std Run Block
1
R1:
AVG.
R2:
CYCLE THROU
Factor6 Factor7:
Factor5:
:
DISPATC Factor8: TIME GHPUT
Factor1: Factor2: Factor3: Factor4: OP_MOV RELEAS
HING STOCKER
OP_DIFF OP_PHOTO OP_ETCH OP_WET
E
E RATE
RULE
S QTY.
Hours
Lots
16
Block 1
2
2
3
2
35
18000
FIFO
2
1358.95
7476
2
5
Block 1
4
2
3
2
35
19500
SSU
4
1034.83
9060
3
10
Block 1
2
4
3
2
55
18000
SSU
4
1894.73
6998
4
8
Block 1
4
4
3
2
55
19500
FIFO
2
877.549
8503
5
11
Block 1
2
2
5
2
55
19500
SSU
2
1895.17
7010
6
2
Block 1
4
2
5
2
55
18000
FIFO
4
890.351
8497
7
15
Block 1
2
4
5
2
35
19500
FIFO
4
1347.63
7453
8
18
Block 1
4
4
5
2
35
18000
SSU
2
1081.39
8978
9
20
Block 1
2
2
3
4
55
19500
FIFO
4
1337.59
7490
10
21
Block 1
4
2
3
4
55
18000
SSU
2
1068.04
8995
11
22
Block 1
2
4
3
4
35
19500
SSU
2
1895.25
6990
12
3
Block 1
4
4
3
4
35
18000
FIFO
4
888.456
8495
13
7
Block 1
2
2
5
4
35
18000
SSU
4
1884.61
7014
14
13
Block 1
4
2
5
4
35
19500
FIFO
2
867.791
8503
15
12
Block 1
2
4
5
4
55
18000
FIFO
2
1339.14
7498
16
1
Block 1
4
4
5
4
55
19500
SSU
4
1012.69
9104
17
6
Block 1
3
3
4
3
45
18750
FIFO
3
1642.32
7197
18
14
Block 1
3
3
4
3
45
18750
SSU
3
934.913
8789
19
9
Block 1
3
3
4
3
45
18750
FIFO
3
1591.25
7307
20
19
Block 1
3
3
4
3
45
18750
SSU
3
927.695
8807
21
17
Block 1
3
3
4
3
45
18750
FIFO
3
1648.65
7180
22
4
Block 1
3
3
4
3
45
18750
SSU
3
924.109
8812
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APPENDIX 3
Appendix 3A Contour Plot for Cycle Time
Appendix 3B Contour Plot for Throughput
Ching-I Tseng, Chanettre Rasmidatta, Aditya Rastogi
Page 28
Design of Experiments
Project Report
APPENDIX 4
Optimal Solution
Constraints
Lower
Name
Goal
Limit
Dispatching is
Rule
in range FIFO
OP_DIFF is in range
2
OP_ETCH is in range
3
OP_MOVE is in range
35
OP_PHOTOis in range
2
OP_WET is in range
2
RELEASE RATE
is in range
18000
Stocker Qty.is in range
2
Avg Cycle Time
minimize 867.7908
Throughput maximize
6990
Solutions
Number
DispatchingOP_DIFF*
Rule
1 SSU
3.74
2 SSU
2.09
3 SSU
2.27
4 SSU
2.21
5 SSU
3.41
6 SSU
2.11
7 SSU
3.81
8 SSU
3.73
9 SSU
2.21
10 SSU
3.65
11 FIFO
3.35
12 FIFO
3.72
13 FIFO
2.39
14 FIFO
3.96
15 FIFO
2.63
16 FIFO
3.68
17 FIFO
3.29
18 FIFO
3.93
19 FIFO
2.32
20 FIFO
3.05
Upper
Limit
SSU
4
5
55
4
4
19500
4
1895.247
9104
Lower
Weight
Upper
Weight
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1 1.620733
1
1
Importance
5
3
3
3
3
3
3
3
3
3
OP_ETCH*OP_MOVE*OP_PHOTO*
OP_WET*
4.87
51.00
2.51
2.89
3.85
40.57
2.74
3.77
3.74
42.06
2.53
3.31
4.76
39.23
3.50
3.33
4.27
36.23
3.75
2.35
3.23
42.56
3.48
3.72
3.44
42.65
3.91
2.30
4.50
50.49
2.39
3.34
4.84
51.25
2.15
3.67
4.67
42.91
2.33
2.18
4.60
40.95
2.44
2.38
3.39
40.82
2.66
2.50
3.74
44.41
2.88
2.67
4.97
53.93
3.47
2.16
4.40
45.84
2.65
3.09
3.27
43.19
3.23
2.60
4.65
38.93
3.25
2.35
4.22
54.59
3.52
3.91
4.74
45.67
2.20
2.30
3.45
48.95
3.12
3.21
Ching-I Tseng, Chanettre Rasmidatta, Aditya Rastogi
RELEASE RATE
Stocker Qty.*
Avg Cycle Time
ThroughputDesirability
18658.56 2.58
948.814 8742.73
0.851915
18666.88 2.74
949.748 8745.53
0.851915
18667.96 2.36
949.869 8745.9
0.851915
18655.67 2.79
948.49
8741.75
0.851915
18669.91 2.42
950.088 8746.56
0.851915
18654.61 3.33
948.372 8741.4
0.851914
18671.45 3.71
950.26
8747.07
0.851914
18653.72 3.76
948.272 8741.1
0.851914
18653.53 2.21
948.251 8741.04
0.851914
18672.18 2.83
950.341 8747.32
0.851914
18000.00 3.10
1351.9
7487.2
0.289401
18000.00 3.19
1351.9
7487.2
0.289401
18000.00 3.25
1351.9
7487.2
0.289401
18000.00 2.01
1351.9
7487.2
0.289401
18000.00 2.82
1351.9
7487.2
0.289401
18000.00 2.94
1351.9
7487.2
0.289401
18000.00 3.01
1351.9
7487.2
0.289401
18000.00 3.35
1351.9
7487.2
0.289401
18000.00 2.80
1351.9
7487.2
0.289401
18000.00 3.67
1351.9
7487.2
0.289401
Page 29