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ARTICLE IN PRESS

Robotics and Computer-Integrated Manufacturing 20 (2004) 91–100

Performance evaluation of an automated material handling system for a wafer fab F.K. Wanga,*, J.T. Linb a

Department of Industrial Engineering and Management, National Taipei University of Technology, No. 1, Chung Hsiao East Rd., Sec. 3, Taipei 10626, Taiwan b Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Taiwan, ROC Received 21 July 2003; accepted 7 August 2003

Abstract Discrete-event simulation model was developed to evaluate the performance of an automated material handling system (AMHS) for a wafer fab with a zone control scheme avoiding all vehicle collision. The layout of this AMHS is a custom configuration. The track option contains turntables, turnouts and high-speed express lanes. The behavior of the interarrival for all stockers from the real data set was analyzed to verify the assumption of the simulation model. The results show that the underlying distributions of most stockers for interarrival times belong to the exponential or Weibull distribution. The simulation results show that the number of vehicles significantly affects the average delivery time and the average throughput. A simple one-factor response surface model is used to determine the appropriate vehicle numbers. This study was also investigated to determine the vehicle numbers in an automated guided vehicle-based intrabay material handling system. r 2003 Elsevier Ltd. All rights reserved. Keywords: AMHS; Interbay; Intrabay; Performance evaluation; Simulation

1. Introduction Semiconductor wafer fabrication is a challenging technological process in this world. The cost of equipment is about 80% of the factory capital costs. This type of process is highly reentrant and creates a large amount of material flow between bays (inter- or intrabay movement). The increasing demand for ultraclean areas of semiconductor fabrication is leading to the automated material handling and control. The main purpose of an automated material handling system (AMHS) is to improve the performance of the overall fabrication process, by reducing manufacturing cycle time and increasing equipment use. This improvement comes by optimizing material deliveries to the required areas during the fabrication cycle. Davis and Weiss [1] provide many benefits of an automating wafer material handling in a wafer fab such as an increase of yield rate, the reduced cycle time and particle contamination, etc. Successful implementation of an AMHS begins with the collection of all the necessary information and ends with *Corresponding author. E-mail address: [email protected] (F.K. Wang). 0736-5845/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.rcim.2003.08.002

the installation, testing, and operation of the equipment. The effect factors of the AMHS performance are described as follows: (1) Factory layout: farm layout (all like equipment are either the same or adjacent), hybrid layout (distributed metrology), and modified hybrid layout (distribute any equipment to facilitate 4–6 contiguous process steps performed in the same bay). (2) AMHS track layout: spine, perimeter, flexible, and track options such as turntables, turnouts, or highspeed express lanes. (3) Transport vehicles: the number of vehicles, the velocities, and vehicle dispatching. (4) Production planning and scheduling, such as throughput rate, WIP, and stocker capacity distribution and loading along the wafer fab. (5) Production control, stocker operation management and operator behavior. Examples are retrieve trends, delays to output port unloads, and lot requests not from retrieve stockers. In general, there are two types of AMHS in the wafer fab. The first is the interbay system, which is transporting

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F.K. Wang, J.T. Lin / Robotics and Computer-Integrated Manufacturing 20 (2004) 91–100

cassettes or boxes of wafers between process bays. The other is the intrabay system, which is transporting cassettes or boxes of wafers within one process bay, also called tool-to-tool AMHS. Interbay systems are typically monorail-type movement systems, where vehicles move material using monorail and interface with AS/RS machines (stockers) in bay areas where materials are processed. Intrabay automation has been shown to increase process equipment utilization and reduce the labor requirement. Five types of intrabay systems automation vehicles are being developed by material handling equipment suppliers: rail robots, rail guided vehicles, automated guided vehicles (AGV); personnel guided vehicles, and overhead transport vehicles. The analysis of an intrabay system can be found in Cardarelli et al. [2], Jefferson [3], Mackulak et al. [4], Wright et al. [5] and Lin et al. [6]. Many authors have studied the performance of an AMHS. Pillai [7] provides a detailed analysis of the needs and requirements for successfully designing and implementing automated material handling control systems in a wafer fab. Pierce and Stafford [8] developed discrete-event simulation models to model the performance of conventional cleanroom material handling manual and automated systems. The cassette delivery time, cassette cycle time, and resource utilization could be used as the performance metrics. The results show that the track design, vehicle count, and velocity can affect system performance. The most practical approach in enhancing interbay AMHS performance is to minimize the travel distances between stockers by using a custom track layout with turntables. Cardarelli et al. [9] present the performance of an automated interbay material handling and storage system. This study was considered the effects of design choices, production planning and scheduling, along with system management and operator behavior. The results show that the storage capacity distribution along the wafer fab is extremely important. Colvin, Lawrence, and Mackulak [10] presents the idea that software-driven simulation is a valuable tool for those evaluating and choosing AMHS for new wafer fabrication facilities. Simulation provides the ability to compare fab automation designs through detailed analyses of system component layouts, system performance, capacity constraints, wafer run rates, operational requirements,

downtime parameters, automation needs, and the integration of all these elements together. Wright et al. [5] use discrete-event simulation to study the effects of a factory layout. They concluded that the modified hybrid configuration could provide the best performance. However, most of the literatures are studied with the interbay system, where the hallway contains a single loop. With the exception, of the paper by Lin et al. [11] where the layout of an interbay system is a combination configuration in which the hallway contains double loops and the vehicles have double capacity. In order to improve the interbay performance, the layout of an interbay system can be a combination configuration in which the track contains turntables, turnouts, and highspeed express lanes (see Fig. 1). Lin et al. [12] proposed that the connecting transport, AMHS, can accomplish the wafers moving tasks by different types of vehicles between bays and within each bay by a single system with interconnected lines. In the connecting transport system, the time that is spent waiting for an empty vehicle is eliminated effectively, and the WIP level can be reduced. Lin et al. [13] investigated the connecting transport AMHS in a simplified 300 mm wafer fab. The simulation results showed that the combination of vehicles had a significant effect on average travel time, throughput, and vehicle utilization. When travel time was the major concern, the suitable method was the combination of Type-A and Type-D vehicles. When throughput is the major concern, the suitable method was the combination of Type-A and Type-C vehicles. When vehicle utilization was the major concern, the suitable method is the combination of Type-A and Type-B vehicles. However, not one method outperformed the others in all operational scenarios. This study is investigated an interbay system which contains 41 stockers, 25 turntable points, and 82 turnout points. Turntables control an intersection of several tracks by rotating vehicles to appropriate track segments. AMHS vehicles access parking areas by using turnouts. An express lane is a specialized track system used for longer moves at higher speeds. A discrete-event simulation model studies the performance of an AMHS. The analysis of an operation is presented in the following section. The simulation model is discussed in Section 3, followed by a discussion of the simulation

Note: S01: stocker; TT1: turntable point; • : turnout point; → : direction. Fig. 1. The layout of an interbay AMHS system.

ARTICLE IN PRESS F.K. Wang, J.T. Lin / Robotics and Computer-Integrated Manufacturing 20 (2004) 91–100

results. Section 5 investigated an AGV-based intrabay material handling system, with a simulation model of a photoprocess area. The conclusions are made along with suggestions for the further research in the final section.

2. The analysis of operation An automated interbay material handling system typically consists of a shop floor control system communicating with an AMHS and an automated equipment control system. An interbay system consists of two subsystems: hallway and stockers. The detailed operations of these subsystems can be found in Cardarelli and Pelagagge [14]. The model captures the flow of lots as they are transported between stockers. In the model, a lot enters the system at a source stocker’s IO port. The lot is then moved to a storage location within the stocker by the stocker robot. Once the lot reaches its storage location, a vehicle is requested for

Track Vehicle RTM Shelf

Output Port Input Port Robot Cassette Fig. 2. The layout of the clean stocker and the track.

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moving the lot to its destination stocker. When the allocated vehicle arrives at the source stocker’s horizontal transfer, the vehicle moves into the stocker. The stocker robot then retrieves the lot and moves it onto the vehicle. Next, the vehicle transports the lot via the AeroTrakt to the destination stocker’s horizontal transfer. The vehicle and the lot move into the destination stocker, where the stocker robot moves the lot from the vehicle to a storage location. Finally, the stocker robot moves the lot to the destination stocker’s IO port, where the lot leaves the system. Fig. 2 illustrates the layout of the clean stocker and the track through the system. Stocker cycle time accounts for the time it takes to pick a lot from any location and place it at any location. It determines the average times from equipment analysis and data collection. However, there is variability in the overall cycle time of 18 s. This is because the length of time required to complete the cycle depends on how far the stocker robot has to move to reach a location. To account for this variability, the stocker cycle time is modeled with a normal distribution. To model the stocker cycle time, a normal distribution with a mean of 18 s and a standard deviation of 2 s was used. The process-flow data is used to describe the movement rate of lots between stockers. There is variability in the lot movement rate. The source of data set is collected from a wafer fab in Taiwan called a from-to-table (see Table 1) shows the moves per hour in the process flow from its mixed products. This data will be determined by the influence of the distribution of the interarrival time for the input rate of the simulation model. The input X (hour per lot) value is the inverse of the value from the from-to table. The data set is grouped by the stocker name, so the parameter of the stocker can be found to represent the behavior of the flow pattern for each stocker from the statistical test.

Table 1 The from-to-table of an interbay system STK01 STK01 STK02 STK03 STK04 STK05 STK06 STK07 STK08 STK09 STK10 — STK39 STK40 STK41 Total

STK02

STK03

0.88 0.29 0.29 0.59

4.16

—

0.00

—

2.05

STK05

STK06

STK07

STK08

STK09

STK10

—

0.25 0.25 1.03 0.09 0.11 0.04 5.59 4.76

0.25 0.25 2.05 0.17 1.22 0.04 3.37 6.98

— — — — — — — — — — — — — — —

5.40 0.98 0.91 0.99

0.32 0.32 0.29 2.53

0.32 2.54 0.29 0.31

2.36 2.36 0.59 0.62

6.67 6.67 —

2.22 2.22 —

4.44 2.22 —

2.22 4.44 —

0.74

2.22

0.74

0.74

1.48

1.96

23.84

8.64

10.86

14.07

0.53 0.53

0.83 2.22

1.11 —

STK04

0.07 0.02 0.02 0.05

—

—

—

12.12

14.33

STK39

STK40

STK41

2.22

2.05 2.02 0.63 0.21 0.21 0.42

2.22 —

—

—

5.00

4.44 9.98

5.00

0.56

0.56

4.44

Total 8.90 7.23 8.57 10.07 2.91 0.60 9.48 19.46 15.55 18.88 — 0.00 5.92 4.44 112.01


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It is often of interest to test or confirm that the interarrival time data is from some particular distribution. Thus, in order to justify the underlying distribution of interarrival time from this data set, a goodness of fit technique is implemented to determine the best fitted division. In this study, four candidate distributions (Exponential, Lognormal, Gamma, or Weibull distribution) are used to find the best fitted distribution. Here, the chi-square test and the Kolmogorov– Smirnov test are used to measure the goodness-of-fit. To perform the chi-square test, the system organizes the data in a frequency table, and computes the difference between the observed and the expected frequency for each time interval. The sum of these differences builds the chi-square statistic. A large chi-square (significance level o0.05) leads to the conclusion that the chosen model does not provide a good fit for the data. To perform the Kolmogorov–Smirnov test, the system computes the maximum distance between the cumulative frequency of the times and the theoretical cumulative frequency provided by the chosen model. If this distance is large enough, the hypothesis (significance level o0.05) that the chosen model fits through the times is rejected. Table 2 is the input data for stocker S01 and the testing results of the stocker S01 by different models are listed in Table 3.

Table 2 The data set for the stocker S01 For stocker S01 From

To

From-to data

X -value (h/lot)

S01 S01 S01 S01 S01 S01 S01 S01 S01 S01 S01 S01 S01

S05 S06 S07 S08 S09 S10 S16 S23 S24 S28 S29 S30 S34

5.40 0.32 0.32 2.36 0.25 0.25 1.48 2.22 1.48 1.11 3.97 0.10 2.96

0.185 3.125 3.125 0.424 4.000 4.000 0.676 0.450 0.676 0.901 0.252 10.000 0.338

From above, the fitted model of S01data is a Weibull distribution, and the maximum likelihood estimation of the parameters is g ¼ 0:847; y ¼ 1:965: The same procedures can be applied to all stockers. Most of the flow move from every stocker can be fitted by the Weibull distribution, but some cannot. From the from-to-table, the interarrival time is not exactly an exponential distribution. However, it can be a Weibull distribution. An exponential distribution is a special case of the Weibull distribution, so the data set still can be approximated to the same family distribution. Consequently, the assumption of the interarrival time from the simulation model is correct at 90% confidence interval. Namely, the input rate is Poisson distribution and the process flow of the interarrival time is an exponential distribution. The zone test is also tested and divided by etch, diffusion, thin film, photo, and implant, respectively. The results were shown that the underlying distributions of most stockers are exponential or of the Weibull distribution. The values of the p-value, b; g; and y for all stockers are shown in Table 4.

3. Simulation model This section provides the assumptions and supporting information used in the design of the simulation model. A simulation model was developed and the model was built and executed using AutoModt simulation software version 8.6. The study evaluated the required number of vehicles that can have the better performance of the throughput movement, the delivery time, the transport time, and the stocker robot utilization. Modeling assumptions are listed as follows: (1) Vehicles have a maximum velocity of 109 ft/min. (2) Turntables have a maximum angular velocity of 90 /s. (3) The average time for a vehicle to cross a turntable is 10 s. (4) Stocker robot cycle times are normally distributed with a mean of 18 s and a standard deviation of 2 s. (5) Interarrival times of lots at the source stockers are exponential or Weibull distribution. (6) The dispatching rule of the lots and vehicles is a combination of the shortest distance with nearest vehicle and the primary encounter first served.

Table 3 The testing results of the stocker S01 by different models Model

w2 test

Exponential Gamma Lognormal Weibull

2.81 2.12 4.17 2.94

with with with with

2 1 1 1

degrees of freedom degree of freedom degree of freedom degree of freedom

p-value

K–S test

p-value

0.246 0.145 0.041 0.087

0.275 0.228 0.199 0.174

0.008 0.064 0.178 0.205


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Table 4 The values of the p-value, b; g and y for all stockers Zone

Stocker #

Fitted distribution

p-value of Chi-square test

p-value of K–S test

Etch Etch Etch Etch Etch Etch Etch Etch Etch Etch Etch

S01 S02 S03 S04 S05 S06 S07 S08 S09 S10 S11

Weibull Exponential Weibull Weibull None Weibull None None Exponential Weibull Weibull

0.086 0.324 0.123 0.105

0.205 0.282 0.220 0.240

0.087

0.205

0.152 0.086 0.202

0.227 0.214 0.207

S12 S13 S14 S15 S16 S17 S18

Insufficient dataa 0.130 0.133

CMP CMP

S19 S20

Insufficient dataa Insufficient dataa

Diffusion Diffusion Diffusion

S21 S22 S23

Weibull Weibull Weibull

Implant Implant Implant

S24 S25 S26

None Insufficient dataa None

Photo Photo Photo Photo Photo Photo

S27 S28 S29 S30 S31 S32

Insufficient dataa Weibull Weibull None Insufficient dataa Insufficient dataa

Diffusion Diffusion Diffusion Diffusion Diffusion Diffusion Diffusion Diffusion Diffusion

S33 S34 S35 S36 S37 S38 S39 S40 S41

None Exponential Insufficient dataa Weibull Insufficient dataa Weibull Weibull Weibull Insufficient dataa

Thin Thin Thin Thin Thin Thin Thin

a

film film film film film film film

Weibull Weibull None Weibull None

b

g

y

0.847

1.965

1.682 0.911

1.735 3.430

0.847

1.965

1.553 2.111

0.794 1.212

0.323 0.219

1.232 1.141

2.726 1.898

0.326

0.327

0.965

2.098

0.385 0.695 0.123

0.283 0.264 0.065

1.343 1.302 1.463

1.244 0.982 1.517

0.213 0.585

0.240 0.368

2.430 1.787

1.036 0.833

0.180

0.160

0.182

0.271

1.204

2.533

0.777 0.195 0.481

0.184 0.247 0.225

1.966 0.944 1.451

1.253 1.898 1.253

0.498

1.417

0.952

Insufficient data mean that there are very few samples to provide the statistical test.

(7) The fab will operate under steady-state conditions. (8) The distributions describing stocker robot cycle times will not change during the simulated period. (9) The distributions describing lot interarrival times will not change during the simulated period. The performance measures collected from the simulation are outlined as follows: (1) Delivery time: The time spent waiting for a vehicle to be allocated plus the time spent waiting for the

empty, allocated vehicle travel to the source stocker plus transport time. (2) Transport time: The time from when a lot is removed from a shelf in the source stocker to when the lot is placed on the shelf at the destination stocker. Thus, transport time includes two-stocker robot cycles (one at the source stocker and one at the destination stocker) and travel time on this interbay system.

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(3) Throughput: The quantity of the cassettes completed transport in an interbay system per hour. A number of trial runs were performed to validate the model and to determine a proper simulation warm-up period. First, it was observed that several statistics in the simulation started to show a smaller variation after about 200 min. Then, there was very little variation among the replications. With this in mind, each simulation in our experiment ran for 1440 min after a warm-up period of 120 min. Statistical test using ANOVA has shown that the replication effect did not significantly affect the statistics collected in the simulation. Therefore, each experiment was replicated three times. The software Design-Expert [15] was used for data analysis and a simple one-factor of response surface model is used to determine the appropriate vehicle number. This experiment design has eight runs where the lowest level of the vehicle number and the upper level of the vehicle number are 70 and 90. Therefore, the total number of simulation experiments performed was 24.

4. The analysis of simulation results The simulation model analyzed different scenarios obtained by altering the number of vehicles available for product movement. The residual analysis shows that the assumptions can be satisfied for all performance measures, so further statistical analysis can be carried out. From the results of the analysis of variance, the vehicle number significantly affects the average delivery

time and the average throughput at 95% confidence level. Ordinary least-squares estimation techniques were applied to develop models for each response variable. Thus, the generated models are as follows: Delivery time ¼ þ 7:43 0:10 vehicle number þ 5:686E-04 vehicle number2 ; Transport time ¼ þ 3:72 0:037 vehicle number þ 2:275E-04 vehicle number2 ; Throughput ¼ 2081:66 þ 69:70 vehicle number 0:42 vehicle number2 : The analysis of variance tables for each response variable are given in Tables 5(a)-(c). The R2 values are 0.9601, 0.6215 and 0.9417, respectively. The residual analysis of these models validated the assumptions. A two-dimensional surface for the desirability function is presented in Fig. 3. Under these models, the optimal setting is found to be (vehicle number=83.36) with the throughput=809, waiting time=2.69, and transport time=2.22. The confirmatory running at that condition (vehicle number=80) shows that all responses satisfy the requirements. The recommendation is to therefore stay with 80 vehicles. The following Figs. 4–6 provide some simulation results of the number vehicles (=80) scenario. The results are obtained by averaging the 10 replications of the 24 h per day. All stockers’ utilization is less than 70% and the crossing number of all nodes is within an acceptable limit. In addition, the distribution of the moving tasks is reasonable to illustrate the status of the vehicle transportation.

Table 5 The analysis of variance Source

Sum of squares

DF

Mean square

(a) For delivery time Model Residual Lack of fit Pure error Cor total

0.085 3.534E-03 3.084E-03 4.500E-04 0.089

2 5 2 3 7

0.043 7.069E-04 1.542E-03 1.500E-04

(b) For transport time Model Residual Lack of fit Pure error Cor total

9.634E-04 5.866E-04 3.366E-04 2.500E-04 1.550E-03

2 5 2 3 7

4.817E-04 1.173E-04 1.683E-04 8.333E-05

(c) For throughput Model Residual Lack of fit Pure error Cor total

5590.56 346.15 342.76 3.38 5936.71

2 5 2 3 7

2795.28 69.23 171.38 1.13

F -value

Prob>F

60.23

0.0003

10.28

0.0454

4.11

0.0881

2.02

0.2782

40.38

0.0008

151.89

0.0010


5. The analysis of an intrabay system A discrete-event simulation model was developed for Bays 27/28 in order to predict the operational perforOne Factor Plot DESIGN-EXPERT Plot

Desirability

Actual Factor X = vehicle number

0.806

0.605

0.403

0.202

0.000 70.00

75.00

80.00

85.00

90.00

vehicle number

Fig. 3. Three-dimensional surface for the desirability function.

mance of the intrabay material handling system. The Bays 27/28 is the one of the set comprising the photoprocess. The layout is illustrated in Fig. 7. AGV are used in this study. The process-flow data is used to describe the movement rate of lots between tools. The source of data set is collected from a wafer fab in Taiwan (see Table 6), which shows the moves per hour in the process flow from mixed products. This intrabay system is designed as a pull system. When a processed lot is picked up at a tool by intrabay transportation AGV, a demand request is generated for a new lot to be transported to that tool. In a pull system, the tool processing time drives the number of intrabay moving per hour. Modeling definitions are listed as follows: (1) Bi-directional control: This is the normal control method for the AGV controller, where AGVs travel in both directions in and out of the process bay. Bi-directional routing requires the AGV controller to determine which AGV should yield the right way if there is a conflict for travel space. (2) Delivery time: Delivery time is the time spent waiting for an AGV to be allocated, plus the time spent waiting for the allocated AGV to travel to

Stocker Robot Utilization 1

80% 70% 60% 50% 40% 30% 20% 10% 0%

Fig. 4. The stocker utilization for 80 vehicles scenario. Car Status, MAIN 60 50

Precentage

40 30 20 10 0

Move to Load

Load

Move to Unload

97

Unload

Move to Park

Fig. 5. The distribution of the moving tasks for 80 vehicles scenario.

Park


98

Node Crossings 1 300

Crossing per hour

250

200

15 0

100

50

0

Fig. 6. The number of crossings on turnout points and turntable points for 80 vehicles scenario.

Fig. 7. The layout of an intrabay system in photoarea (bays 27/28).

Table 6 The data of from-to-table from the intrabay bays 27/28 STK27 STK27 STK28 PH051-1 IF4-In PH105-7 PH105-8 PH901-1 PH901-2 PH901-3 — PH901-6 Total

STK28

PH051-1

IF4-In

PH105-7

PH105-8

PH901-1

PH901-2

PH901-3

—

PH905-6

Total

1.94

1.94

0.74

0.74

0.74

— — — — — — — —

1.94

1.94 11.50 5.40 0.00 0.00 0.00 0.00 0.00

—

—

—

—

—

—

—

0.74

—

1.94

— 1.94 20.78

1.94

1.94

0.74

0.74

5.40 5.40

—

—

—

0.00

5.40

5.40

— 1.94 1.94

the source stocker (or source tool), plus the transport time (as defined below), added on to the loading and unloading time. (3) Transport time: The time from when a lot is loaded onto an AGV until it is unloaded at the destination. (4) Waiting time: AGV is waiting for a stocker load port or a process tool load port to move in the prior

cassette on a multiple load/unload. Or, the AGV is waiting for another AGV to move out of the way. (5) Empty travel: AGV is moving without a cassette(s) on the AGV. (6) Unloading: AGV is at a stocker or process tool unloading a cassette(s). (7) Loaded travel: AGV is moving with a cassette(s) on the AGV.


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Table 7 The simulation results of two scenarios Performance measure

Number of AGVs

Delivery time (minutes) (average/standard deviation) Transport time (minutes) (average/standard deviation) Throughput (lots/hour) (average/standard deviation) Average AGVs utilization (%) (average/standard deviation)

(8) Loading: AGV is at a stocker or process tool loading a cassette(s). (9) Busy: AGV is either processing a task or moving it. (10) Idle: AGV has no assigned tasks and is parked.

A number of trial runs were performed to validate the model and to determine a proper simulation warm-up period. First, it was observed that several statistics in the simulation started to show a smaller variation after about 60 min. Then, there was very little variation among the replications. With this in mind, each simulation in our experiment was run for 1440 min after a warm-up period of 60 min. Statistical test using ANOVA has shown that the replication effect did not significantly affect the statistics collected in the simulation. Therefore, each experiment was replicated 10 times. The total number of simulation experiments performed is 2(scenarios) 10(replications) which are 20. The performance measures collected from the simulation are given as delivery time, transport time, throughput, and AGVs utilization. The simulation model analyzed two different scenarios obtained by altering the number of AGVs available for product movement. The residual analysis shows that the assumptions be satisfied for all performance measures, so that further statistical analysis can be carried out. From the results of the analysis of variance, the AGVs number drastically affects the average delivery time, the average throughput, and the average AGVs utilization at 95% confidence level. The least significant difference method is used to contrast all pairs of the two scenarios under each of the performance measures. Results of the paired test analysis are summarized in Table 7. As can be seen, these two scenarios are ranked best (left) to worst for average delivery time and are ranked best (right) to worst for average throughput and average AGVs utilization. Each value is the mean of the performance data collected in the 10 replications. The simulation results indicated that a balance among delivery time, throughput, and AGVs utilization be realized with AGVs number (=2).

2

3

(3.44/0.040) (1.75/0.0370 (49.3/1.5) (83.58/2.5)

(2.15/0.038) (1.73/0.035) (48.0/1.4) (60.57/2.48)

6. Conclusions The performance evaluation was to analyze an AMHS with a zone control scheme in avoiding all vehicle collisions, considering the effects of the vehicle number. In this study, the fab layout is a custom configuration and the track option contains turntables, turnouts, and high-speed express lanes. The behavior of the interarrival for all stockers from the real data set was shown that the underlying distributions of most stockers belong to an exponential or Weibull distribution. In particular, the following factors were examined: the delivery time, the transport time, the interbay throughput, the stocker robot utilization, and the number of crossings on turnout points and turntable points. The results show that the number of vehicles (=80) were able to meet the requirements. In addition, AGV-based intrabay material handling system with a simulation model of the photoprocess was investigated. The results show that the AGVs number (=2) could meet the requirements. Thus, the number of vehicles on inter- or intrabay system can be determined by a simulation study. These studies concern the fab layout only as a custom configuration and as a track option, which contains turntables, turnouts, and high-speed express lanes for an interbay AMHS system. Further research is needed to compare the performance of a custom configuration with other types of configuration. More works are needed for studying how to use direct transport systems such as a continuous flow transport in 300-mm wafer fab to eliminate the differentiation between interbay and intrabay systems, in which lots would be directly transported from equipment to equipment or from stockers. Acknowledgements The authors are grateful for partial support by National Science Council in Taiwan under the grant (NSC-89-2213-E182-007). References [1] Davis F, Weiss M. Addressing automated materials handling in an existing wafer fab. Semicond Int 1995;18:3.

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