Performance evaluation of an automated material handling system for a wafer fab

Robotics and Computer-Integrated Manufacturing 20 (2004) 91 100 Performance evaluation of an automated material handling system for a wafer fab F.K. Wang a, *, J.T. Lin b 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 capitalcosts. 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 materialhandling and control. The main purpose of an automated materialhandling 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 materialdeliveries 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. Successfulimplementation of an AMHS begins with the collection of all the necessary information and ends with *Corresponding author. E-mail address: fukwun@ntut.edu.tw (F.K. Wang). 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 0736-5845/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.rcim.2003.08.002

92 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 materialusing monorailand 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 materialhandling controlsystems in a wafer fab. Pierce and Stafford [8] developed discrete-event simulation models to model the performance of conventional cleanroom materialhandling manualand 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 practicalapproach in enhancing interbay AMHS performance is to minimize the traveldistances between stockers by using a custom track layout with turntables. Cardarelli et al. [9] present the performance of an automated interbay materialhandling 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, operationalrequirements, 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.

F.K. Wang, J.T. Lin / Robotics and Computer-Integrated Manufacturing 20 (2004) 91 100 93 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 finalsection. 2. The analysis of operation An automated interbay materialhandling system typically consists of a shop floor control system communicating with an AMHS and an automated equipment controlsystem. 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 modelcaptures 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. moving the lot to its destination stocker. When the allocated vehicle arrives at the source stocker s horizontaltransfer, 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 interarrivaltime 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 statisticaltest. Table 1 The from-to-table of an interbay system STK01 STK02 STK03 STK04 STK05 STK06 STK07 STK08 STK09 STK10 STK39 STK40 STK41 Total STK01 5.40 0.32 0.32 2.36 0.25 0.25 8.90 STK02 0.53 0.98 0.32 2.54 2.36 0.25 0.25 7.23 STK03 0.83 0.53 0.91 0.29 0.29 0.59 1.03 2.05 2.05 8.57 STK04 2.22 0.99 2.53 0.31 0.62 0.09 0.17 0.56 2.02 0.56 10.07 STK05 0.88 0.07 0.11 1.22 0.63 2.91 STK06 0.29 0.02 0.04 0.04 0.21 0.60 STK07 0.29 0.02 5.59 3.37 0.21 9.48 STK08 0.59 0.05 4.76 6.98 2.22 0.42 4.44 19.46 STK09 6.67 2.22 4.44 2.22 15.55 STK10 1.11 6.67 2.22 2.22 4.44 2.22 18.88 STK39 0.00 STK40 0.74 2.22 0.74 0.74 1.48 5.92 STK41 4.44 4.44 Total4.16 0.00 2.05 1.96 23.84 8.64 10.86 14.07 12.12 14.33 5.00 9.98 5.00 112.01

94 F.K. Wang, J.T. Lin / Robotics and Computer-Integrated Manufacturing 20 (2004) 91 100 It is often of interest to test or confirm that the interarrivaltime data is from some particular distribution. Thus, in order to justify the underlying distribution of interarrivaltime 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 modeldoes 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 theoreticalcumulative frequency provided by the chosen model. If this distance is large enough, the hypothesis (significance level o0.05) that the chosen modelfits 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 S05 5.40 0.185 S01 S06 0.32 3.125 S01 S07 0.32 3.125 S01 S08 2.36 0.424 S01 S09 0.25 4.000 S01 S10 0.25 4.000 S01 S16 1.48 0.676 S01 S23 2.22 0.450 S01 S24 1.48 0.676 S01 S28 1.11 0.901 S01 S29 3.97 0.252 S01 S30 0.10 10.000 S01 S34 2.96 0.338 From above, the fitted modelof 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 interarrivaltime is not exactly an exponential distribution. However, it can be a Weibull distribution. An exponentialdistribution is a specialcase 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 interarrivaltime 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 exponentialor 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) Interarrivaltimes of lots at the source stockers are exponentialor Weibulldistribution. (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 w 2 test p-value K S test p-value Exponential2.81 with 2 degrees of freedom 0.246 0.275 0.008 Gamma 2.12 with 1 degree of freedom 0.145 0.228 0.064 Lognormal4.17 with 1 degree of freedom 0.041 0.199 0.178 Weibull 2.94 with 1 degree of freedom 0.087 0.174 0.205

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 b g y Etch S01 Weibull 0.086 0.205 0.847 1.965 Etch S02 Exponential0.324 0.282 0.498 Etch S03 Weibull 0.123 0.220 1.682 1.735 Etch S04 Weibull 0.105 0.240 0.911 3.430 Etch S05 None Etch S06 Weibull 0.087 0.205 0.847 1.965 Etch S07 None Etch S08 None Etch S09 Exponential0.152 0.227 1.417 Etch S10 Weibull 0.086 0.214 1.553 0.794 Etch S11 Weibull 0.202 0.207 2.111 1.212 Thin film S12 Insufficient data a Thin film S13 Thin film S14 Weibull 0.130 0.323 1.232 2.726 Thin film S15 Weibull 0.133 0.219 1.141 1.898 Thin film S16 None Thin film S17 Weibull 0.326 0.327 0.965 2.098 Thin film S18 None CMP S19 Insufficient data a CMP S20 Insufficient data a Diffusion S21 Weibull 0.385 0.283 1.343 1.244 Diffusion S22 Weibull 0.695 0.264 1.302 0.982 Diffusion S23 Weibull 0.123 0.065 1.463 1.517 Implant S24 None Implant S25 Insufficient data a Implant S26 None F.K. Wang, J.T. Lin / Robotics and Computer-Integrated Manufacturing 20 (2004) 91 100 95 Photo S27 Insufficient data a Photo S28 Weibull 0.213 0.240 2.430 1.036 Photo S29 Weibull 0.585 0.368 1.787 0.833 Photo S30 None Photo S31 Insufficient data a Photo S32 Insufficient data a Diffusion S33 None Diffusion S34 Exponential0.180 0.160 0.952 Diffusion S35 Insufficient data a Diffusion S36 Weibull 0.182 0.271 1.204 2.533 Diffusion S37 Insufficient data a Diffusion S38 Weibull 0.777 0.184 1.966 1.253 Diffusion S39 Weibull 0.195 0.247 0.944 1.898 Diffusion S40 Weibull 0.481 0.225 1.451 1.253 Diffusion S41 Insufficient data a a 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 traveltime on this interbay system.

96 F.K. Wang, J.T. Lin / Robotics and Computer-Integrated Manufacturing 20 (2004) 91 100 (3) Throughput: The quantity of the cassettes completed transport in an interbay system per hour. A number of trialruns were performed to validate the modeland to determine a proper simulation warm-up period. First, it was observed that severalstatistics 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. Statisticaltest 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 modelis 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 totalnumber 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 residualanalysis shows that the assumptions can be satisfied for all performance measures, so further statisticalanalysis 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 ¼þ7:43 0:10 vehicle number þ 5:686E-04 vehicle number 2 ; Transport time ¼þ3:72 0:037 vehicle number þ 2:275E-04 vehicle number 2 ; Throughput ¼ 2081:66 þ 69:70 vehicle number 0:42 vehicle number 2 : The analysis of variance tables for each response variable are given in Tables 5(a)-(c). The R 2 values are 0.9601, 0.6215 and 0.9417, respectively. The residual analysis of these models validated the assumptions. A two-dimensionalsurface 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 F-value Prob>F (a) For delivery time Model0.085 2 0.043 60.23 0.0003 Residual3.534E-03 5 7.069E-04 Lack of fit 3.084E-03 2 1.542E-03 10.28 0.0454 Pure error 4.500E-04 3 1.500E-04 Cor total0.089 7 (b) For transport time Model9.634E-04 2 4.817E-04 4.11 0.0881 Residual5.866E-04 5 1.173E-04 Lack of fit 3.366E-04 2 1.683E-04 2.02 0.2782 Pure error 2.500E-04 3 8.333E-05 Cor total1.550e-03 7 (c) For throughput Model5590.56 2 2795.28 40.38 0.0008 Residual346.15 5 69.23 Lack of fit 342.76 2 171.38 151.89 0.0010 Pure error 3.38 3 1.13 Cor total5936.71 7

F.K. Wang, J.T. Lin / Robotics and Computer-Integrated Manufacturing 20 (2004) 91 100 97 5. The analysis of an intrabay system 0.806 DESIGN-EXPERT Plot Actual Factor X = vehicle number Desirability 0.605 0.403 0.202 0.000 One Factor Plot 70.00 75.00 80.00 85.00 90.00 vehicle number Fig. 3. Three-dimensionalsurface for the desirability function. A discrete-event simulation model was developed for Bays 27/28 in order to predict the operationalperformance of the intrabay materialhandling 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 toolprocessing time drives the number of intrabay moving per hour. Modeling definitions are listed as follows: (1) Bi-directional control: This is the normalcontrol method for the AGV controller, where AGVs travelin both directions in and out of the process bay. Bi-directionalrouting requires the AGV controller to determine which AGV should yield the right way if there is a conflict for travelspace. (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 80% Stocker Robot Utilization 1 70% 60% 50% 40% 30% 20% 10% 0% Fig. 4. The stocker utilization for 80 vehicles scenario. Car Status, MAIN 60 50 40 Precentage 30 20 10 0 Move to Load Load Move to Unload Unload Move to Park Park Fig. 5. The distribution of the moving tasks for 80 vehicles scenario.

98 F.K. Wang, J.T. Lin / Robotics and Computer-Integrated Manufacturing 20 (2004) 91 100 300 Node Crossings 1 250 Crossing per hour 200 150 100 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 STK28 PH051-1 IF4-In PH105-7 PH105-8 PH901-1 PH901-2 PH901-3 PH905-6 Total STK27 5.40 1.94 1.94 STK28 1.94 1.94 0.74 0.74 0.74 11.50 PH051-1 5.40 5.40 IF4-In 0.00 PH105-7 0.00 PH105-8 0.00 PH901-1 0.00 PH901-2 0.00 PH901-3 PH901-6 1.94 1.94 Total0.00 5.40 5.40 1.94 1.94 1.94 0.74 0.74 0.74 1.94 20.78 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 untilit is unloaded at the destination. (4) Waiting time: AGV is waiting for a stocker load port or a process toolload 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.

Table 7 The simulation results of two scenarios F.K. Wang, J.T. Lin / Robotics and Computer-Integrated Manufacturing 20 (2004) 91 100 99 Performance measure Number of AGVs 2 3 Delivery time (minutes) (average/standard deviation) (3.44/0.040) (2.15/0.038) Transport time (minutes) (average/standard deviation) (1.75/0.0370 (1.73/0.035) Throughput (lots/hour) (average/standard deviation) (49.3/1.5) (48.0/1.4) Average AGVs utilization (%) (average/standard deviation) (83.58/2.5) (60.57/2.48) (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 trialruns were performed to validate the modeland 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 residualanalysis shows that the assumptions be satisfied for all performance measures, so that further statisticalanalysis 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). 6. Conclusions The performance evaluation was to analyze an AMHS with a zone controlscheme in avoiding a l 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 interarrivalfor allstockers from the realdata 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 modelof 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 gratefulfor partialsupport by NationalScience Councilin 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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