1 SRC/ISMT Factory Operations Research Center SRC/ISMT FORCe: Factory Operations Research Center Task NJ-877 Michael Fu, Director Emmanuel Fernandez Steven I. Marcus Atlanta, GA, Oct , 2003 Intelligent Preventive Maintenance Scheduling in Semiconductor Manufacturing Fabs

SRC/ISMT Factory Operations Research Center 2 1.Project Overview: Michael FuProject Overview: Michael Fu 2.Summary of Completed Tasks: Emmanuel FernandezSummary of Completed Tasks: Emmanuel Fernandez Interaction with Industry Deliverables Models, Algorithms, and Software Tools Simulation Case Studies Documentation submitted to SRC website Other documentation Software implementation: PMOST (Jose Ramirez)Software implementation: PMOST (Jose Ramirez) Integration with fab schedulers: collaboration with ASU Students trained 3.Summary of Doctoral and Master Theses: StudentsSummary of Doctoral and Master Theses: Students 4.Continuing and Future Research: Emmanuel FernandezContinuing and Future Research: Emmanuel Fernandez 5.Conclusions: Michael FuConclusions: Michael Fu CONTENTS

3 SRC/ISMT Factory Operations Research Center Michael Fu Robert H. Smith School of Business & Institute for Systems Research University of Maryland 1. Project Overview Summary

SRC/ISMT Factory Operations Research Center 4 (1) Develop, test, and transfer software tools for optimal PM planning and scheduling; (2) Research and validate the models, methods and algorithms for software development in (1); (3) Facilitate the transfer of models, algorithms and tools to 3rd party commercial software vendors. Research Plan (Proposed)

SRC/ISMT Factory Operations Research Center 5 Deliverables (reports) completed: January and July 2002; SRC Pub P005269, P Best Paper in Session, TECHCON 2003 (X.Yao presenter): “Optimal preventive maintenance policies for unreliable production systems with applications to semiconductor manufacturing” Paper submitted for publication IEEE-Trans. Semiconductor Mfg: –“Incorporating Production Planning into Preventive Maintenance Scheduling in Semiconductor Fabs” INFORMS 2003 Annual Meeting: invited talks and an invited session organized and chaired within Applied Probability Cluster. Executive Summary

SRC/ISMT Factory Operations Research Center 6 software tool (PMOST): –Generic Scheduling Simulation Engine –Generic Implementation of PM Scheduling Algorithm summer internships (AMD & Intel) Ph.D. dissertations supported: He, Yao, Hu, Ramirez MS dissertations supported: Crabtree, Jagannathan commercialization feasibility discussions: Adexa, Ibex Processes. NIST internship via Swee Leong Executive Summary

SRC/ISMT Factory Operations Research Center 7 Matilda O'Connor, AMD Nipa Patel,AMD (sign in SRC list) Ying Tat Leung,IBM Wayne F. Carriker, Intel Robin L. Hoskinson, Intel Ben-Rachel Igal, Intel Mani Janakiram, Intel Madhav Rangaswami,Intel Sidal Bilgin, LSI (sign in SRC list) Russell Whaley,LSI (sign in SRC list) Ramesh Rao, National Semiconductor Jan Verhagen, Philips (sign in SRC list) Shekar Krishnaswamy,Motorola (sign in SRC list) K.J. Stanley, Motorola (sign in SRC list) Gurshaman S. Baweja, TI Jason Wang, TSMC (ISMT) James Yang, TSMC (ISMT) Giant Kao, TSMC (ISMT) Jacky Fan, TSMC (ISMT) Industrial Liaisons

SRC/ISMT Factory Operations Research Center 8 Faculty: –Michael Fu, Maryland –Steve Marcus, Maryland –Emmanuel Fernandez, Cincinnati Students: –Xiaodong Yao, Maryland (PhD final defense Nov.2003) –Ying He, Maryland (PhD completed, summer 2002) –Jiaqiao Hu, Maryland (3rd year PhD) –Jason Crabtree, Cincinnati (MS completed, summer 2003) –Jose Ramirez, Cincinnati (3rd year PhD) –Sumita Jagannathan, Cincinnati (3rd year MS) Research Personnel

SRC/ISMT Factory Operations Research Center 9 Year 1 - Implementing the PM scheduling algorithm; developing, distributing, and analyzing PM practice survey to drive PM planning models and algorithms; literature review of research on analytical and simulation-based models for PM planning with production considerations. Year 2 - Developing generic implementation platform for PM scheduling algorithm to facilitate possible transfer to 3rd party software provider; developing, testing, and validating PM planning models and algorithms. Year 3 – Implementing PM planning models and algorithms, validating and testing; training workshop to facilitate transfer to 3rd party software vendor. Task Description (Proposed)

SRC/ISMT Factory Operations Research Center Survey of current PM practices in industry (Report) (P:15-DEC-2001) 2. Models and algorithms to cover bottleneck tool sets in a fab (Report) (P:31-MAR-2002) 3. Simulation engine implemented in commercially available software, with case studies and benchmark data (Report) (P:30-SEP-2002) 4. PM planning/scheduling software tools, with accompanying simulation engine (Software, Report) (P:30-JUN-2003) 5. Installation and evaluation, workshop and consultation (Report) (P:31-DEC-2003) MORE DETAILS later in presentation Deliverables to Industry (Proposed)

11 SRC/ISMT Factory Operations Research Center Emmanuel Fernandez, Ph.D. ECECS Department University of Cincinnati 2. Summary of Completed Tasks

12 SRC/ISMT Factory Operations Research Center Summary of Completed Tasks We summarize here the accomplishments in the project up to this point: Interactions with industry Deliverables Models, Algorithms, and Software Tools Case Studies Documentation submitted to SRC website Other documentation Software Implementation: PMOST Integration with fab schedulers: collaboration with ASU Students trained (Doctoral and Master Theses)

13 SRC/ISMT Factory Operations Research Center Interactions with Industry

14 SRC/ISMT Factory Operations Research Center Interaction with Industry Interactions with industry have been fundamental in guiding our research efforts: Interactions with industry have been fundamental in guiding our research efforts: These facilitated the design, implementation, and proof of concept of our algorithms, models and software tools. These facilitated the design, implementation, and proof of concept of our algorithms, models and software tools. Interactions have taken place in the form of: Summer internships for our students from 2000 through Summer internships for our students from 2000 through Direct collaboration to exchange ideas and formulate problems and solutions, e.g: Direct collaboration to exchange ideas and formulate problems and solutions, e.g: Survey on best practices of PM scheduling; Survey on best practices of PM scheduling; Visits to fabs to interview and obtain feedback from tool managers and operators. Visits to fabs to interview and obtain feedback from tool managers and operators. Periodic teleconferences with MC liaisons. Periodic teleconferences with MC liaisons. Co-authored publications derived from the research work.Co-authored publications derived from the research work.

15 SRC/ISMT Factory Operations Research Center Interaction with Industry Summer Internships During the project, a total of four summer internships were completed at two member companies (2000 to 2002):Summer Internships During the project, a total of four summer internships were completed at two member companies (2000 to 2002): X. Yao, 2000, AMD, Austin, TX: data collection and simulation of one case study.X. Yao, 2000, AMD, Austin, TX: data collection and simulation of one case study. X. Yao, J. Crabtree, 2001, AMD, Austin, TX: software implementation of algorithms and models; built interfaces to integrate to fab systems.X. Yao, J. Crabtree, 2001, AMD, Austin, TX: software implementation of algorithms and models; built interfaces to integrate to fab systems. J. Crabtree, 2002, Intel, Chandler, AZ: data collection, software implementation, and two simulation studies.J. Crabtree, 2002, Intel, Chandler, AZ: data collection, software implementation, and two simulation studies. J.A. Ramírez, 2002, AMD, Austin, TX: data collection and modeling for wafer to calendar-based conversion of PM schedules, and two simulation studies.J.A. Ramírez, 2002, AMD, Austin, TX: data collection and modeling for wafer to calendar-based conversion of PM schedules, and two simulation studies.

16 SRC/ISMT Factory Operations Research Center Deliverables: Models, Algorithms, and Software Tools

17 SRC/ISMT Factory Operations Research Center Deliverables Models and Algorithms, and Software Tools Here we summarize the Models and Algorithms produced by the research team representing the theoretical/academic contributions and basis for implementation in software tools: -Hierarchical Model for Optimal PM Scheduling. -MIP formulation of the PM scheduling problem. -Conversion of wafer to calendar-based PM schedules. - X. Yao Doctoral work.

18 SRC/ISMT Factory Operations Research Center Deliverables Models and Algorithms Hierarchical Model for Optimal PM scheduling Upper MDP Lower MIP WIP PM Schedule PM Policy Objective Constraints Demand Pattern Failure Dynamics

19 SRC/ISMT Factory Operations Research Center Models and Algorithms - MIP Formulation Objective:            N t M i l i i l ii l iii ta taCtICtVb i 111 )( )()()(max  Deliverables

20 SRC/ISMT Factory Operations Research Center Models and Algorithms - MIP Formulation Constraints: (i)for those PM tasks required to begin by period (ii)for those PM tasks prohibited from beginning before period (iii)for all PM tasks in general 1)( 1    l i n t l i ta 0)( 1    l i m t l i ta 1)( 1    N t l i ta l i n l i m Deliverables

21 SRC/ISMT Factory Operations Research Center Models and Algorithms - MIP Formulation Constraints: (iv) whereis the set of PM decisions across all PM tasks, andis a dummy variable holding the value offrom the previous period, i.e. tittaftV i ii,))(),(()(  )( ta i )( t i  )()1( tat i i  )(ta i Deliverables

22 SRC/ISMT Factory Operations Research Center Models and Algorithms - MIP Formulation Constraints: (v) whered i (t)is amount of incoming wafers at tooliin periodt, andX i (t)is the quantity of wafers processed on tooliin period t. (vi) whereKiKi is the wafer throughput coefficient for tool i. 1,...,1,)()()()1(  NtitdtXtItI iiii titVKtX iii,)()(  Deliverables

23 SRC/ISMT Factory Operations Research Center Models and Algorithms - MIP Formulation Constraints: (vii) whereLiLi is the maximum allowed inventory at tool i. (viii) whereis the resource requirement variable for resourcekin periodt. tiLtI ii,)(  tkttagtr i ik,))(),(()(  )(tr k Deliverables

24 SRC/ISMT Factory Operations Research Center Models and Algorithms - MIP Formulation Constraints: (ix) whereR k (t)is the amount of resourcekavailable in periodt. (x),,, (xi) tktRtr kk,)()(  0)(  tV i 0)(  tI i 0)(  tX i 0)(  tr k i tik,,  tliorta l i,, 10)(  Deliverables

25 SRC/ISMT Factory Operations Research Center Models and Algorithms Conversion of Wafer to Calendar-based PM Schedules Estimated due time (date) Deliverables PM window (W: warning, D: due, L: late) (Time period) (Wafer counts/period)

26 SRC/ISMT Factory Operations Research Center Deliverables: Simulation Case Studies

SRC/ISMT Factory Operations Research Center 27 Objectives –Validate PM optimization through simulation studies with real fab data –Simulation studies conducted to compare model-based optimized PM schedule and base- line or historical (“best in practice”) PM schedules. –Lay groundwork for integration of PM optimization into production environment Simulation Case Studies

SRC/ISMT Factory Operations Research Center 28 Five case studies with real fab data. Calendar and/or wafer based PM’s. –Case 1: Metal Deposition process (11 tools, 7days); Best in Practice vs. Optimized Schedule –Case 2: Photolithography process (25 tools, 7 days); Best in Practice vs. Optimized PM schedule –Case 3: Metal Deposition process (29 tools, 7 days); Baseline vs. Optimized PM Schedule –Case 4: Photolithography process (12 tools, 7days); Baseline vs. Optimized PM schedule –Case 5: Thin films process (28 tools, 21 days); Best in Practice vs. Optimized PM schedule. Simulation Case Studies

SRC/ISMT Factory Operations Research Center 29 Simulation Case Studies Results: Optimization made logical decisions and showed good performance gains. –Case 1: up to 14% gain in throughput for one tool. –Case 2: Matched tool availability throughput for “Best-in- Practice” schedule. –Case 3: about 1% average gain in tool availability for entire tool group; 1.7% average gain in total throughput for entire tool group. –Case 4: 1% average gain in tool availability for entire tool; 2.2% average gain in total throughput for entire tool group. –Case 5: up to 6% gain in tool availability for one tool; 0.7% average gain in tool availability for entire tool group; 1% average gain in total throughput for entire tool group.

30 SRC/ISMT Factory Operations Research Center Deliverables: Documentation Submitted to SRC Website

31 SRC/ISMT Factory Operations Research Center Deliverables Documentation submitted and currently available at SRC website The following is the list of all the documentation produced by the research team and available at the SRC website: Annual review presentations Intelligent Preventive Maintenance Scheduling in Semiconductor Manufacturing Fabs; Crystal City, MD, December 13-14, 2001, Pub P Intelligent Preventive Maintenance Scheduling in Semiconductor Manufacturing Fabs; Tempe, AZ, April 9-10, 2002, Pub P Intelligent Preventive Maintenance Scheduling in Semiconductor Manufacturing Fabs; San Jose, CA, November 20-21, 2002, Pub P Reports Survey of Current PM Practices in Industry, Conducted Via Web and Electronic Mail; E. Fernandez, M. Fu and S. Marcus; Univ. of Maryland; 17-Jan-2002; 19pp.; Pub P Abstract: The researchers present the results of survey on the practices employed in the semiconductor manufacturing industry for scheduling Preventive Maintenance (PM) tasks. The survey was distributed by the middle of October 2001, and responses were received until the middle of December Report on Models and Algorithms to Cover Major Bottleneck Tool Sets in a Semiconductor Manufacturing Fab; X. Yao, M. Fu, S. Marcus and E. Fernandez; Univ. of Maryland; 29-Jul-2002; 4pp.; Pub P Abstract: The researchers have developed models and algorithms for optimal PM scheduling based on calendar information of time since last PM, and the time window within which the next PM needs to fall. A computationally tractable mixed Integer/Linear Programming (IP/LP) model for short-term planning horizon, e.g., 1-3 weeks, has been developed, tested and implemented to do the day-to-day actual scheduling of PM tasks across tools within a given family.

32 SRC/ISMT Factory Operations Research Center Deliverables Documentation submitted and currently available at SRC website Reports Preventive Maintenance Optimal Scheduling Tool (PMOST): Ver. 1.0; J. Crabtree, J. Ramirez, E. Fernandez, X. Yao, M. Fu and S. I. Marcus; Univ. of Maryland; 21-Jan-2003; 8pp.; Pub P Abstract: The Preventive Maintenance Optimal Scheduling Tool (PMOST) is a (programmed in C-language) software tool for optimal scheduling of Preventive Maintenance tasks in Semiconductor Fabs. Preventive Maintenance Optimal Scheduling Tool (PMOST): Ver. 1.1; J. Crabtree, J. Ramirez, E. Fernandez, X. Yao, M. Fu and S. I. Marcus; Univ. of Maryland; 10-Jul-2003; 10pp.; Pub P Abstract:The Preventive Maintenance Optimal Scheduling Tool (PMOST) is a (programmed in C-language) software tool for optimal scheduling of Preventive Maintenance tasks in Semiconductor Fabs. PMOST v. 1.1 includes conversion of wafer-based to calendar-based PM schedules. Preventive Maintenance Scheduling Model and Generic Implementation, Mathematical Programming Modeling Languages and Solvers; J. Crabtree, J. Ramirez, E. Fernandez; Univ. of Cincinnati; 29-Jul-2002; 6pp.; Pub P Abstract: This report present a survey on Mathematical Programming Modeling Languages (MDL) and Solvers that can be used in optimization of PM schedules. Papers Optimization of Preventive Maintenance Scheduling for Semiconductor Manufacturing Systems: Models and Implementation; X. Yao, M. Fu, S. Marcus and E. Fernandez-Gaucherand; Univ. of Maryland; 17-Dec-2001; 5pp.; Pub P Abstract: In this paper, the researchers present a two-layer hierarchical modeling framework for addressing the PM optimization problem for cluster tools, i.e., a Markov Decision Process (MDP) model at the higher level, and a mixed Linear Programming (LP) model at the lower level. Production planning data such as WIP levels are incorporated in these models. Paper presented at the 2001 IEEE International Conference on Control Applications, Mexico City, Mexico, Incorporating Production Planning into Preventive Maintenance Scheduling in Semiconductor Fabs; X. Yao, M. Fu, S. Marcus and E. Fernandez-Gaucherand; Univ. of Maryland; 29-Jul-2002; 6pp.; Pub P Abstract: In this paper, a general mathematical model aiming at the optimization of preventive maintenance (PM) scheduling is proposed. The researchers formulate the problem as a finite-horizon Markov decision process (MDP) that incorporates equipment dynamics and production system dynamics. Paper presented at MASM 2002 Conference, Tempe, AZ, 2002.

33 SRC/ISMT Factory Operations Research Center Deliverables Documentation submitted and currently available at SRC website Papers (cont.) Optimal Preventive Maintenance Policies for Unreliable Queueing/Production Systems with Applications to Semiconductor Manufacturing; Xiaodong Yao, X. Xie, M. Fu, S. Marcus and E. Fernandez; Univ. of Maryland; 6-Jun-2003; 5pp.; Pub P Abstract: The reliability of equipment is critical to fab's operational performance, and Preventive Maintenance (PM) scheduling is a very challenging task in semiconductor manufacturing. In this paper, the researchers will study optimal PM policies under the context of unreliable queueing systems. Presented at TECHON 2003 (Awarded as "Best Paper in Session"), August 25-27, 2003, Dallas, TX. Optimal Importance Sampling in Securities Pricing; Y. Su and M. C. Fu; Univ. of Maryland; 21-Jun-2002; 29pp.; Pub P Abstract: To reduce variance in estimating security prices via Monte Carlo simulation, the researchers formulate a parametric minimization problem for the optimal importance sampling measure, which is solved using infinitesimal perturbation analysis (IPA) and stochastic approximation (SA). Convergence of Simultaneous Perturbation Stochastic Approximation for Nondifferentiable Optimization; Y. He, M. C. Fu and S. I. Marcus; Univ. of Maryland; 22-May-2003; 5pp.; Pub P Abstract: This paper considers Simultaneous Perturbation Stochastic Approximation (SPSA) for function minimization. The standard assumption for convergence is that the function be three times differentiable, although weaker assumptions have been used for special cases. However, all previous work appears to at least require differentiability. This paper relaxes the differentiability requirement and proves convergence using convex analysis. Presentations Preventive Maintenance in Semiconductor Manufacturing Fabs; M. Fu; Univ. of Maryland; 15-May-2001; 41pp.; Pub P Abstract: FORCe Kick-off meeting presentation, Seatle, WA, April 26-27, Optimal Preventive Maintenance Policies for Unreliable Queueing/Production Systems with Applications to Semiconductor Manufacturing Fabs; Xiaodong Yao, X. Xie, M. Fu, S. Marcus and E. Fernandez-Gaucherand; Univ. of Maryland; 8-Sep-2003; 13pp.; Pub P Abstract: The reliability of equipment is critical to fab's operational performance, and Preventive Maintenance (PM) scheduling is a very challenging task in semiconductor manufacturing. In this paper, the researchers will study optimal PM policies under the context of unreliable queueing systems. Presented at TECHON 2003 (Awarded as "Best Paper in Session").

34 SRC/ISMT Factory Operations Research Center Deliverables Documentation submitted and currently available at SRC website Other documentation Software Description: Preventive Maintenance Optimal Scheduling Tool (PMOST); SMITLab University of Cincinnati; Univ. of Maryland; 30-Jun-2003; 2pp.; Pub P Abstract: The Preventive Maintenance Optimal Scheduling Tool (PMOST) is a (C-language) software tool for optimal scheduling of Preventive Maintenance tasks in Semiconductor Fabs. PMOST accepts a set of parameters related to the PM optimization process, e.g. planning horizon, number of resources for the PM tasks, cost coefficient related to the PM tasks, etc.. PMOST obtains an optimal solution for that problem via the use of mathematical programming solvers for Linear Programming/Mixed Integer Programming problems. The PMOST system was designed to work with different types of mathematical programming solvers, such as IBM OSL and CPLEX. The system requires a set of data files, defined under specific (standard) formats, used in the optimization process. Thesis-MS: Optimal Preventive Maintenance Scheduling in Semiconductor Fabs; J. Crabtree; Univ. of Cincinnati; 10-Oct-2003; 84pp.; Pub P Abstract: This thesis is spawned from the research project, "Preventive Maintenance in Semiconductor Fabs", sponsored by the Semiconductor Research Corporation (SRC) and International SEMATECH. The project proposes a two-level hierarchical optimization structure that considers important factors such as the work-in-progress (WIP) at a tool and the complex relationships between the chambers of a cluster tool. This thesis focuses on the lower level of the aforementioned hierarchy that deals with PM scheduling. It expands on the work accomplished thus far in the project, specifically analyzing and fixing current issues with the PM scheduling algorithm and creating a software implementation of the scheduling algorithm.

35 SRC/ISMT Factory Operations Research Center Deliverables: Other Documentation

36 SRC/ISMT Factory Operations Research Center Other Documentation (not posted yet at SRC web site) Papers Optimal Preventive Maintenance Scheduling in Semiconductor Manufacturing, X. Yao; E. Fernandez-Gaucherand; M.C. Fu; S.I. Marcus; submitted for publication to IEEE Transactions on Semiconductor Manufacturing, An Algorithm to Convert Wafer to Calendar-Based Preventive Maintenance Schedules for Semiconductor Manufacturing Systems, J.A. Ramírez-Hernández and E. Fernández-Gaucherand., to appear in Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, HI, December, Optimal PM Scheduling in Semiconductor Manufacturing Systems: Case Studies, Univ. Cincinnati, Univ. Maryland, AMD, Intel. In preparation. Survey of Best Practices of PM Scheduling in Semiconductor Manufacturing Systems, J.A. Ramírez, J. Crabtree, E. Fernandez, X. Yao, M. Fu and S.I. Marcus. In preparation. Optimal Joint Preventive Maintenance and Production Control Policies for Unreliable Production Systems, X. Yao, X. Xie, M. Fu, and S. Marcus. In preparation. Presentations Suppliers Teleconference Presentation: Commercialization, M. Fu, E. Fernandez, S.I. Marcus, J. Crabtree, J.A. Ramírez, X. Yao, September 4 th,, 2003, SEMATECH Webex teleconference system. Deliverables

37 SRC/ISMT Factory Operations Research Center Software Implementation: PMOST

38 SRC/ISMT Factory Operations Research Center Software Implementation: PMOST Software implementation of models and algorithms is an objective that has been accomplished with the design and coding of the software Preventive Maintenance Optimal Scheduling Tool (PMOST). The following are the versions produced up to this point: PMOST ver. 1.0: first version of PMOST coded in C-language, running over MS- Windows platforms (Windows 2000 and up). Include a basic text-mode user interface, link with Optimization Library Solutions (OSL) solver from IBM, and generates Mathematical Programming System (MPS) files describing the MIP problem. PMOST ver. 1.1: includes same characteristics of version 1.0 plus the conversion algorithm for wafer-based to calendar-based PM schedules. An installer for MS-Windows is included in this version. PMOST ver. 1.2: first Graphical User Interface (GUI) for PMOST, includes all characteristics of verions 1.0 and 1.1. MS-Windows platform (Windows 2000 and up).

SRC/ISMT Factory Operations Research Center 39 pmost_ui.exe PMOST Block Diagram Software Implementation: PMOST

40 SRC/ISMT Factory Operations Research Center PMOST 1.2 with GUI, Demo Movie Software Implementation: PMOST

41 SRC/ISMT Factory Operations Research Center PMOST 1.1 with text-mode user interface, screen captions The input data used for this exercise was artificially created for illustration purposes only. The user executes the file pmost.exe and the following prompt will be shown: Software Implementation: PMOST

42 SRC/ISMT Factory Operations Research Center PMOST 1.1 with text-mode user interface, screen captions After that, the user will define the “Start Date” and “End Date” in the format requested in the following screenshot: Software Implementation: PMOST

43 SRC/ISMT Factory Operations Research Center PMOST 1.1 with text-mode user interface, screen captions Finally, PMOST will ask for the number of technicians assigned to each period in the planning horizon defined by the “Start Date” and the “End Date”, as follows: Software Implementation: PMOST

44 SRC/ISMT Factory Operations Research Center PMOST 1.1 with text-mode user interface, screen captions PMOST will then produce the MPS file, and finally it will communicate this MPS to the solver selected. The solver will compute the optimal solution that will be decoded by PMOST and written in the output_files directory. The messages presented by PMOST are as follows: Software Implementation: PMOST

45 SRC/ISMT Factory Operations Research Center For this example in particular, the pm_solution.txt file will looks as follows: Tool Name PM Name Old Due Date Optimal Due Date CT01 7 DAY PM 01/06/ :00:00 01/05/ :00:00 CT02 14 DAY PM 01/05/ :00:00 01/06/ :00:00 CT03 28 DAY PM 01/04/ :00:00 01/02/ :00:00 CT04 56 DAY PM 01/03/ :00:00 01/03/ :00:00 CT04 PMCH1 01/01/ :00:00 01/03/ :00:00 CT05 PMCH4 01/02/ :00:00 01/03/ :00:00 CT06 PMCH5 01/03/ :00:00 01/06/ :00:00 CT07 PMCH2 01/04/ :00:00 01/06/ :00:00 CT08 PMCH3 01/02/ :00:00 01/04/ :00:00 CT09 KIT CH2 01/05/ :00:00 01/05/ :00:00 CT10 KIT CH3 01/01/ :00:00 01/01/ :00:00 CT02 7 DAY PM 01/02/ :00:00 01/01/ :00:00 CT04 14 DAY PM 01/03/ :00:00 01/03/ :00:00 CT01 28 DAY PM 01/04/ :00:00 01/05/ :00:00 CT05 56 DAY PM 01/01/ :00:00 01/03/ :00:00 CT01 PMCH1 01/05/ :00:00 01/05/ :00:00 CT10 PMCH4 01/01/ :00:00 01/01/ :00:00 CT04 PMCH5 01/02/ :00:00 01/03/ :00:00 CT06 PMCH2 01/05/ :00:00 01/06/ :00:00 CT05 PMCH3 01/03/ :00:00 01/03/ :00:00 CT03 KIT CH2 01/02/ :00:00 01/02/ :00:00 CT09 KIT CH3 01/01/ :00:00 01/01/ :00:00 PMOST 1.1 with text-mode user interface, screen captions Software Implementation: PMOST

46 SRC/ISMT Factory Operations Research Center Also, a pm_order.txt file can be generated for use it in AutoSched AP simulations as PM orders: PMORDER STNDUEDATE PTIME PTUNITS order1CT0101/05/ :00: hr order2CT0201/06/ :00: hr order3CT0301/02/ :00: hr order4CT0401/03/ :00: hr order5CT0401/03/ :00: hr order6CT0501/03/ :00: hr order7CT0601/06/ :00: hr order8CT0701/06/ :00: hr order9CT0801/04/ :00: hr order10CT0901/05/ :00: hr order11CT1001/01/ :00: hr order12CT0201/01/ :00: hr order13CT0401/03/ :00: hr order14CT0101/05/ :00: hr order15CT0101/05/ :00: hr order17CT1001/01/ :00: hr order18CT0401/03/ :00: hr order19CT0601/06/ :00: hr order20CT0501/03/ :00: hr order21CT0301/02/ :00: hr order22CT0901/01/ :00: hr PMOST 1.1 with text-mode user interface, screen captions Software Implementation: PMOST

47 SRC/ISMT Factory Operations Research Center Integration with Fab Schedulers: Collaboration with ASU

48 SRC/ISMT Factory Operations Research Center Collaboration is under way with the ASU Team with the objective of integrating fab scheduling and optimal PM scheduling in semiconductor fabs. –The goal is integrate both fab scheduling and preventive maintenance to evaluate long-term performances in semiconductor manufacturing systems via simulation analysis. –The research teams have identified the requirements for such integration as well as proposed a work plan to complete the task. –Currently, both teams are working to close the gap in the software implementation and start experiments using simple models (e.g., minifab) for proof of concept. –Integration involves communication between simulation software (customization of ASAP) and the corresponding schedulers (jobs and PMs). Integration of Fab Schedulers: Collaboration with ASU

49 SRC/ISMT Factory Operations Research Center Students Trained

50 SRC/ISMT Factory Operations Research Center Students Trained The following students have participated in the research tasks for this project, and have received substantial training in different topics (e.g., ASAP training, courses in stochastic modeling and decision, simulation analysis and modeling): –Ph.D. Students: Ying He, Maryland (Ph.D. completed, graduated on summer 2002) Jiaqiao Hu, Maryland (3 rd year Ph.D.) José Ramírez, Cincinnati (3 rd year Ph.D.) Xiaodong Yao, Maryland (Ph.D., will graduate in December 2003) –M.Sc. Students: Jason Crabtree, Cincinnati (M.Sc. completed, graduated September 2003) Sumita Jagannathan, Cincinnati (continuing M.Sc.)

51 SRC/ISMT Factory Operations Research Center (Students) 3. Summary of Doctoral and Master Theses

52 SRC/ISMT Factory Operations Research Center Summary of Doctoral and Master Theses M.Sc. Thesis on Electrical & Computer Engineering & Computer Science Title: Optimal Preventive Maintenance Scheduling in Semiconductor Fabs Author: Jason Crabtree, SMITLab, University of Cincinnati. Defense/submission date: August 4 th Abstract: This thesis is spawned from the research project, "Preventive Maintenance in Semiconductor Fabs", sponsored by the Semiconductor Research Corporation (SRC) and International SEMATECH. The project proposes a two-level hierarchical optimization structure that considers important factors such as the work-in-progress (WIP) at a tool and the complex relationships between the chambers of a cluster tool. This thesis focuses on the lower level of the aforementioned hierarchy that deals with PM scheduling. It expands on the work accomplished thus far in the project, specifically analyzing and fixing current issues with the PM scheduling algorithm and creating a software implementation of the scheduling algorithm. (See SRC Publication P007381)

53 SRC/ISMT Factory Operations Research Center Research Proposal Ph.D. on Electrical & Computer Engineering & Computer Science Title: Reinforcement Learning (Neuro-Dynamic Programming) Approach for Production Control of Semiconductor Manufacturing Re-Entrant Lines Author: José A. Ramírez, SMITLab, University of Cincinnati. Defense/submission date: proposal to be defended in December Description: Semiconductor fabs are complex systems characterized by re-entrant lines in the manufacturing process. The scheduling of jobs (control) in this type of systems is a challenging task. Finding optimal scheduling policies, via analytical procedures, is a difficult problem. Generally, it is intractable given the complexity and high dimensionality of such systems. We propose the use of a novel approach in control of high-dimensional and complex systems: Reinforcement Learning (Neuro-Dynamic Programming). Summary of Doctoral and Master Theses

54 SRC/ISMT Factory Operations Research Center Research Proposal Ph.D. on Electrical & Computer Engineering & Computer Science Jose A. Ramírez – SMITLab – University of Cincinnati Description (cont.): Reinforcement Learning (RL) (Neuro-Dynamic Programming (NDP)) has been successfully used to find suboptimal (near to the optimal) policies in complex systems, where the curse of dimensionality is presented as a serious constraint to apply Dynamic Programming approaches for optimization and control. RL and NDP are new and very promissory approaches for a wide spectrum of applications. RL and NDP methods are based in learning from the interaction with the system of interest (e.g., learn an (sub) optimal scheduling policy) or its corresponding model (simulation). From this interaction we maximize the long-term returns (performance index) given the actions (control) applied to the system, and derived from the learning process. Semiconductor manufacturing systems have the essential characteristics to apply these type of approaches: simulation models are available, but analytical modeling is too complex in large scale systems and stochastic events are present (e.g., tool failures, tool maintenance). Summary of Doctoral and Master Theses

55 SRC/ISMT Factory Operations Research Center Xiaodong Yao, Ph.D. Student, University of Maryland, Optimal Joint Preventive Maintenance and Production Control Policies for Unreliable Production Systems Summary of Doctoral and Master Theses

SRC/ISMT Factory Operations Research Center 56 Overview 1.In literature preventive maintenance (PM) and production control have been treated independently. 2.Recent work Boukas and Liu (2001) (continuous flow model) Iravani and Duenyas (2002) (propose and analyze a heuristic policy of “double-threshold” policy) Sloan and Shanthikumar (2002, 2000) (integrated production dispatching and maintenance scheduling in semiconductor manufacturing) 3.Our objective characterization of optimal joint policies for unreliable production systems with either time-dependent failures operation-dependent failures

SRC/ISMT Factory Operations Research Center 57 Systems with time-dependent failures The machine experiences time-dependent failures: Machine deteriorates over calendar time, and can fail while idle. (e.g., calendar-based PMs) flexible production rate, u  [0,P], P is the maximal production rate inventory consumed by a constant demand d, and backlog allowed Upon machine failures, repair has to be initiated with cost c r, and time for repair  r is a r.v. Before machine failures, PM can be applied with cost c p, and time for PM  p is a r.v. as well. inventory holding cost g(·), piecewise linear function of inventory level Objective: find PM / production policy to minimize discounted cost d, constant demand u  [0,P]

SRC/ISMT Factory Operations Research Center 58 Markov-Decision Process Formulation Consider the discrete-time model:

SRC/ISMT Factory Operations Research Center 59 Bellman Equations The optimal cost functions satisfy:

SRC/ISMT Factory Operations Research Center 60 Characterization of optimal policy Theorem 1: J(s,0,n), J(s,1,n), J(s,2,n) are decreasing function in s, for s  0. Remark: This implies that when there is backlog, if choose not to do PM, then optimal production rate is at least as large as demand rate. Theorem 2: J(s,1,n) is an increasing function in n, if the following conditions are satisfied: (1) the machine has IFR; (2) c r  c p ; (3) times for repair and PM are stochastically equivalent or machine failure rate is constant. Corollary: For fixed inventory level, the optimal joint policy has control-limit form w.r.t. machine age. Theorem 3: There exists s* such that  s > s*,  *(s,1,n) = 0 or PM, for all n. Remark: This is an intuitive observation, such that at high inventory level, it’s not optimal to produce.

SRC/ISMT Factory Operations Research Center 61 Numerical Study Fig. 1: the optimal policy Fig. 2 Example: the machine lifetime ~ Weibull (4,5), time for PM ~ U(0,3), time for CM ~ U(0,6), d = 1, P =3, c p = 50, c r = 2 * c p, c + = 1, c - = 10,  = Fig. 2: The relative difference of cost function under the joint optimal policy and independently optimized policy. diff = (J ind – J*)/J*  100%.

SRC/ISMT Factory Operations Research Center 62 Operation-Dependent Failures 1, with prob. q u  {0,1} Operation-dependent failures: Machine deteriorates only when it is producing, and can’t fail while idle. (e.g., wafer-count-based or operation-history based PMs) Random demand: unit demand in each period with prob. q Machine can produce at rate either 0 or 1, u  {0,1} Upon machine failures, repair has to be initiated with cost c r, and time for repair  r is a r.v. Before machine failures, PM can be applied with cost c p, and time for PM  p is a r.v. as well. inventory holding cost g(·), piecewise linear function of inventory level Objective: find PM / production policy to minimize discounted cost

SRC/ISMT Factory Operations Research Center 63 Bellman Equations The optimal cost functions satisfy:

SRC/ISMT Factory Operations Research Center 64 Theorem 4: J(s,1,n) is an increasing function in n, if the following conditions are satisfied: (1) the machine has IFR; (2) c r  c p ; (3)  r  st.  p. Corollary: For fixed inventory level, the optimal joint policy has control-limit form w.r.t. machine age. Theorem 5: There exists s* such that  s > s*,  *(s,1,n) = 0, for all n. Characterization of optimal policy

SRC/ISMT Factory Operations Research Center 65 Numerical Example Example: the machine lifetime ~ Weibull (4,5), time for PM ~ U(0,3), time for CM ~ U(0,6), q = 0.8, c p = 50, c r = 2 * c p, c + = 1, c - = 10,  = Fig. 3: the optimal policy

SRC/ISMT Factory Operations Research Center 66 Conclusions The big picture: Hierarchical Framework for PM planning and scheduling. High Level:  objective: to derive optimal PM policies  methodology: Markov-decision processes Low Level:  objective: to obtain optimal PM schedules  methodology: Mathematical programming

67 SRC/ISMT Factory Operations Research Center 4. Continuing and Future Research

68 SRC/ISMT Factory Operations Research Center Continuing and Future Research Finishing and submission of papers for publication Optimal PM Scheduling in Semiconductor Manufacturing Systems: Case Studies, J. A. Ramírez, J. Crabtree, E. Fernandez, M. Fu, X. Yao, S.I. Marcus, Advanced Micro Devices, Corp., Intel, Corp., in preparation. Survey of Best Practices of PM Scheduling in Semiconductor Manufacturing Industry, J.A. Ramírez, J. Crabtree, E. Fernandez, X. Yao, M. Fu and S.I. Marcus, to be submitted for publication. Optimal Joint Preventive Maintenance and Production Control Policies for Unreliable Production Systems, X. Yao, X. Xie, M. Fu, and S. Marcus, in preparation. Conversion of Wafer-Based PM Schedules into Calendar-Based for Optimal PM Scheduling in Semiconductor Manufacturing, J.A. Ramírez, E. Fernandez, in preparation.

69 SRC/ISMT Factory Operations Research Center Continuing and Future Research Commercialization Continue working with suppliers… Collaboration with other research groups Continue task for integration of job and PM scheduling algorithms in a pilot study with ASU Team. Analysis of simulations from integration of fab and PM scheduling algorithms. Other Xiaodong Yao, Ph.D. Dissertation defense and submission. No cost extension through August 2004.

70 SRC/ISMT Factory Operations Research Center 5. Conclusions

71 SRC/ISMT Factory Operations Research Center Conclusions