1 SRC/ISMT Factory Operations Research Center SRC/ISMT FORCe: Factory Operations Research Center...

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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. 21-22, 2003

Intelligent Preventive Maintenance Scheduling in Semiconductor

Manufacturing Fabs

SRC/ISMT Factory Operations Research Center2

1. Project Overview: Michael Fu

2. Summary 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)• Integration with fab schedulers: collaboration with ASU• Students trained

3. Summary of Doctoral and Master Theses: Students

4. Continuing and Future Research: Emmanuel Fernandez

5. Conclusions: Michael Fu

CONTENTS

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Michael FuRobert H. Smith School of Business &

Institute for Systems ResearchUniversity of Maryland

1. Project Overview

Summary


(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)


• Deliverables (reports) completed: January and July 2002; SRC Pub P005269, P006317

• 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


• software tool (PMOST):– Generic Scheduling Simulation Engine– Generic Implementation of PM Scheduling Algorithm

• summer internships (AMD & Intel)

• Ph.D. dissertations supported: He, Yao, Hu, RamirezMS dissertations supported: Crabtree, Jagannathan

• commercialization feasibility discussions: Adexa, Ibex Processes.

• NIST internship via Swee Leong

Executive Summary


• 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


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


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)


1. 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)

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Emmanuel Fernandez, Ph.D.ECECS Department

University of Cincinnati

2. Summary of Completed Tasks

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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)

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Interactions with Industry

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Interaction with Industry

• 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.

• Interactions have taken place in the form of:• Summer internships for our students from 2000 through 2002.

• Direct collaboration to exchange ideas and formulate problems and solutions, e.g:

• Survey on best practices of PM scheduling;

• Visits to fabs to interview and obtain feedback from tool managers and operators.

• Periodic teleconferences with MC liaisons.

•Co-authored publications derived from the research work.

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Interaction with Industry

•Summer InternshipsDuring 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, 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.A. Ramírez, 2002, AMD, Austin, TX: data collection and modeling for wafer to calendar-based conversion of PM schedules, and two simulation studies.

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Deliverables:Models, Algorithms, and

Software Tools

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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.

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Deliverables

Models and AlgorithmsHierarchical Model for Optimal PM scheduling

Upper MDP

Lower MIP

WIP

PM Schedule

PM Policy

Objective

Constraints

Demand Pattern

Failure Dynamics

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Models and Algorithms - MIP Formulation

Objective:

N

t

M

i

li

i

lii

liii

tataCtICtVb

i

1 1 1)(

)()()(max

Deliverables

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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

lin

t

li ta

0)(1

lim

t

li ta

1)(1

N

t

li ta

lin

lim

Deliverables

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Constraints:

(iv)

where is the set of PM decisions across all PM tasks, and is a dummy variable holding the value of from the previous period,

i.e.

tittaftViii ,))(),(()(

)(ta i

)(ti

)()1( tat ii

)(ta i

Deliverables

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Constraints:

(v)

where di(t ) is amount of incoming wafers at tool i in period t, and Xi(t ) is the quantity of wafers processed on tool i in period t.

(vi)

where Ki is the wafer throughput coefficient for tool i.

1,...,1,)()()()1( NtitdtXtItI iiii

titVKtX iii ,)()(

Deliverables

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Constraints:

(vii)

where Li is the maximum allowed inventory at tool i.

(viii)

where is the resource requirement variable for resource k in period t.

tiLtI ii ,)(

tkttagtriik ,))(),(()(

)(trk

Deliverables

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Constraints:

(ix)

where Rk(t) is the amount of resource k available in period t.

(x) , , ,

(xi)

tktRtr kk ,)()(

0)( tVi 0)( tI i 0)( tX i 0)( tr ki tik ,,

tliorta li ,, 10)(

Deliverables

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Models and Algorithms Conversion of Wafer to Calendar-based PM Schedules

ot Wt Dt Lt

ijlW ij

lD

. . . 1t

ijtC1

ijtC2

ijtC2

2t 3t

ijtD

C

D

t

ijtD

C1

1D

t

ijlD

. . .

. . . . . .

. . . ijlL

ijtC0

ijt

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ijt

ijt

ijt

ijtij

ijt

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ijt

ijt

ijtij

ijtij

t

kkkkk

kkkkkk

k ifrC

ifrCC

1

11

1

ijijr

ijlDD r

Dtt

1

. tool,chamber in rate Throughput: ijrij

. tool,chamber ),(estimated produced wafersofamount Cumulative: ijC ijtk

. tool,chamber PM,for wafersofamount Due: ijD ijl

. tool,chamber at capacity Maximum: ijijtk

Estimated due time (date)

. period , tool,chamber at WIPincomming Estimated: kijt tijk

Deliverables

PM window (W: warning, D: due, L: late)

(Time period)

(Wafer counts/period)

. tool,chamber at proportion rate Throughput: ijijr

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Deliverables:Simulation Case Studies


• 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 CaseStudies


• 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.




• 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.

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Deliverables:Documentation Submitted to

SRC Website

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Deliverables

Documentation submitted and currently available at SRC websiteThe 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 P003262.

•Intelligent Preventive Maintenance Scheduling in Semiconductor Manufacturing Fabs; Tempe, AZ, April 9-10, 2002, Pub P007441.

•Intelligent Preventive Maintenance Scheduling in Semiconductor Manufacturing Fabs; San Jose, CA, November 20-21, 2002, Pub P005082.

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 P003461. 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 2001.

•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 P004304.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.

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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 P005269.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 P006317.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 P004306.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 P003267.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, 2001. •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 P004305.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.

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Deliverables


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 P006072.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 P004145.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 P005903.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 P002234.Abstract: FORCe Kick-off meeting presentation, Seatle, WA, April 26-27, 2001.

•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 P006866.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").

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Deliverables


Other documentationSoftware Description: Preventive Maintenance Optimal Scheduling Tool (PMOST); SMITLab University of Cincinnati; Univ. of Maryland; 30-Jun-2003; 2pp.; Pub P006313.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 P007381.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.

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Deliverables:Other Documentation

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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, 2003.

•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, 2003.

•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 4th,, 2003, SEMATECH Webex teleconference system.

Deliverables

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Software Implementation: PMOST

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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).


pmost_ui.exe

START User Interface main.c

Read Input Data

-Tool/PM data files: *.fam, *.data -Conversion to calendar-time PMs data files -PM schedule: files *.sch -Estimated WIP data files: files *.wip -Debugging file: debug.txt -Converted Schedule File: *.csch

Write MPS file

LP/MIP SOLVER

main.c calls the solver (OSL, CPLEX, etc)

Parse Solution

-Output data: *.set, *.val files -MPS file: *.mps

.mps file

ASAP write_sch_file.c

Output: pm_order.txt

-Planning horizon -Tools family -Number of Technicians

solution file (text file)

pm_solution.txt

create_pm_vectors.c write_set_val_files.c write_mps_file.c write_debug_file.c

parse_osl_solution.c parse_cplexl_solution.c write_solution_file.c write_pm_order_file.c

read_data_file.c read_fam_file.c read_sch_file.c read_wip_file.c

pmost.exe

utils.c General functions used in different parts of the system.

conv2cal (.exe, .c, .h)

Conversion to calendar-time PMs

PMOST Block Diagram


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PMOST 1.2 with GUI, Demo Movie


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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:


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•After that, the user will define the “Start Date” and “End Date” in the format requested in the following screenshot:


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•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:


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•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:


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•For this example in particular, the pm_solution.txt file will looks as follows:

Tool Name PM Name Old Due Date Optimal Due DateCT01 7 DAY PM 01/06/2002 07:00:00 01/05/2002 07:00:00 CT02 14 DAY PM 01/05/2002 07:00:00 01/06/2002 07:00:00 CT03 28 DAY PM 01/04/2002 07:00:00 01/02/2002 07:00:00 CT04 56 DAY PM 01/03/2002 07:00:00 01/03/2002 07:00:00 CT04 PMCH1 01/01/2002 07:00:00 01/03/2002 07:00:00 CT05 PMCH4 01/02/2002 07:00:00 01/03/2002 07:00:00 CT06 PMCH5 01/03/2002 07:00:00 01/06/2002 07:00:00 CT07 PMCH2 01/04/2002 07:00:00 01/06/2002 07:00:00 CT08 PMCH3 01/02/2002 07:00:00 01/04/2002 07:00:00 CT09 KIT CH2 01/05/2002 07:00:00 01/05/2002 07:00:00 CT10 KIT CH3 01/01/2002 07:00:00 01/01/2002 07:00:00 CT02 7 DAY PM 01/02/2002 07:00:00 01/01/2002 07:00:00 CT04 14 DAY PM 01/03/2002 07:00:00 01/03/2002 07:00:00 CT01 28 DAY PM 01/04/2002 07:00:00 01/05/2002 07:00:00 CT05 56 DAY PM 01/01/2002 07:00:00 01/03/2002 07:00:00 CT01 PMCH1 01/05/2002 07:00:00 01/05/2002 07:00:00 CT10 PMCH4 01/01/2002 07:00:00 01/01/2002 07:00:00 CT04 PMCH5 01/02/2002 07:00:00 01/03/2002 07:00:00 CT06 PMCH2 01/05/2002 07:00:00 01/06/2002 07:00:00 CT05 PMCH3 01/03/2002 07:00:00 01/03/2002 07:00:00 CT03 KIT CH2 01/02/2002 07:00:00 01/02/2002 07:00:00 CT09 KIT CH3 01/01/2002 07:00:00 01/01/2002 07:00:00



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•Also, a pm_order.txt file can be generated for use it in AutoSched AP simulations as PM orders:

PMORDER STN DUEDATE PTIME PTUNITSorder1 CT01 01/05/2002 07:00:00 8.000000 hrorder2 CT02 01/06/2002 07:00:00 12.000000 hrorder3 CT03 01/02/2002 07:00:00 55.000000 hrorder4 CT04 01/03/2002 07:00:00 55.000000 hrorder5 CT04 01/03/2002 07:00:00 48.000000 hrorder6 CT05 01/03/2002 07:00:00 5.000000 hrorder7 CT06 01/06/2002 07:00:00 5.000000 hrorder8 CT07 01/06/2002 07:00:00 50.000000 hrorder9 CT08 01/04/2002 07:00:00 50.000000 hrorder10 CT09 01/05/2002 07:00:00 24.000000 hrorder11 CT10 01/01/2002 07:00:00 24.000000 hrorder12 CT02 01/01/2002 07:00:00 8.000000 hrorder13 CT04 01/03/2002 07:00:00 12.000000 hrorder14 CT01 01/05/2002 07:00:00 55.000000 hrorder15 CT01 01/05/2002 07:00:00 48.000000 hrorder17 CT10 01/01/2002 07:00:00 5.000000 hrorder18 CT04 01/03/2002 07:00:00 5.000000 hrorder19 CT06 01/06/2002 07:00:00 50.000000 hrorder20 CT05 01/03/2002 07:00:00 50.000000 hrorder21 CT03 01/02/2002 07:00:00 24.000000 hrorder22 CT09 01/01/2002 07:00:00 24.000000 hr



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Integration with Fab Schedulers: Collaboration with

ASU

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•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

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Students Trained

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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 (3rd year Ph.D.)

• José Ramírez, Cincinnati (3rd 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.)

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(Students)

3. Summary of Doctoral and Master Theses

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Summary of Doctoraland 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 4th 2003.

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


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 2003.

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).


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Research Proposal Ph.D. on Electrical & Computer Engineering & Computer ScienceJose 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).


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Xiaodong Yao, Ph.D. Student, University of Maryland,

Optimal Joint Preventive Maintenance and Production Control Policies for

Unreliable Production Systems



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


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 cr, and time

for repair r is a r.v.

• Before machine failures, PM can be applied with cost cp, 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]


Markov-Decision Process Formulation

.1 i.e., state, in working machine while,produce to:,0

PM do to: control

state machine of changelast thesince periods time repairin machine if :0

state in working machine if :1PMin machine if :2

levelinventory where,, state

tt

t

t

tttt

iPu

PMu

in

i

snis

.,01Pr

,,21Pr

,,10Pr :iesprobabilit lconditiona

1

1

1

nniir

nniip

nniif

tttn

tttn

tttn

Consider the discrete-time model:


Bellman Equations

.1,1,1

0,0,,1,

,0,2,,1, where

,,1,min;,1,min,1,

:state in working machine when

,1,2,10,1,,2,

:PMin machine when

,1,0,10,1,,0,

:repairin machine when

,,0

ndusJf

dusJcfsgnsQ

sJcnsQ

nsQnsQnsJ

ndsJpdsJpsgnsJ

ndsJrdsJrsgnsJ

n

rnu

pPM

u

Pu

PM

nn

nn

The optimal cost functions satisfy:


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) cr cp; (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.


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, cp = 50, cr = 2 * cp,c+ = 1, c- = 10, = 0.95.

Fig. 2: The relative difference of cost function under the joint optimal policy and independently optimized policy. diff = (Jind – J*)/J* 100%.


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 cr, and time

for repair r is a r.v.

• Before machine failures, PM can be applied with cost cp, 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


Bellman Equations

1,1,1110,0,1)1(

1,1,10,0,)(),1,(

,),1,()1(),1,1(,1,

,0,2,,1, where

,,1,;,1,;,1,min,1,

:state in working machine when

,1,2,110,1,)1(

1,2,110,1,1,2,

:PMin machine when

,1,0,110,1,)1(

1,0,110,1,1,0,

:repairin machine when

1

0

10

nsJfqsJcfq

nsJfqsJcfqsgnsQ

nsJqnsJqsgnsQ

sJcnsQ

nsQnsQnsQnsJ

nsJpqsJpq

nsJpqsJpqsgnsJ

nsJrqsJrq

nsJrqsJrqsgnsJ

nrn

nrn

pPM

PM

nn

nn

nn

nn

The optimal cost functions satisfy:


Theorem 4: J(s,1,n) is an increasing function in n, if the following conditions are satisfied:

(1) the machine has IFR; (2) cr cp;

(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


Numerical Example

Example: the machine lifetime ~ Weibull (4,5),time for PM ~ U(0,3),time for CM ~ U(0,6),q = 0.8, cp = 50, cr = 2 * cp,c+ = 1, c- = 10, = 0.95.

Fig. 3: the optimal policy


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

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4. Continuing and Future Research

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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.

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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.

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5. Conclusions

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Conclusions

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