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The Systems Modeling &
Information Technology
Laboratory
1 Intelligent Preventive Maintenance SchedulingIn Semiconductor Manufacturing Fabs
Preventive Maintenance in Semiconductor Manufacturing Fabs
SRC Task NJ-877
FORCe Kick-Off MeetingSeattle
April 26-27, 2001
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Research Plan
(1) Develop, test, and transfer software tools for optimal
PM 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.
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OVERVIEW
• Research Team
• Proposed Research
• Deliverables
•Preview: “Best Practices” Survey in PM
• Methodology Basis: TECHCON 2000 Paper.
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Research Team
• Institute for Systems Research, University of Maryland
Prof. Michael Fu (Project Director)Prof. Steven I. Marcus
Xiaodong Yao (Ph.D. Student) (1 more Ph.D. in Fall)
• Electrical & Computer Eng. & Comp. Sci., Systems Modeling & Information Technology Laboratory University of Cincinnati
Prof. Emmanuel FernandezJason Crabtree (M.Sc. Student)(1-2 new students beginning in September)
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ISR
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Background of Researchers of ISR
Michael Fu Robert H. Smith School of Business Operations Research; Stochastic Modeling; Simulation Methodology (Simulation Area Editor, OR; AE Sim/Stoch Models, Mgmt Sci; Special Issue Editor, TOMACS)
Steven Marcus Dept. of Elect. and Comp. Eng. Stochastic Control; Markov Decision Process; Risk-Sensitive Control. IEEE Fellow. Past director ISR, (interim) Chair ECE Dept. (Editor, SIAM J. Control and Optimization)
Xiaodong Yao Dept. of Elect. and Comp. Eng. Markov Decision Process; Operation Research; System Reliability
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Liaisons
Ramesh Rao, National SemiconductorTAB: Mohammed IbrahimMarcellus Rainey, TITAB: Kishore PottiYin-Tat Leung, IBMTAB: Sarah HoodMan-Yi Tseng (Matilda O’Connor), AMDTAB: Edwin CervantesMadhav Rangaswami, Intel
conference calls with three already (multiple times with AMD)
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OBJECTIVES:
Conduct basic & applied research in modeling,
algorithms and information technology (IT)
implementation for (stochastic) systems and
processes. To serve as a consulting lab in IT for
interdisciplinary projects, e.g., manufacturing,
operational planning, distance education.
APPLICATION AREAS:
Manufacturing & operations management; Security and fault-management in
telecommunication networks; Logistics; Workforce Management; IT learning tools.
SMIT Lab
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Background of Researchers At University of Cincinnati
Emmanuel Fernandez ECECS Dept. (SIE/UA ’91-00) Stochastic Models; Stochastic Decision &
Control Process; Manufacturing, Logistics& Telecommunications Applications; Information Technology. Senior Member IEEE & IIE
Jason Crabtree ECECS Dept., Stochastic Models;Operation Research; Computer Implementation ofAlgorithms. Bach. Mech. & Industrial Eng., Univ.of Cincinnati 2000.
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Research Plan
(1) Develop, test, and transfer software tools for optimal
PM 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.
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Motivation
• The reliability of equipment is critical to fab’s operational
performance;
• Industry calls for analytical models to guide PM practice;
• In academia, the problems of maintenance and production
have been addressed in isolation until very recently;
• Traditional models ignore the impact of other system state
variables (e.g. WIP level, operational status of up-stream or
down-stream tools) on PM scheduling.
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Research Approach
The generic form of the problem of interest:
,min
,CE
Where: • μ is a PM policy;• π is a production policy;• E[C] represents the expected total costs.
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Proposed Framework
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Markov Decision Process Model
Components:• the system state, which includes information such as tool “age”
since last PM, and WIP level at each tool; • the admissible actions in each state; • the cost structure, e.g., costs for “planned” downtime, costs
for “unplanned” downtime, and costs for WIP; • the objective function, which includes weighted profits along
with the cost structure; • sources of uncertainty, e.g., “out of control” events,
tools failure processes, future demand and incoming WIP.
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Distinctions of Proposed Model
• Integration of production control information, e.g.
current WIP levels and anticipated demand;
• description of inter-dependence of different PMs
within a single tool and between tool sets;
• modeling of “out of control” events such as process
drifts, in addition to the failure process of tools.
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Deliverables to Industry
1. Survey of current PM practices in industry (Report) (P:30-SEP-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: Software package with documentation, and report with case studies and benchmark data (Software, Report) (P:30-SEP-2002)
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4. Intelligent PM 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)
Deliverables (Continued)
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SURVEY: PM Best Practices
•Previous NSF/SRC project: Integrating Product Dynamicsand Process Models (IPDPM), ’97-2000
•Interaction with industry (AMD) in 1999-2000
•PM identified as a high priority area
•Faculty visits to industry during 2000: data collection, problem definition
•Summer internship 2000: model validation and simulation
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SURVEY: PM Best Practices
•Finding 1: “Torrents of Data” flowing through the Fabdatabases, mostly unused for modeling and decision making
•Finding 2: PM scheduling focuses on key bottleneck tools, e.g., cluster tools for metal deposition
•Finding 3: PM schedule wafer-count or calendar based
•Finding 4: Each tool group manager has total control of PM scheduling: heuristics usually employed
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SURVEY: PM Best Practices
•Finding 5: Availability of parts can be a problem
•Finding 6: Workforce coordination needed (PM tasks can extend over several shifts)
•Finding 7: Consolidation of maintenance tasks critical:different PMs, or PMs with unscheduled maintenance
•Finding 8: No previous PM Best Practices Survey available
•Finding 9: Need for stochastic PM models in semiconductor manufacturing; little relevant literature available
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Incorporating Production Planning into Preventive Maintenance Scheduling in
Semiconductor Fabs
(TECHCON 2000)
Methodology Basis
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• Academia Research Group Xiaodong Yao (Ph.D. Student) Dr. M. Fu, Dr. S.I. Marcus, Dr. E. Fernandez
• Industry Collaborators: AMD Craig Christian, Javad Ahmadi, Mike Hillis, Nipa Patel (now at Dell), Shekar Krishnaswamy (now at Motorola), Bill Brennan
CollaborationCollaboration
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Overview
1. Problem Context
2. Hierarchical Modeling Approach
3. Markov Decision Process (MDP) Model
4. Linear Programming (LP) Model
5. Case Study
6. Future Development and Implementation
7. Acknowledgements
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Problem Context
Focused on Cluster Tools:• made up of chambers and robots• highly integrated• entire tool’s availability dependent on combination
of all chambers’ status.
Complexity of PM scheduling for cluster tools:• diversity of PM tasks, (types, duration, on whole tool or
on individual chamber, etc.) • WIP • “out of control” events, embedded PM etc.
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Objective
Our proposed models expect to answer two questions:
(1) What is optimal policy for each PM task, i.e. what is
the optimal frequency for PM? (PM planning)
(2) Under optimal policies, we thus have appropriate PM
time window. Now, within this PM window, what is
the best time (shift/day) to do PM? (PM scheduling)
Overall objective is to maximize profits from tools’ operation.
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Hierarchical Approach
A two-layer model structure:
M DPM odel
LPM odel
PM policy
Failure Dynamicsof ToolsDemandPattern
Objective
PMSchedule
W IP
Constraints
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MDP Model
Markov Decision Process (MDP) methodology:• Results in policies that “provides a trade-off between
immediate and future benefits and costs, and utilizes the
fact that observations will be available in the future”;• Four Main Components of an MDP model
a. system states
b: admissible actions in each state
c: objective functions
d: sources of uncertainty.
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State Variables:
Xil(t) = # of days passed or # of wafers produced
since last PM task;
Ii(t) = workload level at tool i.
• Admissible actions: to do PM or not• Sources of uncertainty: tools’ failure dynamics,
and demand pattern.
Objective function:
N
t
M
ii
IPii
tatICtaCtVbE
1 1)(
))(())(()(max
MDP ModelMDP Model
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Subject to the following equations:
)()(
)()()()1(
)1(1)()()1(
)1(11)()1(
0
taftV
tdtVktItI
tatVktXtX
tatXtX
iii
iiiii
Sm
mii
li
li
li
Sm
mi
li
li
li
li
s.t:
)())((
)(0
)()(0
tRtar
LtI
tWtX
ii
li
li
MDP ModelMDP Model
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LP Model
Assume we have already had optimal policies for PMs, from
which such data as PM windows are available.
LP model then comes into play to decide when to do PMs
within their windows.
Assumptions:• Planning horizon is less than the minimum time between any
two consecutive same PM tasks on a chamber• Before planning, it is known with certainty that which PMs
have to be done during this horizon.
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N
t
M
i l
li
liiiii
ta
i
taCtICtVb1 1 1
0
)()()()(max
Objective Function:
Constraints:
)())(),(()6(
)()5(
)()()4(
))(),(()()3(
)()()()1()2(
1)()1(1
tRttar
LtI
tVktTP
ttaftV
tdtTPtItI
ta
ii
iii
iiii
iiii
n
t
li
LP ModelLP Model
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• Mixed IP model;• Constraints (3) and (6) are non-linear, but can
be expressed easily in a “look-up” table form• Basically in line with MDP model, except not including
stochastic data• To maximize the availability versus to match availability
with “demand pattern”.
RemarksRemarks
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MDP v.s. LP
MDP model
LP model
To obtain optimal PM policy
To obtain optimal PM schedule (daily)
PM planning
PM scheduling
Running for long-term (semiannually/annually)
Running for short-term (weekly/bi-weekly)
No commercial software
Off-the-shelf software readily available
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Solving LP Model
Using optimization package:
(1) EasyModeler:• including a Model Description Language• model-data independence • tightly integrated with OSL
(2) OSL (Optimization Solutions and Library)• providing stand-alone solver for LP, MIP,QP or
SLP• including about 70 user callable functions;
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Case Study
• Consider PM tasks from PM1 to PM11;• Planning horizon 7 days • Tool ID from Tool1 to Tool11 • Resources (manpower) constraint• WIP level constraints• Inventory costs• PM costs, (e.g. materials, kits etc.)• Profits from wafer throughput.
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• Comparing results of “best-in-practice” schedule and
“LP model-based” schedule• Using AutoSched AP software, (each PM schedule is
modeled as a “PM order” in ASAP)• Running with the same lots, WIP data as of one
specific
week• Simulating one week• Running 10 replications, respectively.
Case StudyCase Study
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The Average Number of Wafers Completed on Tools
Cluster Tool ID
Nu
mb
er o
f W
afer
s
heuristic
model-based
ResultsResults
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The Average Number of WIPLOT on Tools
Tool ID
Nu
mb
er o
f L
ots
Heuristic
Model-based
ResultsResults
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Model-based schedule outperforms the reference* schedule
both on tools’ throughputs and tools’ WIP level • Consolidating long PM tasks has significant improvement
on throughput, e.g., about 14% improvement for Tool 1
• The improvement is not too much, because the reference
schedule is near optimal• More scenarios should be collected and compared.
*Best-in-practice heuristic
ResultsResults
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Future Work
On Models:• developing computationally tractable MDP model• developing efficient numerical methods for MDP• sensitivity analysis for LP model, etc.
On Implementation:• fine tune model parameters• integrating models into real systems etc.
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Acknowledgements
Thanks to AMD for providing data for case study;
Many thanks to • Craig Christian, for invaluable discussions and
data collection• Javad Ahmadi, for great help on LP implementation• Mike Hillis, for excellent support on group coordination• Nipa Patel, for much help on ASAP simulation• Shekar Krishnaswamy for problem identification.