Intelligent Preventive Maintenance
Scheduling in Semiconductor
Manufacturing Fabs
SRC/ISMT
FORCe:Factory Operations Research Center
Task NJ-877
Michael Fu, Director
Emmanuel Fernandez
Steven I. Marcus
Crystal City, VA, December 13-14, 2001
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SRC/ISMT Factory Operations Research Center
CONTENTS
•Project Summary - Michael Fu
•Optimal Preventive Maintenance
Scheduling Model - Emmanuel Fernandez
•Generic MIP Model
Implementation - Jason Crabtree
•Optimal Preventive Maintenance Policy for Unreliable Queueing systems with
Applications to Semiconductor Manufacturing Fabs - Xiaodong Yao
•“Best Practices” PM Survey -Emmanuel Fernandez
•SMITLab and Project Web Page - Jose A. Ramirez
•NJ 877 FORCe Kick-off Meeting Presentation 04-26-01
•Papers:
•Optimization of Preventive Maintenance Scheduling for Semiconductor
Manufacturing Systems: Models and Implementation
•A Markov Decision Process Model for Capacity Expansion and Allocation
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SRC/ISMT Factory Operations Research Center
Overview
Michael Fu, Ph.D.
Professor, School of Business., Univ. Maryland
Project Summary
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SRC/ISMT Factory Operations Research Center
Research Plan
(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.
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SRC/ISMT Factory Operations Research Center
Executive Summary
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Successful Systems Integration of Software Implementation
of PM Scheduling Algorithm at Member Company in 2001
PM Practices Survey Instrument Developed, Distributed, and
Preliminary Data Analysis Underway
Project Website Up and Running
In Progress Research
– Generic Implementation of PM Scheduling Algorithm
– PM Planning Models (Analytical and Simulation-Based)
SRC/ISMT Factory Operations Research Center
Project Overview
•Review of Project Administration
- Industrial Liaisons, Research Personnel
- Project Management
- Research Progress
• Anticipated Results, Deliverables
• Task Description, Past Year, Next Year
• Technology Transfer
• Review/Summary of Research Approach
• Research Details
• “Best Practices” PM Survey
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Industrial Liaisons
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•
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Gurshaman S. Baweja, Texas Instruments Incorporated
Ben-Rachel Igal, Intel Corporation
Mani Janakiram, Intel Corporation
Ying Tat Leung, IBM Corporation
Marcellus Rainey, Texas Instruments Incorporated
Madhav Rangaswami, Intel Corporation
Ramesh Rao, National Semiconductor Corporation
Man-Yi Tseng, Advanced Micro Devices, Inc.
Jan Verhagen, Philips Corporation
Sidal Bilgin, LSI
Motorola still being decided
SRC/ISMT Factory Operations Research Center
Research Personnel
Faculty:
– Michael Fu, Maryland
– Steve Marcus, Maryland
– Emmanuel Fernandez, Cincinnati
Students:
– Xiaodong Yao, Maryland (advanced PhD)
– Ying He, Maryland (advanced PhD)
– Jiaqiao Hu, Maryland (beginning PhD)
– Jason Crabtree, Cincinnati (advanced MS)
– Jose Ramirez, Cincinnati (beginning PhD)
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SRC/ISMT Factory Operations Research Center
Project Management
• Weekly Site Meetings at Maryland & Cincinnati
• Weekly Teleconferences UMD & UC
• Monthly Teleconferences With Liaisons and PI’s
• Project Website
– http://www.smitlab.uc.edu/PMResults.htm
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SRC/ISMT Factory Operations Research Center
Anticipated Primary Results
(1) Models, algorithms and a suite of software tools will be
developed to automate and/or guide in optimally planning,
scheduling and coordinating PM tasks for bottleneck tools in
a semiconductor fab.
(2) Software will be designed for seamless integration with
existing commercial discrete-event simulation software
packages such as AutoSched AP and WorkStream.
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SRC/ISMT Factory Operations Research Center
Task Description
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.
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SRC/ISMT Factory Operations Research Center
Deliverables to Industry
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)
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SRC/ISMT Factory Operations Research Center
Past Year Progress
and Accomplishments
• Two student internships at member company:
- successful implementation of PM scheduling algorithm
- tested and validated with ASAP simulation and real data
- integrated with MES and PM monitoring databases
• PM Practices Survey Instrument Developed and Distributed
- thus far, 12 responses from 8 companies and 5 countries
- very diverse answers (more details later)
• Investigated analytical (MDP models and queueing models)
and simulation-based approaches to PM planning problem
• Developing generic implementation of PM Scheduling
Algorithm and IT implementation
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Next Year Plans
• Complete implementation of generic PM scheduling algorithm
- further student internships at member companies to
implement, test, and evaluation models and algorithms
- begin facilitating possible transfer to software vendors
• Complete PM Practices Survey Data Analysis and Report,
- make available to member companies
- utilize in research on models and algorithms (see next
bullet)
• Develop MDP and queueing models, in conjunction with
simulation-based approaches, for PM planning problem,
focusing on bottleneck tool sets in the fab
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Technology Transfer
• Software Developed
– MIP model for PM scheduling algorithm in OSL
– ASAP cluster tool model to validate PM scheduling algorithm
– Subroutines to integrate various databases
• Conference Presentations
– INFORMS International Conference, 6/01
– Conference on Control Applications, 9/01
– SRC/ISMT FORCe Annual Review Meeting, 12/01
• Publications
– X. Yao, M.C. Fu, S.I. Marcus, and E. Fernandez,
“Optimization of Preventive Maintenance Scheduling for
Semiconductor Manufacturing Systems: Models and
Implementation,'‘ Proceedings of the 2001 IEEE Conference
on Control Applications, 407-411.
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Model Overview
Emmanuel Fernandez, Ph.D.
Associate Prof., ECECS Dept., Univ. Cincinnati
Optimal Preventive
Maintenance
Scheduling Model
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Project Background
Motivations:
1. Scheduling Preventive Maintenance(PM) tasks for cluster tools
is a very complicated and challenging job.
2. Many factors, like manpower constraints, projected upstream
and downstream WIP, chamber inter-relationships, etc., just to
name a few, come into the decision process.
3. A wealth of information is ready for use from the tool
monitoring system (TMS), the wafer dispatching system (WDS),
etc.
Objective:
• To provide a computer-aided decision making support tool for
cluster tools’ PM scheduling.
• Summer Internships: Xiaodong Yao and Jason Crabtree at AMD
from June to August, 2001. Faculty visits to industry.
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Scheduling Algorithm
Summary:
1. A mixed integer program (MIP) has been formulated to
address the optimization problem for cluster tools’
Preventive Maintenance (PM) scheduling.
2. Four main decision factors in current PM scheduling
practice are identified: chambers status vs. tools
throughput, PM windows, manpower constraints, and
projected WIPs.
3. Optimization’s objective is to maximize profits via tools’
availability, and meanwhile factor into other costs such as
from WIP.
4. The algorithm has been designed to work tightly with
other information systems like TMS and WDS.
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Algorithm kernel
• Mathematically, the kernel of our algorithm is a mixed
integer program, which has been formulated to address the
optimal scheduling problem, and can be solved by using a
standard optimization package, e.g. IBM OSL Optimization
Subroutine Library.
• Obtained as the linear and non-stochastic version of MDP
model formulation.
• The algorithm will be searching for any feasible
consolidation of PM tasks on each tool, choosing the “best”
schedule in terms of maximizing tools availabilities (or tools
throughputs), and meanwhile satisfying manpower
constraints, not exceeding maximal WIP limit and trying to
reduce overall WIP level.
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SRC/ISMT Factory Operations Research Center
Research Approach
The generic form of the problem of interest:
min EC  ,  
  , 
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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Model Statement
Objective:
i


I
max   bi Vi (t )  Ci  I i (t )   Cil  ail (t ) 
a (t )
t 1 i 1 
l 1

N
M
uli
ail (t )  1, for those PM tasks that have to
be finished within window  wli , uli  .
Subject to:
(1)

t  wli
(2) Vi (t )  f i (a i (t ),  i (t )) , for i  1
M ,t 1
N.
(3) I i (t  1)  I i (t )  K i  Vi (t )  di (t ) ,
for i  1 M , t  1 N  1.
(4) I i (t )  Li , for i  1 M , t  1 N .
(5) r(a(t ),  (t ))  R(t ) , for t  1
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N.
SRC/ISMT Factory Operations Research Center
Model Nomenclature
Let N denote the planning horizon, M the number of tools under
consideration. The numbering of PM tasks for each tool is from 1 to
 i , where  i represents the total number of PM tasks for tool i. The
variables and parameters of our model are as follows.
l
 ai (t ) : Binary decision variables for PM task l on tool i at time t, (1:
to do PM; 0: not to do PM).
a (t )
 i : Action vector for all tasks on tool i.
a (t )
: Action vector for all tasks on all tools.

a i (t )
 (t )
. They
 i : Accompanying status vector for PM task vector
are used specifically for those PM tasks whose duration are two
 (t  1)  a i (t )
days. Specifically we have i
for all i.
 (t )
: Accompanying vector for all tools.

V (t )
 i : Availability of tool i at time t.
K
 i : Wafer throughput coefficient for availability of cluster tool i.
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SRC/ISMT Factory Operations Research Center
Model Nomenclature
 I i (t ) : Workload level (total in queue and process) for tool i at time
t.
 d i (t ) : Workload from upstream operations for tool i at time t.
 bi : Weighted profit coefficient for availability of cluster tool i.
 CiI : Cost coefficient for inventory on tool i.
 C il : PM cost for performing PM tasks l on i.
 Li : Workload up limit for tool i at any time.
 f i (a i (t ),  i (t )) : Availability function for tool i under PM status vector
a i (t ) and  i (t ) .
 r(a (t ),  (t )) : Resource function, computing resource required by
tasks status vector a (t ) and  (t ) .
 R (t ) : Total resources available for PM at time t.
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SRC/ISMT Factory Operations Research Center
Finding an optimal schedule
•
An optimal schedule will be chosen with maximal profits from
tools availabilities (or throughputs) among all feasible schedules.
A feasible schedule should satisfy:
•
Any scheduled PM tasks should be in its predefined PM
window.
•
On any day, the total number of resources (e.g. headcount of
maintenance technicians) required by that day’s schedule should
not exceed the projected available resources.
•
On any day, the WIP level effected by projected incoming WIP
and PM schedule on each machine should not exceed a
predefined WIP limit, i.e. it will not schedule a PM task on a
certain day when large WIP is expecting to arrive. A schedule
with low WIP levels is preferred by the algorithm.
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SRC/ISMT Factory Operations Research Center
Simulation Study
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•
A preliminary simulation study of comparison between
a model-based schedule and a reference schedule using
AutoSched AP has been conducted. Real fab data was
used throughout the study.
•
The simulation study showed model-based schedule
outperforms the reference schedule in general. Some
significant improvement on tools’ availability was
recorded in the study, for example, 14% improvement
for a cluster tool was observed in the simulation.
SRC/ISMT Factory Operations Research Center
Jason Crabtree
M.S. Student, Univ. Cincinnati
Generic MIP Model
Implementation
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SRC/ISMT Factory Operations Research Center
Generic Implementation
Objective:
To create a generic model and IT
implementation based on experience
thus far (models, internships,
customizations)
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SRC/ISMT Factory Operations Research Center
Generic Implementation
• The MIP model is designed to be very robust, thus it can
handle a large variety of tools without changing the actual
formulation of the model
• The generic model can be separated into three facets:
– Inputs
– Scheduling algorithm
– Outputs
• Implementation of the generic model then consists of:
– Formulating input data and defining interfaces to collect input data
– Formatting input data into proper form for chosen MIP solver
– Handling of solution data output from solver
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SRC/ISMT Factory Operations Research Center
Inputs and Outputs
A set of tools
Initial schedule
Planning horizon
Projected Incoming WIP
Optimization
Scheduling
Model/algorithm
Optimized Schedule
Estimated Availability
Estimated WIP
Input Data:
• A Tool family, which includes all relevant tools of
interest, for example, a group of cluster tools in thin films
module
• Tool parameters, like throughput rate, maximal WIP level
(limit), inventory cost if applicable
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SRC/ISMT Factory Operations Research Center
Input Data (cont.)
• Monitored items, i.e. PM tasks of interest on all chambers
• Information about PM’s duration (MTTR), manpower
requirement, cost etc.
• Chambers scenarios and their effects on whole tool’s
throughput (availability)
• Planning horizon
• PM tasks initial schedule, each associated with a time
window (warn-date, due-date and late-date)
• Projected incoming WIP in the planning horizon
• Projected manpower (maintenance technicians) available
in the planning horizon
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SRC/ISMT Factory Operations Research Center
Outputs
• Optimal schedule, users can see the optimized schedule
and the initial one in TMS for comparison.
• An estimated availability of each tool in family will be
presented along with an optimal schedule.
• An estimated inventory level of each tool in family will
be presented along with an optimal schedule.
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SRC/ISMT Factory Operations Research Center
Algorithm Flow Chart
Begin
.ini file;
.tool file;
.item file;
System Initialization
and selecting a
machine Family
Specifying a
planning horizon
TMS
database
Dispatch
report
Resource
Data File
Reading in TMS
database, performing
data filtering
Reading in
projected WIP
from WDS
Reading in
projected
resource
Generating
consolidated
tasks vector set
{v}
Computing availability loss
and resources requirement
for each task vector.
Generating MIP
model instance in a
standard format
Chamber
configuration
SIMPLEX and
Branch-and-Bound
algorithms are used
in the default solver
Invoking OSL default
solver to solve
the MIP model
Parsing model solution
and interpreting the
result to users
TMS
End
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System Architecture
RPC(Remote Procedures Call)
Connection
Data
Preprocessing
Model
generating
model.mps
TMS
WDS
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Solution
Parsing
Front-end
Optimization
Solver (OSL)
Back-end
SRC/ISMT Factory Operations Research Center
System Interfaces
User Interface:
• Tool family is selected by user.
• Planning period dates are entered by user.
• Manpower schedule is input by user.
Interface with TMS:
• The TMS PM data file is searched by the software for PM
items due within user-defined planning window.
• A secondary “optimal” PM data file is updated by the software
with the optimal dates from the optimization.
Interface with WDS:
• A projected WIP data file is extracted from WDS periodically.
• The software will use updated WIP data each time when
running the optimization algorithm.
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SRC/ISMT Factory Operations Research Center
Using the Software
Begin
Select Tool
Group
Confirm PM
Items
Enter Planning
Dates
LP Solved On
Remote Server
Enter
Manpower
Schedule
Run
Optimization
Confirm
Optimal
Schedule
Update PM
Records
End
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SRC/ISMT Factory Operations Research Center
Conclusions
• The MIP model is very robust and can handle a wide range
of tools
• Implementation of the generic model consists of formulating
and gathering the required input data, passing data to solver,
and handling the solution data
• The complexity of the final software package is currently
being looked into. Keeping the software small promotes
speed and allows customization but requires that software be
tailored for each implementation. A larger software package
enhances ease of integration but may limit robustness of
software.
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SRC/ISMT Factory Operations Research Center
Xiaodong Yao
Ph.D. Student, Univ. Maryland
Optimal Preventive Maintenance Policy for
Unreliable Queueing systems with
Applications to Semiconductor
Manufacturing Fabs
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SRC/ISMT Factory Operations Research Center
Modeling Framework for PM
planning and scheduling
Two-stage hierarchical framework under development:
•
•
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In the 1st stage (higher level), the objective is to
investigate the structure of optimal policies for PMs,
(for example, PM window with optimal parameters t*
and Dt*), in the presence of stochastic dynamics of
machine failure and demand processes.
In the 2nd stage (lower level), the objective is to
determine exact time to perform PM tasks, taking into
consideration the inter-dependency of PMs, resource
constraints, short-term projected WIP, etc. A mixed
integer program (MIP) has been successfully
developed, and implemented in a specific
environment.
SRC/ISMT Factory Operations Research Center
Model
(Semi-)Markov Decision Processes (MDP) model on 1st stage:
•
•
•
•
•
•
•
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Machines: queueing systems, fab: queueing network
Incorporating system “operating” states (e.g. WIP level,
queue length) and “technical” states (e.g. deterioration degree
of machines) in PM policy
Observable vs. unobservable machine states.
Unobservable states can be estimated based on information
from SPC (statistic process control) or number of wafers
produced since last “renewal” state.
Stochastic process for machine’s deterioration,
e.g., controlled Markov chain.
Independent demand process
Random times (non-negligible) for PM tasks
Cost structure: PM cost, operating cost, and inventory
holding cost, etc.
SRC/ISMT Factory Operations Research Center
Structural Optimal Policy
Structure of optimal policy:
•
•
•
•
•
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To be investigated with the formulation of MDP models
Monotonicity, e.g. control-limit form and/or switching
curve, is promising and interesting
Effect of system “operating” states on PM policy to be
studied.
Comparison study between the derived optimal policy
and (t*, Dt*) policy
Derivation of parameterized policy
SRC/ISMT Factory Operations Research Center
Simulation-based
Optimization
Simulation-based optimization for parameterized policy:
•
•
•
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Monte Carlo simulation is effective for large
optimization problems.
Efficient gradient estimation will be employed in
stochastic approximation algorithm in search for
optimal policy parameters, e.g. threshold values in
control-limit policies.
Unbiased gradient estimators for system performance
w.r.t. structural policy parameters, e.g. (t*, Dt*) will be
obtained.
SRC/ISMT Factory Operations Research Center
Emmanuel Fernandez, Ph.D.
Associate Prof., ECECS Dept., Univ. Cincinnati
“Best Practices” PM Survey
•PM Practices Survey Instrument Developed and
Distributed
•Thus far, 12 responses from 8 companies and 5 countries
•Both commonality and divergence in different issues
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SRC/ISMT Factory Operations Research Center
Jose A. Ramirez
Ph.D. Student, Univ. Cincinnati
SMITLab and Project Web Page
http://www.smitlab.uc.edu
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SRC/ISMT Factory Operations Research Center