The Systems Modeling & Information Technology Laboratory 1 Intelligent Preventive Maintenance...

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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•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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•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.

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