SRC/ISMT FORCe:Factory Operations Research Center Task NJ-877

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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

Crystal City, VA, December 13-14, 2001

Intelligent Preventive Maintenance Scheduling in Semiconductor

Manufacturing Fabs

SRC/ISMT Factory Operations Research Center2

•Project Summary - Michael Fu

•Optimal Preventive MaintenanceScheduling Model - Emmanuel Fernandez

•Optimal Preventive Maintenance Policy for Unreliable Queueing systems with Applications to Semiconductor Manufacturing Fabs - Xiaodong Yao

•Generic MIP ModelImplementation - Jason Crabtree

•“Best Practices” PM Survey -Emmanuel Fernandez

•SMITLab and Project Web Page - Jose A. Ramirez

•Papers:•Optimization of Preventive Maintenance Scheduling for Semiconductor Manufacturing Systems: Models and Implementation

•A Markov Decision Process Model for Capacity Expansion and Allocation

•NJ 877 FORCe Kick-off Meeting Presentation 04-26-01

CONTENTS

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Michael Fu, Ph.D.Professor, School of Business., Univ. Maryland

Project Summary

Overview


(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


• 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)

Executive Summary


•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

Project Overview


• 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

Industrial Liaisons


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)

Research Personnel


• 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

Project Management


(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.

Anticipated Primary Results


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


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)

Deliverables to Industry


• 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

Past Year Progressand Accomplishments


• 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

Next Year Plans


• 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.

Technology Transfer

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Emmanuel Fernandez, Ph.D.Associate Prof., ECECS Dept., Univ. Cincinnati

Optimal Preventive Maintenance

Scheduling Model

Model Overview


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.

Project Background


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.

Scheduling Algorithm


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.


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.

Research Approach


Proposed Framework


Subject to:

( )1 1 1

max ( ) ( ) ( )iN M

I l li i i i i i

a tt i l

b V t C I t C a t

i

(1) ( ) 1, for those PM tasks that have to

be finished within window , .

(2) ( ) f ( ( ), ( )) , for 1 , 1 .

(3) ( 1) ( ) ( ) ( ) ,

il

il

u lit w

i il l

ii i

i i i i i

a t

w u

V t a t t i M t N

I t I t K V t d t

for 1 , 1 1.

(4) ( ) , for 1 , 1 .

(5) r( ( ), ( )) ( ) , for 1 .i i

i M t N

I t L i M t N

a t t R t t N

Objective:

Model Statement


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. )(tali : Binary decision variables for PM task l on tool i at time t, (1:

to do PM; 0: not to do PM). )(tai : Action vector for all tasks on tool i. )(ta : Action vector for all tasks on all tools. )(t

i : Accompanying status vector for PM task vector )(tai . They

are used specifically for those PM tasks whose duration are two days. Specifically we have )()1( tat ii

for all i.

)(t : Accompanying vector for all tools. )(tVi : Availability of tool i at time t. iK: Wafer throughput coefficient for availability of cluster tool i.

Model Nomenclature


)(tIi : Workload level (total in queue and process) for tool i at time t.

)(tdi : Workload from upstream operations for tool i at time t.

ib : Weighted profit coefficient for availability of cluster tool i. I

iC : Cost coefficient for inventory on tool i. l

iC : PM cost for performing PM tasks l on i.

iL : Workload up limit for tool i at any time. f ( ( ), ( ))ii i

a t t : Availability function for tool i under PM status vector

)(tai and )(ti

. r( ( ), ( ))a t t : Resource function, computing resource required by

tasks status vector )(ta and )(t . )(tR : Total resources available for PM at time t.

Model Nomenclature


• 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.

Finding an optimal schedule


• 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.

Simulation Study


Jason CrabtreeM.S. Student, Univ. Cincinnati

Generic MIP ModelImplementation


Objective:

To create a generic model and IT implementation based on experience

thus far (models, internships, customizations)

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

Generic Implementation


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

Optimization Scheduling

Model/algorithm

A set of toolsInitial schedule

Planning horizonProjected Incoming WIP

Optimized ScheduleEstimated AvailabilityEstimated WIP

Inputs and Outputs


• 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

Input Data (cont.)


• 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.

Outputs


System Initializationand selecting a machine Family

.ini file;.tool file;.item file;

TMSdatabase

Dispatch report

Resource Data File

Specifying a planning horizon

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

Invoking OSL default solver to solve the MIP model

Parsing model solution and interpreting the

result to users

End

Begin

Chamber configuration

SIMPLEX and Branch-and-Bound algorithms are used in the default solver

TMS

Algorithm Flow Chart


In terf aces

DataPreprocessing

SolutionParsing

Modelgenerating

OptimizationSolver (OSL)

Back-end

model.mps

TMS

WDSFront-end

RPC(Remote Procedures Call)Connection

System Architecture


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.

System Interfaces


Begin

Select Tool Group

Enter Planning Dates

Enter Manpower Schedule

Run Optimization

Confirm Optimal Schedule

Confirm PM Items

Update PM Records

End

LP Solved On Remote Server

Using the Software


• 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.

Conclusions

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Xiaodong YaoPh.D. Student, Univ. Maryland

Optimal Preventive Maintenance Policy for Unreliable Queueing systems with

Applications to Semiconductor Manufacturing Fabs


Two-stage hierarchical framework under development:

• 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.

Modeling Framework for PM planning and scheduling


(Semi-)Markov Decision Processes (MDP) model on 1st stage:

• 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.

Model


Structure of optimal policy:

• 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

Structural Optimal Policy


Simulation-based optimization for parameterized policy:

• 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.

Simulation-based Optimization

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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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Jose A. RamirezPh.D. Student, Univ. Cincinnati

SMITLab and Project Web Page

http://www.smitlab.uc.edu

SRC/ISMT FORCe:Factory Operations Research Center Task NJ-877

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