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SRC/ISMT FORCe: Factory Operations Research Center Task NJ877. Michael Fu, Director Emmanuel Fernandez Steven I. Marcus Atlanta, GA, Oct. 2122, 2003. Intelligent Preventive Maintenance Scheduling in Semiconductor Manufacturing Fabs. CONTENTS.
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Michael Fu, Director
Emmanuel Fernandez Steven I. Marcus
Atlanta, GA, Oct. 2122, 2003
Intelligent Preventive Maintenance
Scheduling in Semiconductor
Manufacturing Fabs
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.
Faculty:
Students:
Year 1Implementing 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 simulationbased 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.
(Proposed)
1.Survey of current PM practices in industry
(Report) (P:15DEC2001)
2. Models and algorithms to cover bottleneck
tool sets in a fab(Report) (P:31MAR2002)
3. Simulation engine implemented in commercially available
software, with case studies and benchmark data (Report) (P:30SEP2002)
4. PM planning/scheduling software tools, with accompanying
simulation engine (Software, Report) (P:30JUN2003)
5. Installation and evaluation,workshop and consultation
(Report) (P:31DEC2003)
MORE DETAILS later in presentation
Failure Dynamics
Upper MDP
PM Policy
Demand Pattern
Lower MIP
PM Schedule
WIP
Constraints
Deliverables
Models and AlgorithmsHierarchical Model for Optimal PM scheduling
Models and Algorithms  MIP Formulation
Objective:
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Deliverables
Models and Algorithms  MIP Formulation
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
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Deliverables
Models and Algorithms  MIP Formulation
Constraints:
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Deliverables
Models and Algorithms  MIP Formulation
Constraints:
(v)
where
di(t
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is amount of incoming wafers at tool
i
in
period
t
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Xi(t
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is the quantity of wafers processed
on tool
i
in period t.
(vi)
where
Ki
is the wafer throughput coefficient for tool i.
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Deliverables
Models and Algorithms  MIP Formulation
Constraints:
(vii)
where
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is the maximum allowed inventory at tool i.
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Deliverables
Models and Algorithms  MIP Formulation
Constraints:
(ix)
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Rk(t)
is the amount of resource
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Models and Algorithms Conversion of Wafer to Calendarbased PM Schedules
PM window (W: warning, D: due, L: late)
(Wafer counts/period)
(Time period)
Estimated due time (date)

Planning horizon
START
User Interface

Tools family
General functions used in
main.c

Number of Technicians
different parts of the system.
pmost.exe
*.fam, *.data
read_data_file.c

Tool/PM data files:

read_fam_file.c
Conv
ersion
to calendar

time PMs data files
Read
read_sch_file.c
write_sch_file.c

files *.sch
Input Data
PM schedule:
read_wip_file.c
ASAP

: files *.wip
Estimated WIP data files
conv2cal
(
.exe
, .c, .h)
debug.txt

Debugging file:
Conversion to
calendar

time PMs

*.csch
Converted Schedule Fi
le:
create_pm_vectors.c
Write
*.set
*.val

Output data:
,
files
write_set_val_files.c
MPS file
*.mps

MPS file:
write_mps_file.c
write_debug_file.c
.mps
file
main.c
calls th
e
LP/MIP
solver (OSL,
SOLVER
CPLEX, etc)
solu
tion
file (text file)
parse_osl_solution.c
pm_order.txt
Output:
Parse
parse_cplexl_solution.c
Solution
write_solution_file.c
write_pm_order_file.c
pm_solution.txt
Software Implementation:PMOST
PMOST Block Diagram
pmost_ui.exe
Integration of Fab Schedulers:Collaboration with ASU
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 twolevel hierarchical optimization structure that considers important factors such as the workinprogress (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)
Summary of Doctoraland Master Theses
Research Proposal Ph.D. on Electrical & Computer Engineering & Computer Science
Title:Reinforcement Learning (NeuroDynamic Programming) Approach for Production Control of Semiconductor Manufacturing ReEntrant 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 reentrant 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 highdimensional and complex systems: Reinforcement Learning (NeuroDynamic Programming).
Summary of Doctoraland Master Theses
Xiaodong Yao, Ph.D. Student, University of Maryland, Optimal Joint Preventive Maintenance and Production Control Policies for Unreliable Production Systems
Summary of Doctoraland Master Theses
Systems with timedependent failures
u [0,P]
d, constant demand
MarkovDecision Process Formulation
Consider the discretetime model:
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
controllimit 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.
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. 1: the optimal policy
Fig. 2: The relative difference of cost
function under the joint optimal policy
and independently optimized policy.
diff = (Jind – J*)/J* 100%.
Fig. 2
u {0,1}
1, with prob. q
The optimal cost functions satisfy:
Characterization of optimal policy
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
controllimit form w.r.t. machine age.
Theorem 5: There exists s* such that s > s*, *(s,1,n) = 0, for all n.
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
The big picture:
Hierarchical Framework for PM planning and scheduling.
Continuing and Future Research
Continuing and Future Research