1 Optimal Preventive Maintenance Scheduling in Semiconductor Manufacturing Systems: Software Tool & Simulation Case Studies José A. Ramírez-Hernández, Member, IEEE, Jason Crabtree, Xiaodong Yao, Member, IEEE, Emmanuel Fernandez, Senior Member, IEEE, Michael C. Fu, Fellow, IEEE, Mani Janakiram, Steven I. Marcus, Fellow, IEEE, Matilda O’Connor, and Nipa Patel Abstract This paper presents the architecture and implementation of PMOST, a Preventive Maintenance Opti- mization Software Tool, based on algorithms for the optimal scheduling of preventive maintenance (PM) tasks in semiconductor manufacturing operations. We also present results from four complex simulation case studies, based on real industrial data and employing full fab models, to illustrate the use, data needs and outcomes produced by PMOST. These results demonstrate significant improvements in tool production and consolidation of PM tasks. We give a description of the different software modules that compose PMOST, to provide guidelines as well as a template for other implementations of the PM optimization algorithms utilized by PMOST. This work was partially supported by a grant from the Semiconductor Research Corporation (SRC) and International Sematech (ISMT), within the Factory Operations Research Center (FORCe), Task NJ 877.001. José A. Ramírez-Hernández, and Emmanuel Fernandez are affiliated with the Department of Electrical and Computer Engineering, University of Cincinnati, OH 45221-0030, USA (e-mails: [email protected]; [email protected]; address: 822 Rhodes Hall, University of Cincinnati, PO Box 210030, Cincinnati, Ohio 45221-0030. Jason Crabtree is with Integral Analytics Inc., Cincinnati, OH, (e-mail: [email protected]). Xiaodong Yao is with SAS Institute, Inc., (e-mail: [email protected]). Michael C. Fu and Steven I. Marcus are with the Institute for Systems Research, University of Maryland, College Park, MD 20742, USA, emails: {mfu; marcus}@isr.umd.edu. Mani Janakiram is with Intel Corp., Chandler, AZ, USA Email: [email protected]. Matilda O’Connor was with Advanced Micro Devices Inc, Austin, TX 78741, USA. Nipa Patel is with Advanced Micro Devices Inc, Austin, TX 78741, USA (e-mail: [email protected]; address: 5204 E. Ben White Blvd. M/S 563, Austin, TX 78741; phone: 512-602-9441; fax: 512-602-0360). November 30, 2009 DRAFT
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Optimal Preventive Maintenance Scheduling in
Semiconductor Manufacturing Systems:
Software Tool & Simulation Case Studies
José A. Ramírez-Hernández, Member, IEEE, Jason Crabtree, Xiaodong Yao,
Member, IEEE, Emmanuel Fernandez, Senior Member, IEEE, Michael C. Fu,
Fellow, IEEE, Mani Janakiram, Steven I. Marcus, Fellow, IEEE, Matilda
O’Connor, and Nipa Patel
Abstract
This paper presents the architecture and implementation of PMOST, a Preventive Maintenance Opti-
mization Software Tool, based on algorithms for the optimal scheduling of preventive maintenance (PM)
tasks in semiconductor manufacturing operations. We also present results from four complex simulation
case studies, based on real industrial data and employing full fab models, to illustrate the use, data
needs and outcomes produced by PMOST. These results demonstrate significant improvements in tool
production and consolidation of PM tasks. We give a description of the different software modules that
compose PMOST, to provide guidelines as well as a template for other implementations of the PM
optimization algorithms utilized by PMOST.
This work was partially supported by a grant from the Semiconductor Research Corporation (SRC) and International Sematech(ISMT), within the Factory Operations Research Center (FORCe), Task NJ 877.001.
José A. Ramírez-Hernández, and Emmanuel Fernandez are affiliated with the Department of Electrical and ComputerEngineering, University of Cincinnati, OH 45221-0030, USA (e-mails: [email protected]; [email protected];address: 822 Rhodes Hall, University of Cincinnati, PO Box 210030, Cincinnati, Ohio 45221-0030.
Jason Crabtree is with Integral Analytics Inc., Cincinnati, OH, (e-mail: [email protected]).
Xiaodong Yao is with SAS Institute, Inc., (e-mail: [email protected]).
Michael C. Fu and Steven I. Marcus are with the Institute for Systems Research, University of Maryland, College Park, MD20742, USA, emails: {mfu; marcus}@isr.umd.edu.
Mani Janakiram is with Intel Corp., Chandler, AZ, USA Email: [email protected].
Matilda O’Connor was with Advanced Micro Devices Inc, Austin, TX 78741, USA.
Nipa Patel is with Advanced Micro Devices Inc, Austin, TX 78741, USA (e-mail: [email protected]; address: 5204 E.Ben White Blvd. M/S 563, Austin, TX 78741; phone: 512-602-9441; fax: 512-602-0360).
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I. INTRODUCTION
In semiconductor manufacturing systems, Preventive Maintenance (PM) is performed by tak-
ing off-line a specific tool to apply a prescribed maintenance task. PM increases the overall
operational reliability while decreasing unanticipated (expensive) down-time from tool failures.
The importance of the PM operations in the semiconductor industry is clearly illustrated by
the large costs of the tools utilized in the fabrication process. For instance, a new fab using
technology for 300 mm wafers can cost in excess of $3 billion [1], [2]. PM properly applied
is a necessity in the fab to maintain and improve productivity, and to justify enormous capital
investments of this industry. In addition, PM operations are usually based on heuristic methods,
e.g., cumulative experience obtained by the engineers from the fab operations. The application
of optimization methods in this problem is a topic that has received significant attention recently
[3], [4], [5].
The objectives of this paper are as follows. First, to present the architecture and implemen-
tation of a software tool called Preventive Maintenance Optimization Software Tool (PMOST),
based on the PM scheduling optimization algorithm for semiconductor manufacturing operations
proposed in [3], [4], [5]. This software tool receives operational data and baseline PM schedules
to generate an optimized PM schedule. Second, to present the architecture and implementation
of PMOST, in order to provide guidelines and a template, as well as experimental data, that
can help in the adoption of these by others, and also perhaps serve as the basis for generic
third-party commercial tools. Third, to present a set of four complex simulation case studies,
based on real industrial data and using full fab models, to illustrate the use, data needs and
outcomes produced by PMOST. Both the PM optimization algorithms reported in [3], [4], [5]
and PMOST are the result of research supported by the Semiconductor Research Corporation
(SRC) and International Sematech (ISMT) within the “Factory Operations Research Center”
(FORCe) program. The project was justified by the fact that neither algorithms nor software
tools for PM scheduling optimization in semiconductor manufacturing operations were available
previous to this research.
The case studies presented in this paper consisted of simulations of four different tool groups
in photolithography, metal deposition, and thin films processes on which the impact of optimized
PM schedules, obtained with PMOST, versus heuristic and baseline PM schedules was evaluated.
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The simulation experiments were performed in two fabs from different semiconductor companies.
For the experiments, the companies allowed the utilization of industrial data as well as the full
factory simulation models. Moreover, the simulations were conducted under the strict supervision
of the personnel in charge of factory simulations, and according to the simulation practices
utilized by each company.
We also studied the problem of incorporating non-calendar based PM schedules into the PM
scheduling optimization. As a result, a conversion algorithm [6], [7] was designed to provide
estimates of the equivalent calendar-time PM schedules for PM tasks defined under other non-
calendar time units, e.g., number of wafers processed or processing-time elapsed since last PM
task. The algorithm reported in [6], [7] utilizes as input the projections of the Work-In-Process
(WIP) and the system’s parameters (e.g., tool throughput rate, number of chambers), and then
yields estimates of the dates for which the corresponding tool could receive a prescribed non-
calendar time type of PM task. In addition to the fact that calendar-time PM schedules are easy to
use and to implement, in terms of the optimization algorithm given in [3], [4], [5], calendar-time
schedules are preferred because the search space for the optimization problem may be smaller
when compared to the use of other units used to describe the PM schedules. Specific details
of the conversion algorithm are provided in [6], [7]. Moreover, in [7] an overview of how the
calendar-time PM schedules generated by the conversion algorithm are incorporated in the PM
optimization with PMOST is presented, as well as a case study with real industrial data that
demonstrates the accuracy of the conversion algorithm.
The organization of this paper is as follows: Section II presents an overview of the optimal
PM scheduling framework utilized by PMOST. This is followed by a description of PMOST
in section III that describes the data utilized by the software tool and how optimization results
are provided. An overview of the simulation studies and the corresponding optimization and
simulation results are given in section IV and V, respectively. Finally, conclusions are presented
in section VI.
II. OVERVIEW OF PM SCHEDULING OPTIMIZATION
PMOST is based on the modeling framework for optimization of PM schedules given in [3],
[4], [5]. This framework is described as a two-level hierarchical model [3], with a Markov
Decision Process (MDP) [4] at the higher level and a Mixed Integer Programming (MIP)
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formulation [3], [4], [5] at the lower level, as depicted in Fig. 1 below.
Upper MDP
Lower MIPWIP
PM Schedule
PM Policy
Objective
Constraints
Demand Pattern
Failure Dynamics
Figure 1. Two-level hierarchical framework for PM planning and scheduling (adapted from [3], [4], [5]).
The long-term PM planning policies are produced by the MDP, which employs “the available
information in a way that provides a trade-off between immediate and future benefits and costs,
and that utilizes the fact that observations will be available in the future" [8]. In the lower
level, a MIP formulation [3], [4], [5] generates the optimized PM schedules according to an
optimization objective, projections of the Work-In-Process (WIP), and these are subjected to
several constraints. It is this PM scheduling optimization algorithm that is implemented by
PMOST, and the PM planning policy, or frequency for performing the different PM tasks, is
obtained from the baseline, or nominal, schedule employed in daily fab operations. This frequency
is determined by the semiconductor fab operations, and based on recommendations from the
tool’s manufacturer.
Next we present some notation and details on the optimization models and algorithmic solu-
tions, presented previously in [3], [4], [5], which are utilized in PMOST.
As presented in [3], [4], [5], the objectives utilized for the lower level MIP model are as
follows:
MIP Objective 1
max
Tp∑t=1
M∑i=1
(bi · Vi(t)− cI
i · Ii(t)−ρi∑
l=1
cli · al
i(t)
), (1)
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MIP Objective 2
max
Tp∑t=1
M∑i=1
(b′i ·Xi(t)−
ρi∑
l=1
cli · al
i(t)
), (2)
where, using the same notation as in [3], [4], [5], Tp represents the number of time units or
periods in the PM scheduling horizon, M is the number of tools (or tool chambers), Vi(t) is
availability of tool i in period t, bi is the profit coefficient for availability of tool i, Ii(t) is the
workload level (i.e., WIP) for tool i in period t, cIi is the cost coefficient for inventory in tool i,
ρi is the number of PM tasks on tool i, ali(t) is a binary decision variable (1: do PM, 0: don’t
do PM) for PM task l on tool i in period t, and cli is the cost of performing PM task l on tool
i. Moreover, in MIP Objective 2 the quantity Xi(t) represents the wafer throughput of tool i in
period t and b′i is the profit coefficient for throughput on tool i. The above MIP objectives (1)
and (2) would be optimized under constraints such as inventory levels, availability of resources
(e.g., maintenance technicians per period), tools availability and throughput. Notice that each
objective aims to maximize two different performance indices in a tool group. In MIP Objective
1 the goal is to maximize the availability of tools while minimizing inventory and PM task costs.
For MIP Objective 2, the goal corresponds to maximize the tool throughput while minimizing
the PM costs.
The PM scheduling optimization considers a scheduling horizon where PM tasks are specified
by "PM windows" and are delimited by a warning, due and late date, or by the amount of units
completed (e.g., wafers, kilowatt-hours), see Fig. 2.
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Time (day)
Tool
Tool 1
Tool 2
Tool 3
…
Schedul ing Horizon Present
… Warning Due Late
Figure 2. Calendar-time based PM windows.
Thus, the range of time or units completed, as indicated by a PM window, represents the
interval of time or production when a PM task can be applied. The warning represents the
earliest moment when a PM should be conducted, and the due and late dates are the suggested
and latest time to perform a PM task, respectively. The optimization algorithm assigns the
occurrence of these tasks within the associated PM windows. Thus, PM tasks have a nominal
frequency to be performed; for example, every 30 days or every 15000 wafers since the last
PM task was completed. The frequency is determined by the semiconductor fab operations and
based on recommendations from the tool’s manufacturer.
The optimization increases tool throughput and availability by determining due dates of PM
tasks, within the scheduling horizon, e.g., by avoiding periods of high incoming WIP, and
by consolidating PM tasks. Consolidating PM tasks involves scheduling PM tasks to occur
synchronously, if those tasks can be performed concurrently on the tool, thus reducing the total
time to complete all the tasks and increasing overall tool availability. When a consolidation is
obtained, PM tasks with the longest repair time are selected. Scheduling PM tasks by avoiding
periods of high incoming WIP helps ensure that the tools are not down for maintenance during
times when these are most needed.
In the next section, we present a description of the software tool PMOST, which implements
the PM scheduling optimization algorithm.
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III. PREVENTIVE MAINTENANCE OPTIMAL SCHEDULING TOOL (PMOST)
Different operational data from the process is required to formulate the MIP problem (e.g.,
estimated WIP, tool parameters, scheduling horizon). The optimization algorithm [3], [4], [5] was
originally designed to use PM tasks based on calendar-time schedules because of ease of use of
data in this format and dimensionality of the MIP. When non-calendar based PM schedules are
considered (e.g., processing-time based PM tasks), these need to be converted into calendar-time
format by using, e.g., the conversion algorithm in [6], [7].
The data inputs and outputs for the optimization algorithm are illustrated in Fig. 3 below.
As presented, the algorithm receives as data inputs a set of tools, an initial PM schedule, a
scheduling horizon, projected incoming WIP, cost parameters and constraints, as well as the
available resources. As data outputs, it generates the optimized schedule, the estimated tool
availability and the estimated WIP when the optimized PM schedule is utilized.