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Data-Driven Analysis of Downtime Impacts in Parallel Production Systems
Article in IEEE Transactions on Automation Science and Engineering · October 2015
DOI: 10.1109/TASE.2015.2443111
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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 12, NO. 4, OCTOBER 2015
1541
Data-Driven Analysis of Downtime Impacts in Parallel Production Systems
Yang Li, Qing Chang, Guoxian Xiao, and Jorge Arinez
Abstract—Accurate evaluation of the impacts of machine downtime incidents, especially those that cause the most production loss,
is of great importance for deciding where to allocate limited resources in multistage manufacturing systems. In this paper, we
focus on quantitative analysis of the impacts of downtime events in
terms of production loss based on available production information. A complex station concept is introduced to represent a single
station or a parallel structure in a production line. The dynamics of
complex stations are studied. The real-time analysis of the impact
of a downtime event in a parallel production line and in a serial production line is demonstrated to be consistent. Apart from the analytic study, a computational procedure using real-time production
information is developed. A case study is conducted to demonstrate
its potential on real-time production control and resource/budget
allocation in a multistage manufacturing system.
Note to Practitioners—In manufacturing, machine random
downtimes are a major impact on production performance.
Real-time estimation of the impacts of downtime events is potentially very useful in helping plant managers to allocate limited
resources to where they are most needed. This paper presents a
systematic method to estimate system level impacts of downtime
events in a multistage production system with parallel structures.
A practical procedure is presented to fully utilize the available
plant floor data (e.g., downtime data) to provide a quantitative
severity ranking of downtime events and associated stations,
which is very important for resource allocation and prioritizing
continuous improvement projects.
Index Terms—Continuous improvement, data-driven production system analysis, parallel production system, permanent
production loss.
I. INTRODUCTION
M
ANUFACTURING production lines with parallel structures
are widely used in many production systems to achieve a
greater productivity or reliability. A parallel structure can be split into
several sub-lines in parallel. In case one station in a parallel structure
Manuscript received January 29, 2014; revised June 24, 2014; accepted June
01, 2015. Date of publication July 06, 2015; date of current version October
02, 2015. This paper was recommended for publication by Associate Editor T.
Murphey and Editor M. P. Fanti upon evaluation of the reviewers’ comments.
This paper was supported in part by the National Science Foundation under CAREER AWARD CMMI-1351160, and the National Natural Science Foundation
of China under Grant 61273035 and 71471135.
Y. Li is with the School of Mechanical Engineering, Tongji University,
Shanghai, 201804, China (e-mail: yangmli@outlook.com).
Q. Chang is with the Department of Mechanical Engineering, Stony
Brook University, Stony Brook, New York, NY 11794 USA (e-mail:
qing.chang@stonybrook.edu).
G. Xiao is with General Motors R&D, MSR, General Motors Corporation,
Warren, Michigan (MI) 48090 USA (e-mail: guoxian.xiao@gm.com).
J. Arinez is with General Motors Research & Development Center, Manufacturing Systems Research Lab, General Motors Corporation, Warren, Michigan
(MI) 48090 USA (e-mail: jorge.arinez@gm.com).
Corresponding Author: Q. Chang, 3125 Burris Rd, Apt 12, Vestal, NY, 13850.
Phone: +86 18537888436; Email: Yangmli@outlook.com.
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TASE.2015.2443111
fails, parts can still go through other sub-lines to keep production
moving, but with a slower rate. Although tremendous efforts have
been devoted to the performance evaluation on serial transfer lines
[1]–[3], difficulties still exist in studying production lines with parallel structures because of their complex configuration. In addition,
transient characteristics can be potentially very useful in real-time
production control [4]–[9]. The transient analysis of production lines
with parallel structures is even more difficult.
To address the challenges, the advancement of sensor technologies
has enabled manufacturers to distribute sensors in manufacturing plant
floor. Different sensors are installed to measure material flow, quality
problem, equipment faults, etc. Although the wide application of sensors makes production information increasingly transient, detailed and
real time, the utilization of the information for production system performance improvement has largely lagged behind. The sensor data is
mostly used for isolated local control, but is not connected to efficiently
collect, disseminate, and interpret the information at an overall system
level [10]. Consequently, the development of a system level data-driven
method to evaluate the performance of a parallel production system is
an urgent issue not only in theories but also in applications.
Early works on parallel lines focus on evaluating their production
rate using analytical methods [11]–[15]. The performance of parallel
lines is analyzed using equivalent single stations [11]–[13]. However,
the method usually assumes only one station in each sub-line, which
is not always a practical assumption and the overall accuracy is a big
concern. [14], [15] proposes an overlapping decomposition method to
estimate the throughput of parallel lines which allows multiple stations
and buffers in sub-lines in parallel structures. The method takes into
consideration the effects from other parts of a parallel production line
by manipulating the starvation and blockage incidents at the first and
last station in each sub-line as downtime events, and a recursive procedure is applied to estimate the production rate of the system. However,
the convergence of the whole procedure is dependent on the convergence of the serial line method, and the decomposition method is based
on Bernoulli or exponential machine reliability model.
Transient characteristics have significant manufacturing implications. Production transients characterize the process of reaching the
steady state system output. Systems often operate at transient regimes.
For example, in the process of continuous improvement, the machine
parameters change every day or even every shift. Steady state can
hardly be reached. Before steady state can be reached, the system can
suffer significant production loss. Therefore, accurate evaluation of
transients in parallel production systems is of practical importance.
The transient behavior of the transfer line after a sudden station
breakdown can be approximated using metamodels in the form of
first-order continuous exponential delays function [16]. Earlier works
in [17]–[19] have studied the transient behavior of communication
networks. The main focus of the research is on the transient evolution
of the probability distribution of the buffer levels to its stationary
distribution. [20] further extends the results to transfer lines with
Bernoulli machines and characterizes the transients in the production
rate and work-in-process inventory. In [21], the second largest eigenvalue of the transient matrices is used to characterize the transients in
geometric production lines. A Markov chain approach is adopted to
develop the transition matrices. However, the large dimensionality of
the transition matrices impedes the method to be applied to systems
1545-5955 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 12, NO. 4, OCTOBER 2015
with more than two machines. Although stochastic transient analysis
can help us understand how the line dynamics change under uncertainties in a probabilistic sense, it provides little or no insight on how
a downtime event or a sequence of downtime events impact system
level performance.
Petri nets, as a graphical and mathematical tools, have been used
extensively to model and analyze manufacturing systems [22]–[25].
Reference [22] discusses the modeling of a flexible manufacturing
systems (FMS) under uncertainty and evaluation of a rule base for
on-line scheduling. Continuous-time and discrete-time stochastic Petri
nets models with hierarchical structure are developed to construct
the FMS model. Based on the FMS model, the performance of the
rule base is evaluated. [23] develops a new class of stochastic Petri
net by introducing fluid tokens. The equations for the transient and
steady-state behavior of fluid stochastic Petri nets are presented and the
utilizations of the construct in communication network modeling and
reliability is illustrated. Petri nets are usually used to represent simple
production systems with buffers, machines, automated assembly lines,
flexible manufacturing systems, etc. For large scale complex systems,
the construction of Petri net models can be difficult and computational
effort and memory requirements can be high [24], [25].
Data-driven methods have been widely used for system monitoring,
fault diagnosis and system modeling and control [26]–[31]. [29] develops a data-driven approach of key performance indicator (KPI) prediction and diagnosis for a complex industrial process. Efficient KPI
prediction and diagnosis algorithms are developed for dynamic processes based on a data-driven realization of the so-called left coprime
factorization of a process. Reference [30] proposes a data-based realtime state feedback control method for a class of nonlinear systems.
A fast sampling technique is used to sample the state signal and the
zero-order hold and the control switch are used to obtain system information. Based on the sampled data, the feedback gain matrix is calculated and adjusted. Theoretical analysis and simulation are performed
to demonstrate the feasibility of the method.
The method in this paper, on the other hand, is to focus the analysis
on a realization or sample path to study how the system dynamics and
performance measures react to changes based on available plant floor
data. More specifically, the analysis provides more detailed information
on how the line reacts to each individual dynamic event under various
initial conditions, which can be potentially very useful in understanding
system transient behavior.
Among all the dynamic events in a production system, station
random failure is arguably the most significant contributor to production inefficiency [6]. Quantitative evaluation of the impact of each
downtime event plays an essential role in many managerial decisions
at the plant floor, especially in the case of budget allocation and Kaizen
project prioritization. Knowing the true impact of downtime helps not
only avoid costly decisions but also provide control mechanisms to
improve the production efficiency.
Quantifying the true impact of each downtime incident in serial
transfer lines with only single stations serially connected with each
other and buffers are studied in previous works [6]–[9]. This paper
will extend the knowledge to multistage production lines with parallel
structures. Parallel structures impose unique challenges on quantifying
the impact of individual downtime incident. First, the dynamics of
a parallel structure with multiple sub-lines are more complicated.
A downtime event at one station in a sub-line does not necessarily
interrupt stations in other sub-lines. Instead of causing the complete
stoppage of a parallel structure, the downtime event could simply
reduce its output rate. Second, it is more difficult to separate the
starvation and blockage due to a downtime incident at one station from
the downtime incidents at other stations, especially when multiple
downtime events occur concurrently. Deciding the root cause of the
starvation and blockage is indispensable to correctly associate the
production loss to the responsible downtime incident. Third, it remains
a problem the impact of a disturbance caused by a downtime incident
on the production is temporary or permanent. The downtime at one
station may only temporarily reduce the production volume of its
adjacent stations and the production volume can eventually recover
due to the asynchronous of the line.
Therefore, each downtime event has its unique impact on the system
output and it can differ significantly regarding the line configuration,
station location and downtime duration. The objective of this paper
is to reveal the impact of each downtime event in a parallel production system and characterize its transient behavior to guide for realtime production control. The rest of this paper is organized as follows.
Section II provides the system descriptions. Section III investigates
the dynamics of a single parallel structure. Section IV investigates the
permanent production loss in general production lines with multiple
parallel structures. Numerical studies are performed in Section V to
demonstrate that the downtime analysis can assist in system performance improvement in production lines with random downtime events.
The final conclusion and discussion are summarized in Section VI.
II. SYSTEM DESCRIPTIONS
For ease of expression, a continuous flow model is adopted in this
paper to analyze the dynamics of a parallel production line, because
the production dynamics can be conveniently described by integral or
differential equations [32]–[34]. The model assumes that the quantity
of parts in a buffer varies continuously from zero to its capacity. A
production line with multiple parallel structures or single stations is
illustrated in Fig. 1. The following assumptions are made in this paper.
1) In Fig. 1, each rectangle represents a single station or a parallel
,
.
is defined as a comstructure denoted as
plex station. It is directly connected in the main production line.
. There are
comEach circle represents a buffer denoted as
buffers in the parallel production line. For
plex stations and
is also used to denote the maximum capacity of
convenience,
and
is used to denote the buffer level at time inbuffer
stant .
consists of
serial
2) As shown in Fig. 1, a complex station
. If
, there is a single station in the
sub-lines,
, there are
single stations and
complex station. If
buffers,
, in the
sub-line,
.
,
Each rounded rectangle represents a single station denoted as
station in the
sub-line,
and
which is the
. Each circle represents a buffer denoted as
, which is
buffer in the
sub-line. For convenience,
is used to
the
and
is used
denote the maximum capacity of buffer
to denote the buffer level at time instant .
3) A station is a collection of one or more automatic or manual machines (e.g., automatic wielding machines and manual lathe). Stations consisting of only automatic machines usually have constant
processing speeds. For stations consisting of manual operations,
the processing speeds could vary. For both scenarios, we can always find the smallest processing time of a station, which is referred to as the base cycle time. For a station, any production cycle
that is longer than the base cycle time will be treated as a special
random downtime event, referred to as over-cycle event. A station can be down because of tool wear, power outages, as well as
over-cycle.
denotes the speed of station
at time instant and
4)
denotes its base cycle time, with
being the rated speed.
denotes the slowest station in the
sub-line of a complex
5)
, i.e.,
. We consider
station
the situation that there is a single slowest station in each sub-line
IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 12, NO. 4, OCTOBER 2015
the permanent production loss
expressed as
1543
at the complex station
can be
(2)
Fig. 1. The layout of a production line with
complex station
.
A set
is defined to include only
. The
the slowest station in each sub-line of a complex station
and
are denoted as
notations
and
to represent the summation
of production rates of all stations in the set
without and with
, where
and
the downtime events
is the production rate of the unique slowest station in the
sub-line without and with the downtime events.
is defined
, which is the summation of the rated
as
speed of the slowest station in each sub-line of the complex station
. Then, (2) can be rewritten as
complex stations and the
of a complex station in Section III. General situations that there are
multiple slowest stations in a sub-line are discussed in Section IV.
6) In the main production line as shown in Fig. 1, the first complex
station can never be starved and the last complex station can never
be blocked, while starvation and blockage definition for a complex
station will be provided in Section III.
, denotes a downtime event (or an
7)
is down at time for .
over-cycle event) that station
8) The parallel production line is subjected to a sequence of downduring time
,
time events, denoted as
and
.
where
denotes the current time and
denotes a time before .
III. DYNAMICS OF A SINGLE PARALLEL STRUCTURE
To start the analysis of a production line with mixed single stations
and parallel structures, a complex station concept is introduced as described in the system description in Section II, Fig. 1. A complex station
is defined as a station including
sub-lines,
. There, or a
fore, a complex station could be a single station when
.
parallel structure when
Each sub-line in a complex station is a serial line. Therefore, theories
developed for serial lines from previous studies [6]–[9] can be applied.
It has been proved in [6] that if there is a single slowest station (i.e.,
the station with the smallest rated speed) in a serial production line, the
production loss occurred at the slowest station is also the production
loss of all other stations. The systematic impact of a downtime event
can be measured as the production loss at the slowest station when it is
down, starved or blocked because of the event. This production loss is
denoted as the permanent production loss caused by the event.
at the
sub-line
Suppose there is a downtime event
. The permanent production loss
caused by
of complex station
the event can be measured as
(1)
where
and
are the production
without and with downtime event during
volume of station
. It is noted that
can be measured in normal
is just the rated speed
of
production and the rate
.
station
It is clear that the permanent production loss due to downtime events
at a complex station is the summation of permanent production losses
is subject to
at all its sub-lines. Assume that a complex station
during
,
a sequence of downtime events
(3)
can be measured in normal
Similarly, the value of the rate
is just
. Therefore, any disturbance
production and the rate
contributes to a perevent resulting in a decrease of the rate
.
manent production loss of the complex station
In serial lines, it is well defined that a station is starved if it is up and
the upstream buffer is empty, and a station is blocked if it is up with
the downstream buffer is full and the downstream station does not take
a part from this buffer. However, there is no straight forward definitions for starvation and blockage of a complex station. For a complex
, even its upstream buffer is empty,
may still have WIP
station
which may maintain the same production rate of the complex station.
is full and the downstream
Similarly, if the downstream buffer of
may still have availmachine does not take a part from this buffer,
able space which can accept parts from its upstream complex stations.
Therefore, a complex station can be reasonably treated as being starved
or blocked if the duration of the upstream buffer being empty or the
downstream buffer being full is long enough to cause the rate
to decrease.
in front of a complex station
Definition 1: Assume buffer
is empty, this event can be denoted as
to represent
is empty at time for a duration of .
is defined to be
buffer
causes permanent production loss at
as evaluated in
starved if
(3).
in the downstream of a complex
Definition 2: Assume buffer
is full, and the downstream station
does not take a
station
, this event can be denoted as
part from the buffer
to represent buffer
is full at time for a duration of
.
is defined to be blocked if causes permanent production loss
as evaluated in (3).
at
Note that this definition is applicable for a complex station consisting
of single station or multiple sub-lines. In the case of single station,
or causes immediate stoppage of the station
.
IV. ANALYSIS OF A SEQUENCE OF CONCURRENT DOWNTIME EVENTS
IN A PARALLEL PRODUCTION LINE
In this section, we will discuss how downtime events impact a parallel production system with multiple complex stations. It is not unusual that there may be multiple slowest complex stations in a parallel
production line, where a slowest complex station
is defined as
the complex station with the smallest rated speed
, i.e.,
. The output of the end-of-line complex station is used as the output of the line [3], [34], and permanent production
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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 12, NO. 4, OCTOBER 2015
loss at this end-of-line complex station is defined as the permanent production loss of the line. The following Proposition 1 will prove that the
permanent production loss of a production line can be evaluated with
the production loss at the last slowest complex station, where the last
slowest complex station refers to the slowest complex station being
closest to the end-of-line complex station. For convenience,
is
used to refer to the last slowest complex station.
Proposition 1: Given a realization of the production process subject
to a sequence of downtime events
during
,
for the end-of-line complex station
the necessary and sufficient condition for permanent production loss
because of a downtime event
is
(7)
and
.
is the time for buffers between the first station
and station
in the
sub-line of the complex station
to become full. Similarly,
one can always find the smallest possible downtime duration
such
that (7) is satisfied, i.e.,
where
(8)
(4)
Proposition 1 indicates that if a downtime event causes a production
loss to the last slowest complex station
, then it also causes the
same amount of permanent production loss to the production line. This
naturally applies to a production line with a unique slowest complex
station since the slowest station is one that is closest to the end-of-line
station.
Additionally, Proposition 1 also applies to serial production lines
when all the complex stations consist of single stations. Therefore,
to make the paper consistent, we redefine the notation
as the
last slowest station in the
sub-line of a complex station
. Then,
based on Proposition 1, the permanent production loss of a complex
station
caused by a disturbance event can still be evaluated using
(3). Therefore, Definitions 1 and 2 for a complex station being starved
and blocked keep unchanged.
Evaluating the impacts of downtime events to a production line with
multiple complex stations are very important in real-time production
control, such as prioritizing the limited resources to the most needed
location. To understand the permanent production loss caused by an
arbitrary downtime event, analyzing the starvation and blockage condition of the last slowest complex station is important. For convenience,
we use
and
to denote
is starved and
blocked at a given time , and
and
denote
that
is not starved or blocked at .
Proposition 2: Given a realization of the production process
subject to a sequence of downtime events
during
,
, the necessary and sufficient
condition for permanent production loss because of a downtime event
is
(5)
where
and
.
is the time for buffers between station
and the end-of-line
station
in the
sub-line of the complex station
to become
empty. Based on Proposition 2, one can always find the smallest possible downtime duration
such that (5) is satisfied, i.e.,
(6)
Proposition 3: Given a realization of the production process subject
to a sequence of downtime events
during
,
Proposition 4: Given a realization of the production process subject
during
,
to a sequence of downtime events
the necessary and sufficient condition for permanent production loss
because of a downtime event
is
(9)
where
.
(10)
.
is the time for buffers between station
and the slowest station
in the
sub-line of the complex station
to become empty
or full
. We can always find the shortest possible
downtime duration of the downtime event such that (9) is satisfied
(11)
of a downtime event
The smallest possible downtime duration
which will not cause permanent production loss for the line can be
evaluated using (6), (8), and (11). The threshold
is defined as the
opportunity window of the station
. If the actual downtime duration
is less than this threshold , there is no permanent production loss.
However, if
exceeds , the permanent production loss due to
becomes nonnegative. The opportunity window
for the station
is the time it takes, from time , for the last slowest complex station
to just become starved
or blocked
.
However, to link the permanent production loss to associated downtime events in a parallel system becomes more complicated than in
a serial line. In serial lines, the last slowest station only operates at
two speeds: its rated speed and zero. The permanent production loss
caused by a downtime event
in a serial line is proportional to
and can be expressed as
, where
is the downtime duration and
is the opportunity window of the
station
at time . However, in a parallel production system, the last
slowest complex station can operate at more than two rates, and its rate
keeps changing. Therefore, it is very difficult to evaluate
the permanent production loss based on the changing
. For
a downtime event
, the value
only indicates
the longest possible duration of a permanent production loss caused by
. There is no simple proportional relationship between the permanent
production loss and the value
in parallel systems.
IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 12, NO. 4, OCTOBER 2015
1545
For ease of discussion, a notation
is used to represent a permanent production loss caused by a downtime event . For a parallel
system subjected to a sequence of downtime events
,
when contains only one downtime event
, the
permanent production loss of the system caused by
can be calculated based on Proposition 1 as
(12)
is the opportunity window of the station
, which can be
where
determined from (6), (8), or (11) depend on the location of
.
If
contains more than one downtime event, the rate
keeps changing subject to downtime events
. In addition, it
,
is possible that two or more downtime events will overlap, i.e.,
. In this case, it is even more difficult to
evaluate the permanent production loss and attribute the loss to associated downtime events. For convenience, a notation
is adopted to denote whether a downtime event causes permanent
production loss. Specifically,
indicates that the event
does not result in permanent production loss and
indicates
that the event causes permanent production loss.
Usually, the starvation, blockage and breakdown events of every
complex station can be obtained from production lines. Using real data
or simulation, it can be determined if a complex station is starved or
blocked based on Definitions 1 and 2. In addition,
can be easily
determined based on Propositions 2 to 4. Then the permanent production loss caused by a downtime event to overall system can be calculated as
(13)
It is possible that two or more different downtime events may result
in overlapping permanent production loss. It is reasonable to attribute
the permanent production loss to associated downtime events by using
any allocation rules. For example, the permanent production loss in
the overlapping period can be equally shared among the corresponding
events [6].
The permanent production loss caused by each station can also be
quantified. The permanent production loss of each disruption event can
be further aggregated and attributed to the corresponding stations. Assume that there is a sequence of disruption events
caused
by station
. The permanent production loss caused by
can be
represented as
(14)
It is important to note that if all complex stations in a general production line include only one sub-line with one single station, then it
becomes a serial production line, which is actually a special case of a
general production line. Therefore, with the complex station concept,
the above analysis unifies serial production lines and parallel production lines.
V. NUMERICAL EXAMPLE AND RESULT
Although the above analysis is based on a deterministic system, we
can numerically prove that the permanent production loss can provide
a good indicator or priority in reducing machine downtime to improve
system performance and output. Extensive numerical studies are performed and one simulation study is selected to illustrate the point.
Fig. 2. Layout of the machining line. (a) The original production line. (b) The
virtual serial production line.
TABLE I
PARAMETERS OF BUFFERS IN THE PARALLEL PRODUCTION SYSTEM
TABLE II
PARAMETERS OF STATIONS IN THE PARALLEL PRODUCTION SYSTEM
A production line used in this simulation case study is shown in
Fig. 2. Fig. 2(a) shows the original production line and Fig. 2(b) shows
the virtual serial production line with complex stations. The production
line consists of four complex stations and three buffers with complex
and
to be parallel structures and
and
to be single
stations
stations. Parameters of the production line is shown in Tables I and II,
which are modified data from a real production line, for confidential
reasons. The parameters include initial buffer levels, buffer capacities,
station cycle time, mean time between failure (MTBF), and mean time
to repair (MTTR). It is assumed that there are exponential distributions for MTBF and MTTR for convenience. In addition, there are two
maintenance staff on the plant floor. A breakdown station can only be
repaired by the available maintenance staff.
Fig. 3 demonstrates the permanent production loss of each station on
a per shift basis over a 6 shift period. The permanent production loss is
determined based on (14). It can be observed that the permanent production loss caused by downtime events varies shift-to-shift for each
station. Allocating permanent production loss to each downtime event
and station can naturally represent the performance of each station.
This provides a possible indication of resource allocation rule: prioritizing the highest permanent production loss stations. Fig. 4 demonstrates accumulated permanent production loss for each station during
a 6 shift period.
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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 12, NO. 4, OCTOBER 2015
Fig. 5. The accumulated blockage and starvation time of each station.
Fig. 3. Attributed permanent production loss at the station level due to random
downtime events.
Fig. 6. Comparison of the system output before and after maintenance schedule
change.
TABLE III
EXTRA PRODUCTS BOTTLENECKS SHOULD PRODUCE IN SHIFT 6
Fig. 4. The allocated permanent production loss of each station.
In earlier works [8], [9], a bottleneck is proved to be the station that
its upstream stations have more blockage time than starvation time and
downstream stations have more starvation time than blockage time.
Based on the accumulated blockage and starvation time of each sta,
, and
(marked by arrows)
tion shown in Fig. 5, stations
are found to be bottlenecks. In Fig. 4, stations
,
, and
have
the highest accumulated permanent production loss. The stations with
the highest permanent production loss indicate the exact same bottlenecks. Although the bottleneck identification methods in [9], [35], and
[36] can identify all the local bottlenecks, the significance of the bottlenecks is just based on heuristics. It is important to note that the permanent production loss method provides quantitative evaluation of the
impact of each downtime event to the overall system, and therefore
provides a quantitative real-time production control guidance, such as
prioritizing the resource or budget to the station which has the highest
permanent production loss. We further illustrate the point with the following scenarios.
To improve the overall system performance, three maintenance policies are adopted. In policy 1, the maintenance priority is based on
first-come-first-serve basis, i.e., no production control. This is the base
case. In policy 2, the maintenance priority is based on the ranking of
permanent production loss. In policy 3, the maintenance priority is
based on the aforementioned bottleneck method. Since the bottleneck
method cannot provide the exact ranking, it is assumed that the top
three bottlenecks have the same maintenance priority without losing
generality.
Fig. 6 illustrates the system output comparisons of the three maintenance policies. The result shows that the permanent production loss
based policy can lead to the largest production improvement comparing
with the base policy and the bottleneck based policy. It can be concluded that the permanent production loss method can bring more benefits than the existing bottleneck identification methods by providing a
severity ranking of bottlenecks.
An alternative way to improve the system output is to make the bottlenecks work extra time, which is not an unusual practice in the plant
floor operation. A natural question arises about how much extra time
or how many extra products the bottlenecks should work. Although
the existing bottleneck analysis can identify one or more bottlenecks,
there is no detailed information of the quantifiable impact of each bottleneck to the overall system. In practice, the extra time or effort are
estimated based on engineers’ experience or heuristic rules. However,
evaluating the permanent production loss of each station can provide a
quantifiable solution. For the same simulation study, the top three stations causing the largest permanent production loss amount are summarized in Table III. It is validated that by making up for the amount
of loss of each station will increase the same amount of system output.
VI. CONCLUSION AND DISCUSSION
In this paper, the concept of complex station is introduced to represent a single station or a parallel structure in a production line. The
dynamics of a single complex station and general production line with
complex stations are studied. This research unifies the analysis of serial
production line and parallel structures in terms of downtime impacts.
The analysis suggests that the impacts of any downtime events are only
apparent when the last slowest complex station is starved or blocked.
IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 12, NO. 4, OCTOBER 2015
The quantitative results of the event-based allocation provide a natural
ranking of stations in terms of permanent production loss. The numerical analysis indicates that the natural ranking can be useful for resource
allocation and prioritizing continuous improvement projects.
In the future, the relationship between production loss ranking and
throughput bottleneck relations will be further investigated. A real-time
production control method will be further developed.
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