Flexible Manufacturing System Optimization by Variance
Minimization: A Six Sigma Approach Framework
Wa-Muzemba Anselm Tshibangu
Department of Industrial and Systems Engineering, Morgan State University,
1701 E Cold Spring Lane, Baltimore, MD 21251, U.S.A.
Keywords: Lean Six Sigma, Robust Design, Optimization, Doe, Fms, Variance Minimization, Simulation.
Abstract: From the performance view point, manufacturing strategy relates to the decision about where to focus
concentration among quality, speed, dependability, flexibility and cost. This study analyzes a hypothetical
flexible manufacturing system (FMS) and aims to illustrate an optimization procedure based on a variance
reduction applied on two strategic performance measures, namely the Throughput Rate (TR) and the Mean Flow
Time (MFT). The study uses a Taguchi robust design of experiments (DOE) methodology to model and simulate
the hypothetical FMS, analyzes the output of the simulations, then proposes a unique and hybrid (empirical-
analytical) methodology to quickly uncover the optimal setting of operating parameters. The robust design is used
to guarantee the system stability necessary to improve the system and validate the outcomes. Using the key
principle of the Six Sigma methodology that advocates a reduction of variability to improve quality and processes
the proposed methodology quickly reaches a near optimum by considering both the main and interaction effects
of the control factors that will minimize the variability of the performances. Fine-tuned follow-up runs may be
necessary to compromise and uncover the true optimum.
1 INTRODUCTION
Accomplishing excellence, global competition, and
catching up with the rapid technological changes and
advances in manufacturing and information
technology, are forcing manufacturers to optimize all
possible manufacturing processes and operations for
the purpose of delivering high quality products in a
short period of time. Achieving the above requires a
strategic decision-making at the corporate level that
involves the coordination of additional sub-strategies
for marketing, engineering, manufacturing, research
and development.
At the tactical and operation levels a variety of
approaches, including mathematical programming,
queuing networks, computer simulation, Artificial
Intelligence (AI), and others, are among the most
proposed techniques for the design and control of
production and manufacturing systems. When it comes
to find the best and optimal setting of the operational
parameters Lean Six Sigma is emerging nowadays as
one of the most rapid and powerful techniques for
process and/or system continuous improvement. It has
been noticed however, that the usefulness and
appropriateness of any of these techniques depend on
the nature of the problem and systems under
consideration.
The drastic reduction of product life cycles has lead
manufacturing flexibility to become a competitive
weapon in many industries, increasing the popularity
of Flexible Manufacturing Systems (FMS). The
performance of an FMS is influenced by several
complex design and operational control" issues
requiring an optimal setting of operational parameters.
Thus, the problem of identifying the most optimal
configuration of FMSs is gaining importance in today’s
operation and production management strategies. For
that reason this study simulates a flexible
manufacturing system. The selection of a poor, non-
suitable or inappropriate combination of an FMS’s
Tshibangu, W-M.
Flexible Manufacturing System Optimization by Variance Minimization: A Six Sigma Approach Framework.
DOI: 10.5220/0006436702950303
In Proceedings of the 14th Inter national Conference on Informatics in Control, Automation and Robotics (ICINCO 2017) - Volume 1, pages 295-303
ISBN: 978-989-758-263-9
Copyright © 2017 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
295
design variables and control measures may
consequently lead the system to exhibit
counterproductive behaviors in the form of work-in-
process storage queues, vehicle blocking due to path
contention, and even a shop locking phenomenon. The
proposed model used in this study results in smooth
materials and vehicles flow, high productivity
environment free of adverse behaviors.
The research is motivated by both the Six Sigma
governing principle, that seeks performance
improvement through a reduction of variability and the
Six Sigma methodology that uses the DMAIC roadmap
to seek and implement the best solution.
Lean and Six Sigma principles based on Little’s
law and reduction of variance, respectively recommend
a stable system or process before implementing an
improvement/optimization scheme. Robust DOE is
used to render the system insensitive to uncontrollable
factors (noise) and guaranty system stability.
Simulation is used because it becomes difficult if not
impossible to apply strict analytical models to study
manufacturing systems behaviors.
The optimization of the modeled system is
subsequently implemented and achieved through a
minimization of the performance variation followed by
an optimal adjustment of the performances mean.
2 LITERATURE REVIEW
There is still a limited number of reported system
optimization using Lean, Six Sigma or both combined.
Sharma (2003) mentions that there are many
advantages of using strategic Six Sigma principles in
tandem with lean enterprise techniques, which can lead
to quick process improvements. More than 95% of
plants closest to world-class indicated that they have an
established improvement methodology in place, mainly
translated into Lean, Six Sigma or the combination of
both. “Lean” is an integrated system of principles,
practices, tools and techniques that are focused on
reducing waste, synchronizing workflows, and
managing production flows (de Koning and de Mast
2006). Shihata (2014) applies “Lean” technique to
optimize the flow of solutions in a refrigerator
assembly line. David Forgaty (2015) uses Lean Six
Sigma to optimize the process of bid data extraction in
manufacturing. Valles et. al 2009 use a Six Sigma
methodology (variation reduction) to achieve a 50%
reduction in the electrical failures in a semi-conductor
company dedicated to the manufacturing of cartridges
for ink jet printers. Han et al. 2008 also use Six Sigma
technique to optimize the performance and improve
quality in construction operations.
The pursuit of optimization has intensified the
demand for higher process/product development speed,
manufacturing flexibility, waste elimination, better
process control, and efficient manpower utilization to
gain competitive advantages (Karim et al.2010). The
Six Sigma philosophy maintains that reducing
‘variation’ will help solve process and business
problems (Pojasek, 2003). The strategic use of Six
Sigma principles and practices ensures that process
improvements generated in one area can be leveraged
elsewhere to a maximum advantage, resulting in
quantum increasing product quality, continuous
process improvement resulting in corporate earnings
performance (Sharma 2003).
3 SYSTEM CONSIDERATIONS
There are 9 machines (workstations) in the system to
process 15 different part types (jobs). Seven of these
workstations are typical machining centers, such as
turning, milling, drilling, etc. The two remaining
stations are used as a receiving station for loading
when jobs enter the system, and a shipping station for
unloading when the jobs exit the system.
The throughput rate (TR) and the mean flow time
(MFT) are used to track the performance of the
simulated system. Note that these indicators also give a
measure of a third one, the work-in-process (WIP)
through Little’s law, considered as the backbone
equation governing Lean principles. The two indicators
have been selected to serve the purpose of this research
while additional measures such as Machine Utilization
(MU) and AGV Utilization (AU) are also used in this
study, more as benchmarks to evaluate the goodness of
the developed model.
The research considers a sequence of machine
visitation with a number of operations uniformly
distributed between 2 and 8. The corresponding
processing times range from 5 to 30 minutes. Table 1
illustrates the shop conditions. The processing of jobs
within the FMS is modeled, following the basic
assumptions (Tshibangu 2013).
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Table 1: Shop Configuration.
Part Types Considered for
Production
15
Arrival Time Between Parts
EXPO(5) and EXPO(15)
Machines (Workstations)
9 (including one loading
and one unloading
stations)
Queue Discipline
FIFO, SPT
Material Handling System
(AGV) - Size
Variable from 2 to 9
Speed of AGV
100-200ft/min
AGV Dispatching Rule
FCFS, STD
Buffer Capacity
8 to 40 for workstations
2 to 8
Infinite for workstation 1
Loading/Receiving Sations
1 (workstation 1)
Unloading/Shipping Stations
1 (workstation 9)
Path Direction
Mixture of uni- and bi-
directional paths
4 THE ROBUST DESIGN
A robust system immune to the noise factors during the
actual operations will secure a valid optimization
procedure as the Six Sigma technique assumes a stable
and predictable system. Lean Six Sigma also advocates
the use of a roadmap methodology known as DMAIC
(Define- Measure-Analyze-Improve and Control). This
study follows a similar procedure. In the following
sections each one of these steps will be referred to with
the initial letter, e.g., D, M, A, I, C.
4.1 Formulating the RD Problem - (D)
The objective in formulating a robust design problem
is to find those control factor settings for which noise
has a minimal effect on the performance measures.
Three concepts are needed to define in a precise
manner the robust design problem): (i) functional
characteristics, (ii) control parameters, (iii) and sources
of noise.
4.1.1 Functional Characteristics
These are basic, measurable quantities that determine
(from the management or the experimenter perception)
how well and how smoothly the manufacturing system
operates. The functional characteristics of this study
are the performance measures. Five measures are
computed but only two (TR and MFT) will be used in
the illustration of the single optimization formulation
model. The other three (machine utilization, material
handling system utilization and work-in-process) are
monitored and used as guideline or benchmarks to
evaluate the goodness of the developed model.
4.1.2 Control Factors
Also referred to as controllable inputs or process
variables, their operating values are fixed by the
engineering management team and/or by the top
management of the firm. This research considers five
input variables: fleet size (number of AGVs), vehicle
speed (speed of AGVs), queue discipline (machine
scheduling rule), AGV dispatching policy, and buffer
size. Control parameters can be controlled both in the
real world and during the simulation runs.
4.1.3 Sources of Noise
Sources of noise in contrast are identified as the
variables that are impossible or expensive to control in
the real world but can be controlled during the
simulation experiments. This research study considers
interarrival rate and machine reliability as source of
noise. They will be varied at two different levels
during simulation. Machine reliability is considered
through the Mean Time Between Failure (MTBF) and
Mean Time To Repair (MTTR).
4.2 Operational Steps for RD
Implementing the robust design formulation as applied
throughout the next sections of the study requires the
following steps:
1. Define the performance measures of interest,
the controllable and uncontrollable factors.
Flexible Manufacturing System Optimization by Variance Minimization: A Six Sigma Approach Framework
297
2. Plan the experiment by specifying how the
control parameter settings will be varied and
how the effect of noise will be measured.
3. Carry out the experiment and use the results to
predict improved control parameter settings
(optimization).
4. Run a confirmation experiment to check the
validity of the prediction.
4.3 Experimental Conditions
Knowing that material handling dynamic introduces a
lot of randomness in an FMS and because one of the
objectives is to design a robust system, this research
considers mainly those parameters that are directly
related to the material handling system performance.
It should be noted that the machine utilization
(MU) is not directly taken into account as a
performance criterion because an FMS is a highly
capital intensive system. Thus, it must operate at a high
machine utilization of 85% or above.
The WIP is not considered as a direct objective
performance but rather is monitored as a benchmark as
it is directly related to the two performance measures
studied through Little’s law. This law, also known as
the Lean methodology governing equation and first
principle of manufacturing systems, states that the
work-in-process (WIP) is directly proportional to the
flow time (lead time), the proportionality constant
being production exit rate (TR).
AGV utilization is not included in the developed
model as a primary objective function either. However,
it is used as secondary objective function and indicator
of the system congestion. An AGV system utilization
rate of 100% suggests that the system is highly
congested while an utilization in the range of 80-90%
indicates rather a highly smooth flow of material in the
system. AGV utilization values less than 70% suggest
a poorly used vehicle fleet.
Also, although the research is particularized only to
two functional characteristics, the developed and
proposed model is a generalized model that can
accommodate as many characteristics as needed for a
specific experiment, research and/or application.
4.4 Simulation Experiments - (M)
To formulate the robust design and be able to
subsequently (in a further research study) construct a
metamodel for the simulated FMS, a 2
v
5-1
experimental
design augmented with five center points is used. It
should be noted that adding a center point to a 2
k
factorial design is a method that will provide some
protection against pure quadratic effects that can be
easily captured by a 3
k
because to fit a quadratic
model, all factors must be run at least at three levels.
Since a 2
k
design will support main effects plus
interactions model, some protection against curvature
is already inherent in the design (Tshibangu 2013).
One can test to determine if the quadratic terms are
necessary. Table 2 and Table 3 depict the experimental
values for the control and noise factors,
respectively.The center points consist of n
c
(n
c
= 5 in
this study) replicates run at the point x
i
= 0 (i = 1,2,…,
k).
The experimental design under this study resulted
into 21 various configurations across all eight noise
factor combination.
Table 2: Settings of the Control Factors.
Factor
Control Factor
Low
Level
(-1)
High
Level
(+1)
Center
Point
(0)
X
1
Number of
AGVs
2
9
(6)
X
2
Speed of AGV
100
200
(150)
X
3
Queue
Discipline
FIFO
SPT
(SPT)
X
4
AGV
Dispatching
Rule
FCFS
SDT
(SDT)
X
5
Buffer Size
8
40
24
After the robust design process was completed, the
experimental runs were carried out accordingly. The
output results of the various simulation experiments are
partially displayed in Tables 4 and 5 just for illustration
purpose. These results are the average of the three
replications used in this research study.
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Table 3: Settings of the Noise Factors.
Designation
Low Level (-1)
High Level (+1)
X
6
EXPO(15)
EXPO(5)
X
7
EXPO(300)
EXPO(800)
X
8
EXPO(50)
EXPO(90)
A well-planned experiment makes simple the analysis
needed to predict the improved or optimal parameter
settings. In this research, 8 measurements (over the set
of noise factor combinations) are taken for each
performance measure of interest, i.e., throughput rate,
mean flow time, machine utilization, work-in-process,
AGV utilization, for each of the 21 simulated design
configurations over a set of 8 noise combinations, and
averaged across three replications.
The expected value of each function estimate is
obtained by simulating the system for 60,000 minutes
with 3 independent replications. For each replication, a
warm-up time of 15,000 minutes is set in order to
remove the initial transient effects. The remaining
45,000 minutes represent more or less a month
continuous operation. For each design configuration
simulated, the mean
y
and the variance
2
of these 3
independent replications have been estimated.
Table 4: TR Simulation Results (parts/day).
Noise
1
Noise
2
Noise
3
Noise
4
Noise
5
Noise
6
Noise
7
Noise
8
Des 1
53.87
94.00
33.63
91.87
99.70
76.13
77.23
61.17
Des 2
25.47
25.93
23.23
25.70
26.00
25.63
25.63
23.93
Des 3
90.13
95.37
68.13
93.43
99.80
83.03
100.70
92.40
Des 4
24.40
24.13
22.07
23.87
25.47
22.60
25.07
23.30
Des 18
41.07
93.97
32.80
91.87
99.63
76.03
46.83
44.20
Des 19
25.87
26.03
25.17
26.23
26.23
25.90
25.77
24.23
Des 20
89.53
96.37
70.97
93.27
99.33
83.00
101.83
94.63
Des 21
91.23
95.77
73.17
92.30
99.93
84.10
101.23
91.80
Because the intent is to minimize the Var TR and MFT
the variances with respect to noise factors (variance
(wrtnf)
) are computed for each run. Table 6 partially
depicts the values of
i
y
and log
2
(wrtnf)i
at various
design configuration for each of the two primary
performance. The logarithm of
2
wrtnf
is taken to
improve statistical properties of the analysis. The
objective of the proposed scheme is to quickly seek
Table 5: MFT Simulation Results (min/part).
Noise
1
Noise
2
Noise
3
Noise
4
Noise
5
Noise
6
Noise
7
Noise
8
Des 1
18.99
1.83
32.8
0.26
0.45
4.26
11.98
16.12
Des 2
43.47
33.06
45.07
32.81
34.7
32.63
43.72
43.74
Des 3
8.71
0.81
7.61
1.22
0.38
2.07
8.03
7.99
Des 4
42.34
17.73
40.42
21.07
29.88
14.21
42.45
40.62
…..
…..
.....
…..
…..
….
…..
…..
…..
Des 18
26.14
1.18
33.77
1.7
0.45
4.28
21.99
23.69
Des 19
43.95
34.92
43.13
34
34.73
34.75
43.93
44.46
Des 20
8.6
0.93
7.63
1.77
0.33
2.09
7.98
8.03
Des 21
8.6
1.08
7.68
1.36
0.44
2.08
8.05
7.96
for a near optimum by making TR and MFT variances
as small as possible and while shifting their means as
close as possible to maximum and minimum,
respectively. The focus is to minimize the variances.
For each design configuration,
2
wrtnf
is first calculated
before deriving the log
2
(wrtnf)i
that will be used to
enhance analysis sensitivity.
Table 6: Average and Log
2
(wrtnf)i
for TR (parts/day)and
MFT (min/part).
Design
Config.
MFT
i
y
MFT log
2
(wrtnf)i
Design
Config.
TR
i
y
TR
log
2
(wrtnf)i
Des 1
10.84
2.12
Des 1
73.45
2.71
Des 2
38.65
1.52
Des 2
25.19
0.02
Des 3
4.60
1.15
Des 3
90.38
2.05
…..
…..
…..
…..
.....
......
Des 9
18.09
1.32
Des 18
.....
......
Des 10
3.92
0.97
Des 19
65.8
2.86
……
……
Des 20
25.68
-0.34
Des 20
4.67
1.13
Des 20
91.12
2
Des 21
4.65
1.13
Des 21
91.191
1.91
4.5 Effects on Variances and Means - (a)
After calculating the log
2
(wrtnf)i
for each design
configuration defined in the robust DOE formulation,
the effects of each control factor on the mean and the
variance (or log
2
wrtnf
) are calculated by using the
normal probability data plotting technique.
The computed effects at high and low level will be
used in identifying the controllable factor levels
(settings) that have the largest effect on log
2
wrtnf
. The
results of the effects of various input factors on TR and
MFT variances are given in Tables 7 and 8. It can be
Flexible Manufacturing System Optimization by Variance Minimization: A Six Sigma Approach Framework
299
seen (in bold) for instance, that for TR, the control
factor X
1
(fleet size) has the highest effect on the
variance while the parameter X
3
(queue discipline) has
the most significant effect on the mean flow time
variability. Figures 1 and 2 provide a Minitab visual
display of control factor’s magnitude effect on the
performance variabilities.
The same procedure is applied to TR and MFT
means
y
in order to determine the effects of the
control parameters on these two performance measures
as depicted in Tables 10 and 11.
Once identified, these factors will be set at the
settings (levels) that minimize log
2
wrtnf
. The author
had proposed a four-step optimization procedure
(Tshibangu 2013) that represented a departure from the
traditional approaches in the sense that interactions
between factors were for the first time considered and
integrated in the optimization approach. Interaction
effects on both TR and MFT log
2
(wrtnf)
MFT are
depicted in Figures 3 and 4 for illustration purpose.
Table 7: Effects of the Control Factors on Log 2(wrtnf) TR.
Control
Factors
Effect TR log
2
wrtnf
at Level (+1)
Effect TR log
2
wrtnf
at Level (-1)
Delta
X
1
2.57
0.05
2.53
X
2
1.463
1.08
0.38
X
3
1.26
1.36
-0.10
X
4
1.29
1.33
-0.04
X
5
1.20
1.46
-0.26
Table 8: Effects of Control Factors on Log 2(wrtnf) MFT.
Control
Factors
Effect MFT log
2
wrtnf
Level (+1)
Effect on log
2
wrtnf
at Level(-1)
Delta
X
1
1.62
1.66
-0.04
X
2
1.61
1.56
0.05
X
3
1.49
1.78
-0.29
X
4
1.63
1.64
-0.01
X
5
1.60
1.67
-0.07
Table 9: Effects of Control Factors on TR.
Control
Factors
Effect TR Avg.
at Level (+1)
Effect TR Avg.
at Level (-1)
Delta
X
1
76.31
34.97
41.34
X
2
58.18
55.00
3.17
X
3
58.35
52.94
5.40
X
4
55.60
55.69
-0.10
X
5
53.00
55.08
-2.09
Table 10: Effects of Control Factors on MFT.
Control
Factors
Effect MFT Avg.
at Level (+1)
Effect MFT Avg.
at Level(-1)
Delta
X
1
8.25
25.97
-17.73
X
2
12.63
20.90
-8.267
X
3
13.86
20.35
-6.49
16.97
17.24
-0.27
X5
17.61
16.60
1.01
Figure 1: Effects of Control Factors on Log 2(wrtnf) TR.
Figure 2: Effects of Control Factors on Log 2(wrtnf) MFT.
4.6 Optimization Procedure - (I, C)
Let us assume that X
v
T
, X
m
T
, and X
0
T
, are not empty sets
representing the vectors of controllable factors that
have a significant effect on the variance, the mean, and
neither, respectively. Implementing the four-step
optimization procedure (Tshibangu, 2013) for TR the
following results are obtained at the end of Step 3, just
before the follow-up confirmatory runs (Step 4): X
v
T
:
[X
1
(-1), X
2
(-1)], pending tradeoff (X
1
and X
2
need
adjustment and follow-up)
X
m
T
: [X
5
(-1)], confirmed,
X
0
T
: [X
4
(-1), X
5
(-1)], confirmed.
Small follow-up experiments are needed to
determine the tradeoff and economical settings, while
adjusting the mean to optimum when possible. Factors
needed in the follow-up and mean adjustment runs are
X
1
(-1), X
2
(-1). X
2
is used as tuning factor to adjust the
mean. Its effect on the mean is tested at level (-1) first,
and levels (+1) and (0) next. A quick look at the
collected data (Table 4) reveals that levels (0) and (+1)
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300
Figure 3: Interaction Effects of Control Factors on Log
2
(wrtnf)
TR.
Figure 4: Interaction Effects of Control Factors on Log
2
(wrtnf)
MFT.
are the best X
2
(AGV speed) settings for mean
improvement. However, this has to be confirmed by
the results of the follow-up runs. Because X
1
has a
large effect on both mean and variance in opposite
directions, then a trade-off is found at the center point.
Based on this analysis, the most robust optimal setting
is implemented as displayed in Table 11.
Table 11: Most Robust TR Design Configuration.
Factor
Variable Name
Value-code
Natural Value
X
1
AGV Fleet Size
0 (-1?)
6 (3)
X
2
AGV Speed
0 (-1?)
150 (100) ft/min
X
3
Machine Rule
+1
SPT
X
4
AGV Rule
-1
FCFS
X
5
Buffer Capacity
-1
8 units
Note that this design configuration is not among the 21
designs originally simulated. This illustrates the
powerfulness of the applied approach.
Follow-up and confirmatory experiments have been
carried out under these system conditions. The results
of the follow-up indicate that setting X
2
at level (0) is
the best implementation in terms of TR maximization.
In addition, the follow-up runs also confirm the first
intuition about X
1
trade-off level. The center point has
been proven to be the best compromise. Because X
1
is
also considered as the most expensive component or
input parameter to implement, the overall economical
setting was confirmed by varying the AGV fleet size (3
to 8 AGVs) around the value found to be the optimal
with regard to the throughput rate. The final design to
be implemented as optimal is therefore, X
1
(0), X
2
(0),
X
3
(+1), X
4
(-1), X
5
(-1).
Machine utilization, WIP, and AGV utilization are
additional information that can be used in deciding
which system configuration to implement. At this
stage, the implemented design, highlighted in bold in
Table 12 seems to represent the best option leading to
the highest TR (100 parts/day), an excellent machine
utilization (89.73%), an acceptable WIP (81 parts/day)
and a relatively high AGV utilization (97.87%).
The equivalent optimal performance under failure-
free robust design configuration is indicated between
parentheses in the optimum column (6 AGVs).
Table 12: TR Optimization Follow-Up/Confirmation Runs
under various AGV Fleet Size (X
1
) and AGV Speed (X
2
).
X
2
X
1
(*) System saturated
5 AGVs
6 AGVs
7 AGVs
8 AGVs
9 AGVs
TR
100
TR
150
TR
200
(TR*
ZF
)
(parts/day)
*
87.57
99.80
*
100
99.90
(100)
87.67
99.87
99.83
99.73
100
99.90
99.87
99.93
99.93
MU
100
MU
150
MU
200
(MU*
ZF
)
(%)
*
79.70
89.71
*
89.73
89.79
(89.72)
79.47
89.76
89.77
89.55
89.78
89.76
89.77
89.77
89.76
WIP
100
WIP
150
WIP
200
(WIP*
ZF
)
(parts/day)
*
377
78
*
81
77
(81)
380
79
78
100
78
79
81
80
80
Flexible Manufacturing System Optimization by Variance Minimization: A Six Sigma Approach Framework
301
Table 13: Most Robust MFT Design Configuration.
Factor
Variable Name
Coded
Value
Natural
Value
X
1
AGV Fleet Size
+1
9
X
2
AGV Speed
+1
200
ft./min
X
3
Machine Rule
+1
SPT
X
4
AGV Rule
-1
FCFS
X
5
Buffer Capacity
-1
8 units
Note that if X
2
(AGV speed) has been set at high level
(+1), i.e., 200 ft./min, there would have been a slight
depreciation in the TR, almost 5% decrease in WIP,
and an excellent AGV utilization. The AGV utilization,
excluded from the table for space reason, ranged from
89.20% to 100% with an optimal of 97.87% at 6 AGV-
fleet. The decision on which configuration to
implement depends on the FMS management and
alignment with company’s goal or “menu du jour”.
Because the purpose is to maximize TR, then X
2
is set
up to coded level (0) or 150 ft./min.
Following the same procedure for MFT leads to the
implemented best MFT optimal robust design
configuration displayed in Table 13. Note that this
design corresponds to the simulated design # 13.
In the follow-up experiments, X
1
(AGV fleet size)
has been identified as the tuning (mean adjustment)
factor because it has a large effect on the mean and less
effect on the variability of the MFT. X
1
being the most
expensive component of the system has been varied at
different settings to identify its economical setting.
In order to gain some insight into the impact of
AGV rules, and also determine whether or not the X
4
X
5
interaction effect observed has any effect on the MFT
the follow-up runs and confirmation included testing
X
4
at low level (FCFS rule), and high level (STD rule).
The MFT minimum of 0.3666 min/part is achieved
with the following coded values for the variables X
1
(0), X
2
(+1), X
3
(+1), X
4
(-1), X
5
(-1) (Table not
displayed). Using the natural values, the optimum of
MFT is achieved with a fleet of 6 AGVs, at 200ft/min,
SPT queue discipline, FCFS AGV dispatching rule,
and a buffer capacity of 8 units.
5 CONCLUSIONS
This research uses a quick empirical technique to
optimize the FMS performances modeled using
discrete-event simulation and robust DOE. Data
analysis confirms prior knowledge about the number of
vehicles. TR variability with respect to noise is
influenced by the following factors, ranked according
to their importance: AGV Fleet size X
1
, AGV speed X
2
,
AGV dispatching rule X
4
, buffer capacity X
5
, and
machine scheduling rule X
3
. The following interaction
effects contribute to TR variability: AGV Fleet size X
1
and all other factors, to the exception of AGV speed,
i.e., X
1
X
3
, X
1
X
4
, X
1
X
5
. Interactions such as X
3
X
4
and
X
4
X
5
also account for the TR variability. Overall, the
interactions with an impact on TR are as follows, in
ascending order of magnitude: X
1
X
2
, X
1
X
3
, and X
2
X
3
with X
2
X
3
is almost equal to X
3
X
4
.
AGV fleet size X
1
seems to have the most
significant effect on the MFT. AGV speed X
2
, machine
rule X
3
come next, and the buffer capacity X
5
at a
relatively lower degree. Interaction X
1
X
2
has a large
effect in influencing the MFT, while the effects of
X
1
X
3
, X
3
X
5
, X
4
X
5
also need to be considered.
Based on the performance of SPT/FCFS and
SPT/STD on TR and MFT it can be stated that a
combination of machine scheduling and AGV
dispatching rules that include job/part information
(local rule) in the implemented queue discipline might
yield better system performance. Note also that X
5
,
identified as non-significant on the mean and the
variance, could have been set at high level, i.e., a
buffer capacity of 40. The resulting design
configuration in this case would have been the same as
the simulated design #17. Results indicate that this
would result into a MFT of 0.7876, almost the double
the MFT with X
5
at low level (Capacity = 8). Not only
is this design not economical, but it does not yield the
optimal performance measure. This finding suggests
that, the principle of setting the non-significant control
factors at any level when they do affect neither the
mean nor the variance may lead to non-optimum
design configurations. Thus, effects of interactions
should be considered even when main effects are not
significant, as is in the case of the proposed
optimization procedure. Future research intends to
compare the effectiveness of the proposed procedure
against other popular, well known and established
techniques.
ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics
302
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