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

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 performance’s 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

Noise Factor

Low Level (-1)

High Level (+1)

X

6

Interarrival

EXPO(15)

EXPO(5)

X

7

MTBF

EXPO(300)

EXPO(800)

X

8

MTTR

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

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

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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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

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

89.76

WIP

100

WIP

150

WIP

200

(WIP*

ZF

)

(parts/day)

*

377

78

*

81

77

(81)

380

79

78

100

78

79

81

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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