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International Journal of Engineering & Technology IJET-IJENS Vol:16 No:02 8
160802-4747-IJET-IJENS © April 2016 IJENS I J E N S
Abstract— In this research, the manufacturing complexity of
the Saudi Airlines Engineering Industries (SAEI) is measured to
determine the complexity of their maintenance plants. We
analyze the results based on the measurement of the complexity
model to determine the most influential operations affecting the
maintenance process and causing delays using the Pareto analysis
(ABC analysis). When the complexity is considered for the
planned and actual durations, there is no part mix ratio available
for the data, and the planned and actual durations result in
minor complexity measurements. The levels of complexity for the
planned and actual durations are 1.375 and 2.1123, respectively.
An ABC analysis is also conducted, and the results indicate that
certain processes affect both plans.
Index Term— Complexity; Pareto Analysis; ABC analysis;
I. INTRODUCTION
TODAY’S dynamic environment makes it difficult for
factories and manufacturing plants to achieve their objectives.
To achieve these targets, factories and manufacturing plants
are often required to perform at their best capabilities. To
survive with the changing environment, companies objectives
to be more flexible in their processes and systems to fulfill
customers’ demands. This flexibility may yield benefits, such
as increased production and product customization. However,
if not controlledorganized, such flexibility might lead to
higher costs, longer lead times, , larger inventories, and
customer dissatisfaction.
This study has two aims. The first objective is to measure
the complexity of maintenance lines. Saudi Airlines
Engineering Industries (SAEI) has provided us with the data
for one maintenance line. The line has a different number of
processes. The second objective is to determine the factors
that can help reduce the complexity of these lines. Such a
reduction can be realized in many ways, such as JIT, product
& process standardization and other techniques used for
complexity management. However, these methods do not
answer the following question: How complex is the system
and to what degree can the complexity be reduced? Changing
the part mix ratio can help to reduce the complexity level.
The main objectives of the study are to
1. Measure the complexity of maintenance lines.
R. Alamoudi is with the Department of Industrial Engineering, King Abdulaziz University, Jeddah, Saudi Arabia.
M. Balubaid are with the Department of Industrial Engineering, King
Abdulaziz University, Jeddah, Saudi Arabia (e-mail: [email protected]).
2. Determine the factors that can help reduce the
complexity of these lines.
II. LITERATURE REVIEW
In this section, we discuss the various definitions of
complexity and attempt to identify the characteristics of
complexity and complex systems. We provide a brief
overview of the literature on complexity to lead into the
proposed model of measuring the complexity of
manufacturing systems.
According to Park and Kermer [1] there is no widely
accepted common definition of complexity due to the
vagueness that the term itself has.. Weaver [2] explained that a
complex system is a large number of parts that interact in a
non-simple manner. Yates [3] states five characteristics of
complex systems. He proposed that complexity rises whenever
one or more of the following five characteristics are present:
(a) significant interactions; (b) high number of parts, degrees
of freedom, or interactions; (c) non-linearity; (d) broken
symmetry; and (e) non-holonomic constraints. Allen and
Torrens [4] define a complex system as one that can respond
in more than one way to its setting.
Acorrding to Sedra [5], the main characteristics of complex
systems are collected under structural (static) and behavioral
(dynamic) features in the literature. The structural feature of
complexity illistrate the number of parts, variety of parts,
strength of interactions, connective structure, and hierarchical
structure (see Table I). The behavioral aspect involves the
characteristics of dynamism, nonlinearity, being far from
equilibrium, historicity, adaptively, self-organization,
emergent structures, and evolution (see Table II).
TABLE I
STATIC CHARACTERISTICS OF EVALUATING COMPLEX SYSTEMS
Measuring the Complexity in an Airplane
Engine Maintenance Plant
Rami H Alamoudi, and Mohammed A Balubaid*
International Journal of Engineering & Technology IJET-IJENS Vol:16 No:02 9
160802-4747-IJET-IJENS © April 2016 IJENS I J E N S
TABLE II
DYNAMIC CHARACTERISTICS OF EVALUATING COMPLEX SYSTEMS
Park and kremer [1] discussed that complexity for
manufacturing systems can be categorized into two broad
main areas equivalent to application or focus areas: design
complexity and manufacturing complexity. In addition Park
and Kremer [1] discussed how these types of complexity have
been defined beyond ambiguous and quantified through
different approaches.
Research have showed that complexity can affect a
manufacturing company’s performances, and those of its
supply chain [6]. Where Perona and Miagliotta [6] model
suggests that the ability to control complexity within
manufacturing and logistic systems can improve efficiency
and effectiveness at a supply chain wide scale.
Deshmukh et al. [7] have formulated an entropic measure
for static manufacturing complexity. However, it is designed
to be applied to only flexible manufacturing systems (FMSs).
Cho et al [8] proposed a novel model that can capture both
direct and indirect interactions among resources, which are not
limited to machining or forming operations.
We will apply this model in the current study. An
explanation of the model is provided in the next part.
A. Measurement Using a Complexity
1. Let us consider a manufacturing system that produces
n different types of parts and consists of m machines.
2. The interaction index matrix, which accounts for the
existence of interactions among processes in terms of
the processing time and waiting time (l), will be:
(1)
3. Matrix (Pl) is called the processing time matrix,
where diagonal elements represent processing times
and off-diagonal elements are zeros and is given as
(2)
4. The interaction matrix ( l), which represents
processing time-based interaction and waiting time-
based interaction, is given as
(3)
5. The total interaction matrix is
(4)
When we consider part mix ratios if they exist in the
model, then the overall interaction matrix will be
(5)
where
6. The normalized direct interaction matrix is
(6)
where
7. The normalized general interaction matrix is
(7)
which reflects all higher-order (indirect) interactions
over k connections (arcs), i.e., k=1 corresponds to
direct interactions, k=2 corresponds to second-order
interactions over 2 connections, and so on.
8. The overall influence of the i-th machine in the
system is (8)
ljlijlil=
0
1
ìíî
nni
ll
n
ll PΛPΛPΛΠΠ
1111
yl =1l=1
n
å
π̂i= p̂
ijj =1
må
Indices to show self-
interaction in terms
of process time.
Indices for influence of
machine of machine
in terms of waiting time. ljli+1jlil
=0
1
ìíî
International Journal of Engineering & Technology IJET-IJENS Vol:16 No:02 10
160802-4747-IJET-IJENS © April 2016 IJENS I J E N S
9. The normalized influence of the i-th machine in the
system is (9)
10. Finally, the static complexity can be calculated using
Shannon’s entropy theorem:
(10)
III. COMPLEXITY MODEL
In this section, we measure the manufacturing complexity
of the SAEI Airplane Engine Repair Facility using the model
presented above. We gathered the data from SAEI. The data
are shown below, where the expected starting and ending
dates of each process for each module are listed. We were
provided with three schedules of three different engines that
were processed in one production line.
A. First Engine
The schedule of the first engine detailed with planned and
actual dates is shown in Table III. TABLE III
FIRST ENGINE PLAN AND ACTUAL DATES OF OPERATION
ST
EP
S
OPERA
TION
PLANNED ACTUAL DURA
TION
DIFFE
RENCE ST
AR
T
EN
D
DURA
TION
ST
AR
T
EN
D
DURA
TION
1
MOD.
REMOV
AL
1-AP
R-
14
3-AP
R-
14
3
1-AP
R-
14
20-AP
R-
14
20 -17
2
MOD.
DISASS
EMBLY
4-AP
R-
14
8-AP
R-
14
5
21-AP
R-
14
28-M
AY
-14
38 -33
3 CLEANI
NG
9-AP
R-
14
10-AP
R-
14
2
29-MA
Y-
14
30-M
AY
-14
2 0
4 N.D.T
11-AP
R-
14
11-AP
R-
14
1
31-MA
Y-
14
1-JU
N-
14
1 0
5 BENCH
INSP.
12-AP
R-
14
14-AP
R-
14
3
2-JU
N-
14
4-JU
N-
14
3 0
6
PARTS
REPAIR
(MRP)
15-AP
R-
14
19-M
AY
-14
35
6-JU
N-
14
10-JU
N-
14
5 30
7
QEC
PARTS
REP. (R.SHO
P)
15-
AP
R-
14
19-
MAY
-14
35
6-
JU
N-
14
10-
JU
N-
14
5 30
8
PARTS
PURCHA
SING
(SC.)
15-
AP
R-
14
19-
MAY
-14
35
6-
JU
N-
14
10-
JU
N-
14
5 30
9
PARTS
REPAIR
(R.SHO
P)
15-
AP
R-
14
19-
MAY
-14
35
6-
JU
N-
14
10-
JU
N-
14
5 30
10 KIT
20-
MA
Y-
14
20-
MAY
-14
1
11-
JU
N-
14
12-
JU
N-
14
2 -1
11
MOD.
ASSEMB
LY
21-
MA
Y-
14
30-
MAY
-14
10
13-
JU
N-
14
23-
JU
N-
14
11 -1
12
MOD.
INSTAL
LATION
31-
MA
Y-
14
4-
JU
N-
14
5
24-
JU
N-
14
2-
JU
L-
14
9 -4
13 TEST
5-
JU
N-
14
9-
JU
N-
14
5
3-
JUL
-14
4-
SE
P-
14
64 -59
B. Second Engine
The schedule of the second engine detailed with planned
and actual dates is shown in Table IV. TABLE IV
SECOND ENGINE PLAN AND ACTUAL DATES OF OPERATION
ST
EPS
OPERAT
ION
PLANNED ACTUAL DURAT
ION
DIFFER
ENCE STA
RT
EN
D
DURA
TION
STA
RT
EN
D
DURA
TION
1
MOD.
REMOV
AL
24-
FEB
-14
26-
FE
B-
14
3
24-
FEB
-14
17-
MAR-
14
22 -19
2
MOD.
DISASSE
MBLY
27-
FEB
-14
3-
MAR-
14
5
18-
MA
R-
14
15-
AP
R-
14
29 -24
3 CLEANI
NG
4-
MA
R-
14
5-
MAR-
14
2
16-
AP
R-
14
17-
AP
R-
14
2 0
4 N.D.T
6-MA
R-
14
6-M
AR-
14
1
18-AP
R-
14
19-AP
R-
14
2 -1
5 BENCH
INSP.
7-MA
R-
14
9-M
AR-
14
3
20-AP
R-
14
2-M
AY
-14
13 -10
6
PARTS
REPAIR
(MRP)
10-MA
R-
14
13-AP
R-
14
35
3-MA
Y-
14
14-JU
N-
14
43 -8
7
QEC
PARTS
REP.
(R.SHOP
)
10-
MA
R-
14
13-
AP
R-
14
35
3-
MA
Y-
14
14-
JU
N-
14
43 -8
8
PARTS
PURCHA
SING
(SC.)
10-
MA
R-14
13-
AP
R-14
35
3-
MA
Y-14
14-
JU
N-14
43 -8
9
PARTS
REPAIR
(R.SHOP
)
10-
MA
R-14
13-
AP
R-14
35
3-
MA
Y-14
14-
JU
N-14
43 -8
10 KIT 14- 14- 1 15- 16- 1 0
⌣pi
=p̂i
p̂i
i=1
m
å
International Journal of Engineering & Technology IJET-IJENS Vol:16 No:02 11
160802-4747-IJET-IJENS © April 2016 IJENS I J E N S
AP
R-14
AP
R-14
JUN
-14
JU
N-14
11 MOD.
ASSEMB
LY
15-
AP
R-14
24-
AP
R-14
10 15-JUN
-14
1-
JU
L-14
17 -7
12 MOD.
INSTALL
ATION
25-
AP
R-14
29-
AP
R-14
5 2-
JUL
-14
9-
JU
L-14
8 -3
13 TEST
30-
AP
R-14
4-
M
AY
-14
5 10-JUL
-14
14-
JU
L-14
5 0
C. Third Engine
The schedule of the third engine detailed with planned and
actual dates is shown in Table V. TABLE V
THIRD ENGINE PLAN AND ACTUAL DATES OF OPERATION
ST
EPS
OPERAT
ION
PLANNED ACTUAL DURAT
ION
DIFFER
ENCE STA
RT
EN
D
DURA
TION
STA
RT
EN
D
DURA
TION
1 MOD.
REMOV
AL
20-JAN
-14
22-
JA
N-14
3 20-JAN
-14
27-
JA
N-14
8 -5
2 MOD.
DISASSE
MBLY
23-JAN
-14
27-
JA
N-14
5 28-JAN
-14
23-
FE
B-14
27 -22
3 CLEANI
NG
28-
JAN
-14
29-JA
N-
14
2
24-
FEB
-14
25-FE
B-
14
2 0
4 N.D.T
30-
JAN
-14
30-JA
N-
14
1
26-
FEB
-14
13-M
AR-
14
16 -15
5 BENCH
INSP.
31-JAN
-14
2-FE
B-14
3
14-MA
R-14
19-M
AR-14
6 -3
6 PARTS
REPAIR
(MRP)
3-FEB
-14
9-
M
AR
-14
35
20-
MA
R-
14
23-
AP
R-
14
35 0
7
QEC
PARTS
REP. (R.SHOP
)
3-
FEB
-14
9-M
AR
-14
35
20-MA
R-
14
23-AP
R-
14
35 0
8
PARTS
PURCHA
SING
(SC.)
3-
FEB
-14
9-
MAR
-14
35
20-
MA
R-
14
23-
AP
R-
14
35 0
9
PARTS
REPAIR
(R.SHOP
)
3-
FEB
-14
9-
MAR
-14
35
20-
MA
R-
14
23-
AP
R-
14
35 0
10 KIT 10-
MA
10-
M1
24-
AP
10-
M17 -16
R-
14
AR
-14
R-
14
AY
-14
11
MOD.
ASSEMB
LY
11-
MA
R-
14
20-
M
AR
-14
10
11-
MA
Y-
14
19-
M
AY
-14
9 1
12
MOD.
INSTALL
ATION
21-MA
R-
14
25-M
AR
-14
5
20-MA
Y-
14
24-M
AY
-14
5 0
13 TEST
26-MA
R-
14
30-M
AR
-14
5
25-MA
Y-
14
28-JU
N-
14
33 -28
D. List of Processes
The list of processes is shown in Table VI. TABLE VI
LIST OF PROCESSES
# PROCESSES
1 MOD. REMOVAL
2 MOD. DISASSEMBLY
3 CLEANING
4 N.D.T
5 BENCH INSP.
6
PARTS REPAIR (MRP)
QEC PARTS REP.
PARTS PURCHASING
PARTS REPAIR
7 KIT
8 MOD. ASSEMBLY
9 MOD. INSTALLATION
10 TEST
E. Explanation of Each Process in Table VI
1. Module Removal: Disassembling the engine into
different modules.
2. Module Disassembly: Disassembling each module
to several kits, i.e., the kits from which the module is
assembled.
3. Cleaning: Cleaning the kits for further processes.
4. N.D.T: During aircraft maintenance, nondestructive
testing (NDT) is the most economical way of
performing inspection, and this is the only way to
discover defects. To maintain a defect-free aircraft
and ensure a high degree of quality and reliability.
5. Bench Inspection
6. Process number 5 is a decision and must be chosen
among 4 processes:
a) Parts Repair (MRP): Material requirements
planning is a control system used
to manage manufacturing processes. Most MRP
systems are software based, although MRP can
also be performed by hand.
International Journal of Engineering & Technology IJET-IJENS Vol:16 No:02 12
160802-4747-IJET-IJENS © April 2016 IJENS I J E N S
b) Quick Engine Change (QEC): Engine
manufacturers define this process. For example,
GE defines full QEC engine as an engine ready
for installation, including basic engine hardware,
all buyer-furnished equipment, quick engine
change hardware and, depending on the engine
model, exhaust nozzle and inlet cowl. Rolls
Royce defines QEC as a basic engine plus
electrical system, fuel, oil and air systems.
c) Parts Purchasing and Replacing: If the part is
damaged and cannot be repaired, it must be
purchased from abroad.
d) Parts Repair: Repairing the parts damaged if
capable.
7. Kit: Kitting is reassembling the kits comprising each
module.
8. Module Assembly: Assembling each module from
the kits.
9. Module Installation: Assembling the engine from
the modules created in the previous process.
10. Testing: Testing the engine.
F. Complexity Calculation
In this section, we calculate the complexity for the planned
duration and compare it against the actual duration. The
calculation of the planned operation model is provided, and
the actual operation model is included in Appendix A.
1) Complexity calculation for planned operation
We determine the complexity of the planned duration by
first calculating the interaction index matrix (see Table VII).
TABLE VII
INTERACTION INDEX MATRIX FOR EACH ENGINE
Second, the process time matrix is calculated as shown
below in Table VIII
TABLE VIII
PROCESS TIME MATRIX FOR EACH ENGINE
Third, Table IX include the interaction matrix for each
engine.
(TABLE IX) INTERACTION MATRIX FOR EACH ENGINE
International Journal of Engineering & Technology IJET-IJENS Vol:16 No:02 13
160802-4747-IJET-IJENS © April 2016 IJENS I J E N S
Fourth, the total interaction matrix is calculated by adding
the summation of each cell (see Table X). (TABLE X)
TOTAL INTERACTION MATRIX
The summation of the total interaction matrix is 411.
Fifth, the normalized direct interaction matrix is calculated
by dividing the total of each cell by the summation of the total
interaction matrix (see Table XI):
TABLE XI
NORMALIZED DIRECT INTERACTION MATRIX
Before the final steps, the normalized interaction matrix is
calculated for each engine ( see Table XII).
TABLE XII
NORMALIZED INTERACTION MATRIX
In Table XIII, the normalized general interaction matrix is
included. TABLE XIII
NORMALIZED GENERAL INTERACTION MATRIX
Finally, table showing the summation of each row, the
influence of each operation in the system, and the natural
logarithm (Ln) of the influence and the complexity level is
provided below in Table XIV
.
International Journal of Engineering & Technology IJET-IJENS Vol:16 No:02 14
160802-4747-IJET-IJENS © April 2016 IJENS I J E N S
TABLE XIV
NATURAL LOGARITGM OF TE INFLUENCE
The level of complexity for the planned durations is
approximately 1.375, meaning that the planned operation
schedule is in a state of minor complexity level. The next step
is to calculate the complexity for the actual operation schedule
to compare between both plans and determine the next course
of action.
2) Complexity calculation for actual operation
The level of complexity for the actual operation is 2.1123,
representing a slight increase over the calculation of the
planned operation. Here, a minor complexity level exists as
well. Unfortunately, unlike the planned operation, there is a
significant difference when comparing the influences of each
step in both plans.
IV. ABC ANALYSIS
The complexity calculations for both the planned and actual
operation models indicate that the 5th
and 6th
steps have the
greatest influence on the system, i.e., nearly 36% each. We
conducted an ABC analysis (Pareto Diagram) to prioritize and
identify the most important sequences affecting the
complexity calculation by comparing the influence levels.
This will help management in tracking the most influential
sequences in the operation plan.
A. Determining the Most Influential Sequence in the
Operation Model
In this section, we present the Pareto diagrams starting with
the planned operation schedule, followed by the actual
operation schedule. TABLE XV
CUMULATIVE INFLUENCE OF PLANNED OPERATION
The Table XV above illustrates that operations 6, 5, 8, 7,
and 4 are the most influential sequences affecting the
complexity
, and their cumulative influences amount to nearly 80%,
meaning that if we can focus on these processes first and
investigate the causes behind the delays occurring in these
processes, we can eliminate 80% of the problem.
Unfortunately, analysis of the actual operational schedule
indicated that there is a variance in the process.
TABLE XVI
CUMULATIVE INFLUENCE OF ACTUAL OPERATION
Table XVI illustrates that processes 1, 9, 5, 10, 6, 2, and 8
are the most influential sequences affecting the complexity.
This means that a total of 7 processes affect the complexity in
a severe way, in contrast to the planned operation, in which 5
processes are of particular interest.
V. CONCLUSIONS
When implementing the complexity for the planned and
actual durations, no part mix ratio was available for the data,
and the planned and actual durations resulted in minor
complexity measurements. The levels of complexity for the
planned and actual durations were 1.375 and 2.1123,
respectively.
We also conducted an ABC analysis and found that some
processes affected both plans:
Parts Repair (MRP)
QEC Parts Rep
Parts Purchasing
Parts Repair
Mod. Assembly
According to the analysis, we recommend the following
actions to reduce the complexity level and maintain the
stability of process times:
International Journal of Engineering & Technology IJET-IJENS Vol:16 No:02 15
160802-4747-IJET-IJENS © April 2016 IJENS I J E N S
1. Complexity model:
The development of a static complexity measure can
support managerial decisions on improving system
operations. Hence, the proposed complexity measure
is one in which both direct and indirect interactions
are characterized by the form of influences.
2. Part mix ratio:
A part mix ratio should be determined and
implemented to reduce the complexity of the planned
durations. Unfortunately, as noted above, when we
spoke with SAEI engineers, they informed us that
they had not established a part mix ratio because
engine maintenance was not periodically
implemented. Thus, SAEI engineers should establish
a part mix ratio for the engines and should implement
it in the complexity measurement calculations to
reduce the complexity level for both the actual and
planned durations in a manner that will increase
machine and man power utilization and thus reduce
the delay time and cycle time.
3. A system should be implemented to follow up and
inspect the workers to prevent delays. This system
should be based on the planned durations after
implementing the part mix ratio and reaching a
suitable degree of complexity.
The productivity report should be resumed in the future
because a measurable method to track progress in a
quantitative manner is now available.
ACKNOWLEDGMENT
We would like to thank SAEI for providing us with the
data. In addition, we like to thanks Eng. Mohammed hussain
and Eng., Alhusan Naita for their data collections to carry out
this work.
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[3] Yates (1978) , “Complexity and the limits to knowledge”, American Journal of Physiology - Regulatory, Integrative and Comparative
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[4] Allen and Torrens (2005) “Knowledge and complexity”, Futures, Vol.37, No.7, pp. 581-584.
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