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Facilitating AHP-TOPSIS method for reliability analysis of a marine LNGDiesel Dual Fuel Engine
Article in International Journal of Performability Engineering · July 2014
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International Journal of Performability Engineering, Vol. 10, No. 5, July 2014, pp. 101-114.
© RAMS Consultants
Printed in India
Facilitating AHP-TOPSIS Method for Reliability Analysis of
a Marine LNG-Diesel Dual Fuel Engine
CHENGPENG WAN1 , XINPING YA N1,2 , DI ZHA NG2* , JING SHI3 ,
SHANSHA N FU2
1
School of Energy & Power Engineering, Wuhan University of Technology, Wuhan,
430063 P. R. CHINA
2
Engineering Research Center for Transportation Safety (Ministry of Education), Wuhan,
430063 P. R. CHINA
3
Mangement School, University of Liverpool, Liverpool, L697ZH, U.K.
(Received on November 11, 2013, revised on Feb. 15, April 07 and April 30, 2014)
Abstract: Recent years, with the rapid development of world economy, energy
consumption is sharply increaseing and the environment is deteriorating. Liquefied
Natural Gas (LNG), a clean renewable energy which can be used as ship fuel, is drawing
attentions from more and more countries over the world. However, the conversion of the
LNG-diesel dual fuel engine (DFE) in China as a new research is just in its infancy,
therefore the operability and safety of the technology have to be further concerned. In
view of this, taking the China inland's first transformed marine DFE GC6135ACz as an
example, a risk assessment on the failures of DFE engine has been carried out by analytic
hierarchy process (AHP) and technique for order preference by similarity to ideal solution
(TOPSIS) method. Key factors for failures of DFE as well as the optimal risk control
options (RCOs) have been obtained by expert survey data, so as to enhance the safety
level of marine LNG-diesel DFEs.
Keywords: marine LNG-diesel dual fuel engine, AHP, TOPSIS, reliability
assessment
1. Introduction
Growing g lobal energy demand pro moted by the prosperity of international seaborne
trade and the increasingly stringent emission restriction have facilitated the development
of a green marine energy- Liquefied Natural Gas (LNG), wh ich is with superior emission
performance compared to traditional marine fuels (e.g., marine diesel o il (MDO) and
heavy fuel oil (HFO)) under suitable co mbustion conditions [1]. Therefo re, the use of
LNG in internal co mbustion engines has been researched to reach the optimu m case ,
considering both engine performance and environ ment impact [2]. As one of the most
important and common ways to apply LNG as a marine fuel, LNG-diesel Dual Fuel
Engines (DFEs) have been used on LNG carriers for decades. In recent years, various
studies have been conducted on its application on other types of vessels, so as to extend
the scope of the LNG fuel usage. Like all the crit ical systems of ships [3], the LNG-diesel
DFE is also an important and comp lex system consists of different co mponents that
cooperate with each other in order to function properly.
A series of studies have been carried out from various aspects to improve the
______________________________________________
*Corresponding author’s email: fred.zhangdi@gmail.com
101
102
Chengpeng Wan, Xinping Yan, Di Zhang, Jing Shi, Shanshan Fu
reliability of the DFE system. An electronic control unit parameter calib ration system for
dual-fuel automobile was developed to improve the reliability of system and record
historical data [4]. Han [5] investigated the gasoline-diesel dual fuel operation on a single
cylinder research engine, and the results indicated that it is difficult but important to have
an accurate and reliable control over the ignition in the dual fuel applications . In addition,
injection t iming has been wildly studied and the relationship between injection t iming and
emission condition has been revealed [6, 7]. The injection timing is a crucial issue that
plays an important ro le in combustion performance and determines the amount of
emissions as well as the fuel consumption. Moreover, appropriate injection timing can
suppress engine knock and improve engine reliability as well [8].
However, the marine LNG-diesel DFE is just in its early stage of development in
Chinese shipping industry, where the majority of the LNG-diesel DFEs are converted
fro m tradit ional diesel engines on trail ships with a service life time less than seven years
in the Yangtze River, wh ich correspondingly increases the instability and uncertainties of
the DFE system. Fu rthermore, uncertaint ies are involved in evaluation of the failu re risk
of a LNG-diesel DFE as objective data collection would usually be infeasible. Thus, in
order to achieve the aim of identify ing the hazards of LNG-diesel DFE and provid ing
informat ion for daily operations, an analytical hierarchy process (AHP) method is
implemented as it is a comprehensive framework to cope with intuitive, rational, and
irrational data when dealing with mult i-object ive, mu lti-criterion and mult i-actor decisions
with and without certainty for any number of alternatives [9]. The A HP approach
organises the basic rationality by breaking down a problem into its smaller constituent
parts and then calls for simp le pairwise comparison judgements to develop priorities in a
hierarchy. The technique for order preference by similarity to ideal solution (TOPSIS)
method is used to find the optimal alternative, which is the closest to the ideal solution
and farthest away from the negative ideal solution with a description of accurate
Euclidean distance [10]. Therefore, the co mbination of the AHP and TOPSIS methods
provides more informat ive results [11] in the reliability analysis and decision making.
The reminder o f this paper is organised as follo w. Sect ion 2 briefly reviews the AHP
and TOPSIS method respectively, and introduces the main steps to conduct the reliability
analysis. Section 3 demonstrates how the proposed methods can be applied to indentify
key factors that influence the LNG-d iesel DFE most and to obtain the best risk control
options (RCOs) by investigating a converted LNG-diesel DFE used on a trial vessel. The
experts’ assessment data as well as the RCOs are further analysed in Section 4 and the
paper is summarized in Section 5 with a conclusion of the results and contributions of this
hybrid method.
2. Methodolog y
2.1 Procedure of AHP-TOPSIS Method
In order to conduct the AHP-TOPSIS method, a hierarchical structure for risk assessment
is established as Figure 1.
The research goal is in the top level, which can be divided into several smaller
elements that constitute the Criteria Level (wh ich may contain one or more sub -criteria
levels). Index Level consists of elements that come fro m upper levels. In general,
elements in this level are basic assessment units which can be estimated direct ly. Those
elements that influence the goal most will be chosen as the assessment criteria (Key
Factors) used in the following steps along with the proposed RCOs in the bottom level.
Facilitating AHP-TOPSIS Method for Reliability Analysis of a Marine LNG-Diesel Dual Fuel Engine
103
The main procedure for the AHP-TOPSIS method can be described in a series of steps as
follows:
Step 1: construct the hierarchical model fro m research goal and identify the standard
to measure the pairwise comparison of different evaluation indexes . After that, a pairwise
comparison matrix can be established;
Goal
A1
B1
...
Goal Level
...
Bn
B1
C1
...
An
Bn
B1
...
O1
...
...
Cn
Om
Criteria Level
Bn
Index Level
Key Factors
RCOs Level
Figure 1: Hierarch ical Structure for Reliability Assessment
Step 2: carry out the pairwise comparisons in each level of the hierarchical structure
in terms of their relative importance to the goal and calculate the weighting vectors of the
elements in the corresponding level. Meanwhile, their consistencies need to be checked in
order to achieve a convincing result;
Step 3: estimate the overall weight of each element/factor in terms of failure risk and
those with relative high importance will be selected as key factors;
Step 4: identify the RCOs based on the key factors in step 3 and establish the
decision matrix in terms of the assessment criteria with respect to the key factors;
Step 5: normalise the decision matrix to unify the unit of matrix entries and then
weight it with the weights of assessment criteria;
Step 6: determine the positive ideal solutions (PIS) and negative ideal solutions
(NIS);
Step 7: calculate the distance fro m PIS and NIS fo r each RCO respectively, so as to
obtain relative closeness of each RCO;
Step 8: rank the RCOs according to their closeness.
2.2
The AHP Method
AHP was developed by Satty [12] and designed to solve complex mult i-criteria decision
problems. AHP requires the decision makers to deliver judgments on the relative
importance of each criterion and then specify a preference for each decision alternative
considering all criteria. AHP is especially appropriate for co mplex decisions which
involve the comparison of decision criteria that are difficu lt to quantify [13]. It bases on
the assumption that when facing a co mplex decision , the natural hu man reaction is to
cluster the decision criteria according to their co mmon characteristics. The AHP method
can be expressed in following steps [10, 19]:
104
Chengpeng Wan, Xinping Yan, Di Zhang, Jing Shi, Shanshan Fu
(1) Construct a comparison matrix
A pairwise comparison matrix of criteria is constructed using a scale of relat ive
importance. A simp lified evaluation scale fro m 1 to 5 is shown in Table 1.
Table 1: The Relational Scale for Pairwise Co mparisons
Scale of
importance
1
2
3
4
5
reciprocal
Interpretation
Two factors are Equall y important
The former factor is more important than latter one, Slightly
The former factor is more important than latter one, Moderately
The former factor is more important than latter one, Fairly
The former factor is more important than latter one, Strongly
When the latter factor is more important, it will be a reciprocal, that’s
a ji = 1/a ij
After the calculation of relative importance, the pairwise co mparison matrix is
converted into a single-value co mparison matrix. The quantified judgements on pairs of
criteria Ai and Aj are represented by a n n single-value co mparison matrix A:
 1
1/ a
12
A  aij  


1/ a1n
a1n 
a2 n 
(1)


1/ a2 n
1 
where, a ij is the relative importance of criteria Ai and Aj .
(2) Calcu late the importance degree of each element
The weighting vector of a specific element k can be calculated through Equation (2).
wk 
a12
1
n
1 n
(
a
kj
/
aij ) (k  1, 2,....., n)


n j 1
i 1
(2)
where, a ij is the entry of row i and colu mn j in a co mparison mat rix of order n and Wk
is the weighting vector of a specific element k in the pairwise comparison matrix.
(3) Consistency test
The consistency of pairwise co mparisons has to be checked before achieving a
convincing result. The comparisons will be considered reasonable only if the consistency
ratio is equal to or less than 0.10[14]. An appro ximation of the ratio can be obtained using
the algorithm described in Equation (3).
CR 
CI
RI
(3)
Where, CR is the consistency ratio and RI (shown as Table 2) is the random index [14]
in terms of the matrix size. C I is the consistency index that can be obtained fro m Equation
(4).
 n
(4)
CI  max
n 1
Facilitating AHP-TOPSIS Method for Reliability Analysis of a Marine LNG-Diesel Dual Fuel Engine
where,
105
is the maximu m weighting value of a n n comparison matrix.
Table 2: Average rando m index (RI) values
2.3
Matrix Size (n)
2
3
4
5
6
7
8
9
10
RI
0
0.58
0.90
1.12
1.24
1.32
1.41
1.45
1.49
The TOPSIS Method
The TOPSIS method was developed by Hwang and Yoon [15] and modified by
Hwang, Lai, and Liu [16]. It is a method for identifying solutions from a fin ite set of
alternatives, with a basic principle that the chosen alternative should has the shortest
distance from the positive ideal solution and the farthest distance from the negative ideal
solution. As a useful method in dealing with mu lti-attribute or mult i-criteria
decision-making problems in the real world, TOPSIS has been successfully applied to
various aspects like hu man-resource management, t ransportation and manufacturing
[10].The TOPSIS method can be expressed as the following:
(1) Establish a decision matrix
When conducting a TOPSIS analysis, the decision problem should be well structured
and represented in a form of decision mat rix D with m rows and n columns, representing
the alternatives and the evaluation criteria, respectively [17]. Matrix D that consists of
original information is shown as Equation (5).
 x11
x
D   21


 xm1
x1n 
x22
x2 n 
(5)


xm 2
xmn 
Each variable xij in matrix D describes the performance of alternative Oi (i =1,
2,..., m) with respect to the criterion Cj (j =1, 2,..., n).
x12
(2) Normalise the decision matrix
It is essential to normalise the data in order to transform it into a dimensionless
matrix, which allows the comparison of the criteria fro m different sources [18].
Normalised value rij of each variable xij is calculated through Equation (6).
rij  xij /
m
x
i 1
2
ij
, j  1, 2,..., n
(6)
(3) Obtain the weighted normalised decision matrix
The weighted normalised decision matrix (Vij ) can be obtained by mult iplying the
normalised decision matrix by its associated weights with Equation (7).
vij  w j  rij , i  1, 2,..., m, j  1, 2,..., n
(7)
Where, wj is the weight of jth criterion.
(4) Identify the positive ideal solutions (PIS) and negative ideal solutions (NIS)
In a TOPSIS, the PIS (A+ ) and NIS (A-) are defined as Equation (8).
A+  (v1 , v2 ,..., vn )  {(max{vij } j  J 1), (min{vij }) j  J 2};
i
i
i
i
A  (v1 , v2 ,..., vn )  {(min{vij } j  J 1), (max{vij }) j  J 2}
Where, J1 and J2 represent the criteria benefit and cost, respectively.
(8)
106
Chengpeng Wan, Xinping Yan, Di Zhang, Jing Shi, Shanshan Fu
(5) Calcu late Euclidean distances
The Euclidean distances from the PIS (d j +) and the NIS (d j -) of each alternative Oi can
be calculated as:
di 

i
d 
n
 (v
 v j  ) 2 , i  1, 2,..., m ;
 (v
 v j ) , i  1, 2,..., m
j 1
n
j 1
ij
ij
(9)

2
(6) Calcu late the relat ive closeness to the ideal solution
The relative closeness S j for each alterative with respect to PIS is calculated using
Equation (10).
Sj 
d j
d j  d j
, j  1, 2,..., m
(10)
Where, 0 ≤ S j ≤ 1.
(7) Rank the alternatives
As the distance to both PIS and NIS are considered in last step, the larger value of
result S j represents a better alternative Oj that is close to positive ideal and far fro m
negative ideal solution. Therefore, the solution with the largest Sj should be ranked at the
top when choosing the most preferable alternative.
3. Case Study
In this study, performance degradations of co mponents are considered as “failures”. The
selection of such elements is conducted based on literature review and extensive
discussions with domain experts in the area, whose details are listed as below.
Expert No.1: an experienced seafarer with more than 10 years as a chief engineer
onboard;
Expert No.2: a p rofessor engaged in marit ime research for mo re than 12 years ;
Expert No.3: a p rofessor engaged in marine engineering for more than 8 years.
In addition, the model in this case study is developed based on the data of the first
refitted LNG-diesel dual fuel powered vessel in the Yangtze River. It is a ferryboat with
two main engines typed GC6135ACz, of which rated power is 105.2Kw and rated speed is
1,500r/ min. Referring to the hierarchical structure of assessment model, this section is to
demonstrate how the proposed methodology can be applied to identify key factors and the
optimal RCOs.
3.1
Es tablishment of AHP Model and Comparison Matri x (Step 1)
As shown in Figure 2, the failure of LNG-d iesel DFE is set at the top level. The elements
in Criteria Level are regarded as system failures and machine element failu res. Each
element in this level is investigated based on its associated elements/factors given in
sub-criteria level and Index Level. These elements/factors are chosen because they are
claimed to be the most significant ones associated with majo r causes that lead to failures
of the marine DFE.
Facilitating AHP-TOPSIS Method for Reliability Analysis of a Marine LNG-Diesel Dual Fuel Engine
107
Cause 1.1
Control
system failure
...
Cause 1.4
Cause 2.1
Cooling
system failure
Cause 2.2
Cause 2.3
Cause 3.1
Lubrication
system failure
System failure
...
Cause 3.4
Cause 4.1
LNG fuel
system failure
...
Cause 4.5
Dual fuel
system failure
Cause 5.1
Diesel fuel
system failure
LNG-diesel
DFE failure
...
Cause 5.5
Cause 6.1
Vantilation
system failure
Cause 6.2
Cause 6.3
Cause 7.1
major motion
components failure
...
Cause 7.4
Machine
element failure
Cause 8.1
major fixed
components failure
...
Cause 8.4
Figure 2: The Hierarch ical Structure of Failure Modelling of LNG-diesel DFE
Taking “system failure” layer as an example, which is consist of five factors, namely,
“control system failure”, “cooling system failure”, “lubrication system failu re”, “dual fuel
system failure” and “ventilat ion system failu re”, the matrix fo r this level can be formed
via Equation (1), co mbined with weighted average expert judgements (the relative weight
of every expert is assigned equally). For the purpose of convenient, “control system
failure”, “cooling system failure”, “lubricat ion system failure”, “dual fuel system failure”
and “ventilation system failure” are respectively represented by P1, P2, P3, P4 and P5.
P1
P2
P3
P4
P5
P1
1.00
2.50
1.67
1.00
1.00
P2
0.40
1.00
0.75
0.42
0.75
P3
0.60
1.33
1.00
0.67
2.67
P4
1.00
2.40
1.50
1.00
2.00
P5
1.00
1.33
0.38
0.50
1.00
108
Chengpeng Wan, Xinping Yan, Di Zhang, Jing Shi, Shanshan Fu
3.2
Calcul ati on of Rel ati ve Weight of each Element in Different Levels (Step 2)
As shown in Table 3, the weights of this level’s elements can be calculated using Equation
(2).
Table 3: Weights of each Element in “System Failure”
Elements
Weight
Rank
P1
0.25
2
P2
0.12
5
P3
0.21
3
P4
0.27
1
P5
0.15
4
After the calculation of each element’s weight, the consistency of pairwise
comparisons can be checked using Equation (3) and Equation (4):
CI
CR 

RI
5.1967  5
5 1
 0.043  0.1
1.12
Similar process can be further imp lemented to other levels so that the weighting
vectors of all levels are obtained.
3.3
Identi ficati on of Key Factors (Step 3)
By mult iplying the weighting vectors of relevant associated upper level elements, the
overall weights of each element/factor are shown in Tab le 4.
Table 4: Overall Weights of Each Element in Index Level
Cause
Nu mber
1.1
Influencing Factors (Index Level)
Overall Weight
Rank
Start-up failure
0.0319
15
1.2
Firing failure
0.0544
4
1.3
Reversal failure
0.0600
3
1.4
Speed regul ati on fault
0.0413
9
2.1
Jam or leakage of fresh (sea) water pip ing
0.0324
14
2.2
Fresh(sea) water pump fault
0.0414
8
2.3
Fresh water valve damage
0.0162
24
3.1
Pressure limiting val ve fault
0.0445
6
3.2
Oil pump faul t
0.0788
2
3.3
Sensor failu re
0.0362
11
4.1
Separator fault
0.0302
17
4.2
Injection pump fault
0.0331
13
4.3
Electronic governor fault
0.0216
20
4.4
Oil supply piping damage
0.0173
23
4.5
Fuel injector fault
0.0421
7
Facilitating AHP-TOPSIS Method for Reliability Analysis of a Marine LNG-Diesel Dual Fuel Engine
109
5.1
Natural gas pipeline damage
0.0100
30
5.2
Gas injection valve fault
0.0041
32
5.3
LNG processing system failure
0.0112
29
5.4
ECU fau lt
0.0188
22
5.5
Safety control system failure
0.0147
25
6.1
Leakage of exhaust valves
0.0315
16
6.2
Cracking of valve disk (rod)
0.0214
21
6.3
Supercharger bearing damage
0.0135
26
6.4
Turbi ne fault
0.0461
5
7.1
0.0380
10
0.0917
1
7.3
Piston crown ablation
Piston ring abnormal wear, adhesi ve and broken
Connecting rod bending
0.0293
18
7.4
Cran kshaft fatigue damage
0.0332
12
8.1
Over wear of cylinder liner
0.0220
19
8.2
Cavitations of cylinder liner
0.0116
28
8.3
Crack and corrosive damage of cylinder cover
0.0127
27
8.4
Bearing shell damage
0.0088
31
7.2
As shown in Table 4, there are 32 factors that influence the reliab ility of LNG-diesel
DFE. However, only parts of them are selected in order to simplify the further steps of
RCO identification. The selected factors are those which have relatively high importance
degrees. Specifically, a threshold value of 50% [20] of total importance degree is used in
selecting the safety critical factors (SCFs) in this study (50% is not a fixed value which
may need to be adjusted in terms of d ifferent situations). Thus, nine influencing factors,
namely, “piston ring abnormal wear, adhesive and broken” (C1), “oil pump fau lt” (C2),
“reversal failure” (C3), “firing failu re” (C4), “turb ine fau lt” (C5), “pressure limiting valve
fault” (C6), “fuel injector fault” (C7), “fresh (sea) water pu mp fault” (C8) and “speed
regulation fault” (C9), are identified as the SCFs in terms of failure risk of the DFE. These
nine factors are responsible for a comparatively high overall weight of importance degree
accumulated to 50.03 percent. Moreover, the selected factors are approximately in
accordance with the result of another similar research [21], which in turn supports the
rational selection in this study to some extent. The normalised weights of the key factors
are shown as Table 5.
Table 5: Normalised Relat ive Eeight of each SCF
Key Factors
Weight
C1
0.183
C2
0.158
C3
0.119
C4
0.109
C5
0.092
C6
0.089
C7
0.084
C8
0.083
C9
0.083
110
3.4
Chengpeng Wan, Xinping Yan, Di Zhang, Jing Shi, Shanshan Fu
Identi ficati on of RCOs and Establishment of Decision Matri x (Step 4)
In terms of the SCFs of LNG-diesel DFEs, the corresponding countermeasures are listed
as follow:
RCO 1: strictly co mply with the design specifications when refitting LNG-diesel
DFEs, and reinforce routine inspection and management to dual fuel system;
RCO 2: conduct maintenance work regularly according to the technical maintenance
table, and adjust maintenance items and period according to the operating conditions of
LNG-diesel DFE and different environ ment;
RCO 3: conduct crew training;
RCO 4: select suitable working mode for LNG-diesel DFEs according to different
conditions.
By using a scale of rating fro m 0 to 10 (fro m least effective to extremely effective),
the degrees of utility of each RCO have been evaluated through merged expert grading
data with respect to the criteria co mposed of nine key factors. The decision matrix D made
up with alternative ratings is as follo w:
D=
C1
C2
C3
C4
C5
C6
C7
C8
C9
O1
3.67
2.33
2.67
6
4.33
3
8.67
3.33
9.33
O2
8.67
6.67
6
8.67
7.33
4.33
9.33
4
5.33
O3
5
4.33
5
8.33
7
3.67
7
5
5
O4
3.33
3.33
3.33
8.67
7.33
6
8.67
4
4
3.5 Normalisation and Weighting of the Decision Matrix (Step 5)
By using Equation (6), each variab le in decision mat rix can be calculated so as to
normalise the decision mat rix. Then, weighted normalised decision matrix (Vij ) can be
obtained by mult iply ing it with associated weights (in Tab le 5) using Equation (7), shown
as below.
3.6
C1
C2
C3
C4
C5
C6
C7
C8
C9
O1
0.060
0.041
0.036
0.041
0.030
0.030
0.043
0.033
0.062
O2
0.142
0.118
0.081
0.059
0.051
0.044
0.046
0.040
0.035
O3
0.082
0.076
0.067
0.057
0.049
0.037
0.035
0.050
0.033
O4
0.055
0.059
0.045
0.059
0.051
0.061
0.043
0.040
0.026
Identi ficati on of Positi ve Ideal Solutions (PIS) and Negati ve Ideal Solutions
(NIS) (Step 6 )
Through Equation (8), the PIS and NIS can be obtained as follows :
A+= (0.142, 0.118, 0.081, 0.059, 0.051, 0.061, 0.046, 0.050, 0.062);
A-= (0.055, 0.041, 0.036, 0.041, 0.030(1), 0.030(4), 0.035, 0.033, 0.026).
3.7
Calcul ati on of Distances and Relati ve Closeness (Step 7)
The Euclidean distances from the PIS (d j +) and the NIS (d j -) of each alternative Oi can be
calculated through Equation (9) and their relat ive closeness can be obtained using
Equation (10). Taking RCO 4 as an examp le,
Facilitating AHP-TOPSIS Method for Reliability Analysis of a Marine LNG-Diesel Dual Fuel Engine
111
(0.055  0.142)2  (0.059  0.118)2  (0.045  0.081)2
d  (0.059  0.059)2  (0.051  0.051)2  (0.061  0.061)2  0.117 ;
(0.043  0.046)2  (0.040  0.050)2  (0.026  0.062)2

(0.055  0.055)2  (0.059  0.041)2  (0.045  0.036)2
d  (0.059  0.041)2  (0.051  0.0302  (0.061  0.030)2  0.047
(0.043  0.035)2  (0.040  0.033)2  (0.026  0.026)2

Thus, the relative closeness of O4 is,
S4 
3.8
0.047
 0.287
0.117  0.047
Ranking of the Alternati ves (Step 8)
Similar processes can be imp lemented to other RCOs and the final ran king can be seen in
Table 6.
Table 6: Final Ranking of the RCOs
RCO 1
d+
0.129
d0.037
Sj
0.223
Rank
4
RCO 2
0.033
0.129
0.796
1
RCO 3
0.084
0.063
0.427
2
RCO 4
0.117
0.047
0.287
3
It is clear that the optimal RCO would be regular maintenance work which has the
shortest distance from PIS and furthest distance from NIS, ranking the first with highest
relative closeness.
4. Discussion and Vali dati on
According to the matrix (Vij ) in Sect ion 3.5, ranking of each RCO in respect of different
criteria are represented in the Table 7.
Table 7: Ranking of each RCO with Different Criteria
RCO 1
RCO 2
RCO 3
RCO 4
C1
C2
C3
C4
C5
C6
C7
C8
C9
4
1
2
3
4
1
2
3
4
1
2
3
3
1
2
1
3
1
2
1
4
2
3
1
2
1
3
2
3
2
1
2
1
2
3
4
It can be seen that RCO 2 gets the highest value for almost all assessment criteria
compared to other RCOs, making it a pro minent utility in controlling the SCFs that
influence the reliab ility of LNG-diesel DFEs. RCO 1 contains the majority of the lowest
values, which results in its last place in the performance ranking. Though RCO 2 is
claimed to be the best alternative, it does not mean that other alternatives cannot reduce
the failure risk of LNG-diesel DFEs. Instead, other alternatives may also be applied under
certain circu mstances to improve the reliab ility of the system.
112
Chengpeng Wan, Xinping Yan, Di Zhang, Jing Shi, Shanshan Fu
Co mpared to the results in [22], which listed the priorities of RCOs by evaluating
their “overall effectiveness” (shown as Table 8) on the basis of experts ’ judgements, the
final ran king of the RCOs is in harmony with this study, which partially validates the
rationality of the proposed approach. In addit ion, regular maintenance work,
recommended as RCO 2, is a significant part of the daily operation. It is not only the
obligation of crew on ship, but has also been enforced as a regulation by many shipping
companies, marit ime safety administrations and other maritime organizations [23].
Table 8: Utility Evaluation of RCOs [22]
Over
Effectiveness
Rank
RCO 1
RCO 2
RCO 3
RCO 4
2.2186
3.4490
2.7369
2.5242
4
1
2
3
5. Conclusions
As various factors may influence the operational safety of DFE, this paper presents an
analytical method using the techniques of an AHP and the TOPSIS, fo r the reliability
assessment of DFE and solution selection for the best alternatives to control operational
risk. The p roposed method is further demonstrated and validated with a case study. The
criteria of “p iston ring abnormal wear, adhesive and broken”, “oil pu mp fau lt”, “reversal
failure”, “firing failu re”, “turbine fault”, “pressure limiting valve fault”, “fuel injector
fault”, “fresh (sea) water pump fau lt” and “speed regulation fault” are identified as the
SCFs through the AHP method. Moreover, regular maintenance work is estimated having
the highest utility priority among all RCOs by applying the TOPSIS method. The results
of this study provide useful information for the marine engineers and shareholders in
order to reduce the failure risk of DFEs. The proposed method can be fu rther applied as a
subjective approach for other risk management areas.
Acknowledgements: Th is work is supported by National Science Foundation of China
(NSFC) under grant No. 51209165, the EU FP7 Marie Cu rie IRSES project “ENRICH”
(No. 612546), the Fundamental Research Funds for the Central Universities (WUT:
2013-IV-121), and the Innovation Groups Project of Hubei Province Natural Science
Foundation (No: 2013 CFA 007).
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114
Chengpeng Wan, Xinping Yan, Di Zhang, Jing Shi, Shanshan Fu
Cheng peng Wan is currently working towards a Ph.D. in the School of Energy and
Power Engineering at the Wuhan University of Technology (WUT), P.R. China. He
received his Bachelor degree in Marine Engineering fro m WUT. His research interest is
focused on the formal maritime safety assessment, risk based multip le attribute decision
making and uncertainty treatment in risk assessment.
Xinping Yan is Professor and Director of Intelligent Transport Systems Research Centre,
Wuhan University of Technology, China. Prof. Yan received h is BSc in Marine
Machinery Design and Manufacture fro m Wuhan University of Water Transportation
Engineering, China in 1982, M Sc in Marine Eng ineering fro m the same university in 1987,
PhD in Mechanical Eng ineering fro m Xi’an Jiaotong University , Ch ina in 1997. Pro f.
Yan’s major research interests include marit ime safety and security analysis.
Di Zhang is Assistant Professor of Intelligent Transport Systems Research Centre, Wuhan
University of Technology, Ch ina. He received his B.Sc. in Navigation Technology, M.Sc.
in Traffic Information Engineering & Control and Ph .D. in Veh icle Operat ion
Engineering fro m Wuhan University of Technology in 2005, 2008 and 2011 respectively.
Dr. Zhang’s major research interests include risk assessment and decision science applied
in marine systems. He is associate fello w of Royal Institute of Navigation (AFRIN).
Jing Shi is a Ph.D. candidate in Management School at Un iversity of Liverpool, currently
doing research on sustainable packaging and green supp ly chain. After graduating from
North-eastern University in China with B.Eng. in Automat ion, he worked as a quality
engineer in a pump manufacturer. His interest sparked in product development and
manufacturing operations, he achieved an M.Sc. (Eng.) in Product Design and
Management at the University of Liverpool.
Shanshan Fu is a Ph.D. candidate in Intelligent Transportation Engineering at Wuhan
University of Technology, P.R. China. She received her B.Sc. in Logistics Engineering
fro m Wuhan University of Technology in 2010 and M .Sc. in Intelligent Transportation
Engineering fro m the same university in 2013. Shanshan’s major research interests
include risk assessment and LNG vessel risk analysis.
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