The Application of Fuzzy Comprehensive Evaluation on Special Equipment
Risk Assessment
Yuan-rong Zhang 1, Jian Zhang 2, Yu-dong Li3 Chao Ji4
1,
Fujian Special Equipment Inspection and Research Institute, Fuzhou 350008, China
Fujian Special Equipment Inspection and Research Institute, Fuzhou 350008, China
3,
Business School, Sichuan University, Chengdu 610065, China
4,
Business School, Sichuan University, Chengdu 610065, China
(11253511623@qq.com, 232141081@qq.com, 3635308167@qq.com,4815481560@qq.com)
2,
Abstract – This paper uses fuzzy comprehensive
evaluation method to assess the safety level of special
equipments. An assessment model that examines quantity
and quality factors was presented. The proposed model has
two dimensions, the possibility and severity of accidents. The
possibility of accidents was evaluated by dimensions of
people, equipment, management and environment.
Emergency response was concerned in judging the severity
of accidents. Indicators of the assessment model were
established based on expert opinions collected via
questionnaires. Analytic Hierarchy Process was utilized to
calculate the weights of indicators in each layer to construct
the assessment model. Finally, the fuzzy comprehensive
evaluation method was used to assess the safety level of a
portal crane in the case company.
Keywords - Risk assessment, Special Equipment, Fuzzy
comprehensive evaluation.
I. INTRODUCTION
China has categorized boiler, pressure vessels
(including cylinders), pressure pipelines, elevators, chain
blocks, motor vehicles in plant, passenger transport
telphers and large amusement facilities as special
equipments [1]. Special equipments were widely used in
various areas of national economy and people’s daily life.
Once accident occurred with special equipments,
significant loss and serious adverse social impact will
happen[2]. Take the year of 2011 for sample, according to
the statistics, there are 296 cases of accidents related to
special equipments occurred in China. These accidents
caused direct losses of 66.81 million Yuan, with 310
people killed and 247 people injured.
Safety assessment can get comprehensive information
referring to safety statue and risk level of special
equipments in service. It is useful both for enterprises’
risk management improvements and safety supervision
institutions’ risk control [3]. In the recent 10 years, risk
based inspection (RBI) has been widely used overseas to
assess the risk of pressure vessels [4]. RBI is a method for
using risk as a basis to prioritize and manage the efforts of
an inspection program [5]. But the bases for safety
management on special equipments in China are still
experiences and laws [6].
II. CONSTRUCTION OF SPECIAL EQUIPMENT RISK
ASSESSMENT MODEL
A. Constructing the Index System
According to the characteristics of risk and examining
domestic and international literature, this study uses the
two dimensions, the possibility and severity of accidents,
to classify the risk level.
The present safety management of special equipments
are mainly depended on the inspection to equipments.
Factors of people, management and environment are
usually not concerned. Statics shows that most accidents
are related to people directly or indirectly [7]. This study
developed a systematic hierarchy index system by
examining domestic and international literature [8] [9] [10]
and conducting a questionnaire study. The index system
was shown in Fig. 1.
B. Establishment of assessment model
Regarding the established index system, the weights
of each layer should be calculated for a complete
equipment risk assessment model. Analytic Hierarchy
Process is a simple, flexible and practical multi-criteria
decision making method presented by professor T. L.
Saaty in the early 1970s[11].
The basic steps of AHP in this study are as follow:
Step 1: Define the problem and create hierarchical
structure for every relevant factor by experts.
Step 2: Design AHP questionnaires and distribute to
respondents. Transform geometric means of
questionnaires into the pairwise comparison matrix.
Step 3: Calculate the weights of each layer and the
consistency ratio (CR).
The calculation results of each layer are shown as
vectors, all the CR was less than 0.1.
(a)Weights of the accident possibility indicators
A1=
（0.4668，
0.2776，
0.1603，
0.0953）
B1= (0.0836,0.4443,0.4721)
0.3448，
0.1852，
0.0995
C1= 0.3705，
Quality of security annex D13
Fatigue D2
Quality of equipment C4
Quality of safety protection devices D14
Work environment D3
Work satisfaction D4
Skills C2
Experience D5
Educational level D6
Quality of measuring control device D15
Materials quality D16
Technological level D17
Mainly confined to the force structure D18
Quality of system controlled electric power
D19
Safety knowledge D7
Operating specifications D12
Equipment factors B2
Consciousness of Safety operation D11
Technique level C5
Quality of important parts D20
Hours worked D10
Work situation
C3
Possibility of accidents A1
Personal factors B1
Physiological and
psychological C1
Physiological healthy D1
Design level D21
Safety control technology D22
Type tests and examine D23
Equipment installation D24
of enterprise C7
Safety management
Safety management system D33
Quality management of Equipment
manufacturer D34
Security responsibility system D35
Equipment maintenance D26
Equipment modification D27
Years in service D28
Archives of security technology D29
Self inspection of Equipment safety D36
Complete degree of safety identification D30
Investment on enterprise safety management
D37
Performance load D31
Operation
environment C9
Corrective efforts of hidden danger D38
Comprehensiveness of safety monitoring
D41
Timely manner of safety monitoring D42
Quality of safety monitoring D43
Operating site order D47
Operation space of equipment D48
Facility Layout D49
Material stocking D50
Humanity and natural C10
Scale of safety monitoring team D40
Environment factors B4
Safety education and training D39
Safety supervision C8
Management factors B3
Equipment reparation D25
Use of equipment C6
Personnel allocation of safety administration
D32
Engineering level of examination D44
Engineering level of risk warning D45
Publicity efforts of safety knowledge and
regulations D46
Natural environment of Equipment
operation D51
Corrosion D52
Group safety awareness D53
Severity of accidents A2
Emergency response B6
Consequences B5
Energy conversion
of Equipment
operation C11
Population scale of
accident influence
C12
Possible casualties
C13
Possible direct
economic loss C14
Social influence
C15
Effectiveness of
emergency
measures C16
Emergency
response speed C17
Self-help ability of
the crowd damaged
C18
Fig. 1 Index system for special equipment
0.2017，
0.2454，
0.1019
C2= 0.3720，
0.1634，
0.2970
C3= 0.5396，

0.1634，
0.2970
B2= 0.5396，
C4= 0.050，
0.039，
0.071，
0.077，
0.027，
0.027,0.172,0.337
0.3196，
0.1220
C5= 0.5584，
C6= (0.2598,0.1602,0.2153,0.0818,0.0825,0.0508,0.0252,0.1245)
0.3333
B3= 0.6667，
C7= 0.2022,0.2370,0.1763,0.1168,0.0627,0.0856,0.0422,0.0773
C8= 0.0504,0.2049,0.1751,0.1640,0.2437,0.0826,0.0793
0.2500
B4= 0.7500，
C9= 0.1512,0.4098,0.3207,0.1183
(b) Weights of the accident severity indicators
A2=  0.7500,0.2500
0.2483,0.4903,0.0966,0.1203
B5= 0.0445，
0.5396，
0.1634
B6= 0.2970，
III. APPLYING OF THE MODEL
A. Introduce of the Fuzzy Comprehensive Evaluation
Method
An actual decision making question is often
influenced by many attributes or factors, people need to
make a comprehensive evaluation by these attributes or
factors. In most cases, these attributes or factors are fuzzy,
to make comprehensive evaluation of these fuzzy factors
is called fuzzy comprehensive evaluation [12][13].
The basic procedures of multi-level fuzzy evaluation
are as follows [14]:
① Partition factor set of evaluation into several
subsets according to certain criteria:
s
U   ui
i 1
② Utilize single level fuzzy comprehensive
evaluation for every ui
Determine level set：V = v1 , v 2, ，v n ，n

r22

rm 2
r 1
ir
1
should be determined before the evaluation. The single
level evaluation result of ui is：
Pui  A  R  (b1 , b2 ,...,bn )
③ Utilize single
level fuzzy comprehensive
evaluation for subsets
Regard ui as a comprehensive factor，and use Pui to
construct the evaluation matrix to calculate the final result.
If the division in the first step ui（i=1,2,…，s）is
still too much, it can be divided into 3 or more levels.
The M10-30 type portal crane was made in May 1989
and was installed in 1990 in Quanzhou harbor. The
original design for the biggest elevating capacity is 10
tons, and the hoisting extent maximum 30 m, minimum
8.5 m. At the beginning of putting into use in 1990, as
port workload is not heavy, equipment utilization was not
high; the load of door crane is small, and crane safe
technology to little effect on performance.
Since 1999, due to the rapid economy development in
Quanzhou, equipment load and utilization has increased
significantly. To meet the increasing production capacity
requirements, the company entrusted Shanghai Donggang
Machinery Corporation to modify the hoist boom in
November 2001. Rated lifting weight was increased to 16
tons after the modification.
After putting into use for 22 years, fatigue crack of
metal structure and aging electrical system would
probably be the hidden risk of accidents.
C. Determination of Membership Functions
As the index system includes both qualitative and
quantitative indicators, the judgments were made by
scoring the indicators from 1 to 100.
In this study, the risk range was divided into five
levels, which was shown in Tab. II. The original data was
collected by questionnaires and geometric means of
scores was calculated.

represents the grade number of evaluation.
Establish evaluation matrix
r12
r  pi
B. Backgrounds of Case Portal Crane
C10= 0.1059,0.5816,0.3090
C11=  0.7500,0.2500
 r11
r
21
R= 
 

rm1
 a
Weight vectors Ai  ai1 , ai 2 , , aipi ,
 r1n 
 r2 n 

 

 rmn 
Data rij denotes the degree that factor i belongs to
level j in the evaluation. It is usually calculated from the
scoring of factors by a function.
TABLE II
RISK RANGE AND SET
Evaluation
set
V
Scores
Good
（
level 1
）
≥90
Preferably
（level 2
）
80
General
（level
3）
Poorer
(level
4)
70
60
Extremely
poor
（level 5
）
≤50
According to the evaluation level given in Tab. II and
experts’ opinions, the formulas of membership functions
were presented below:
0  x＜80
0
( x  80) / 10
1

Good: u（x）= 
Preferably:
0
u（x）= ( x  70) / 10

1
(90  x) / 10

0

General:
0
( x  60) / 10
u（x）= 

1
(80  x) / 10


0
Poorer:
0

u（x）= ( x  50) / 10

1
(70  x) / 10


0
80  x＜90
90  x  100
0  x＜70
70  x＜80
x  80
80＜x  90
90＜x  100
0  x＜60
60  x＜70
x  70
70＜x  80
80＜x  100
0  x＜50
50  x＜60
x  60
60＜x  70
70＜x  100
Extremely poor:
1
(60  x) / 10
0

u（x）= 
0  x＜50
50  x＜60
60  x  100
We can get fuzzy judging analysis sets according to the
formula Pui  A  R :
PA1= 0.14 0.28 0.31 0.11 0.16 
Taking the same procedure, the result of severity of
accidents can be calculated:
PA2= 0.14 0.18 0.37 0.31 0.00 
E. Analysis results and recommendations
In this study, risk matrix [15] was used for measuring
overall risk level of special equipment. Hidden risks are
divided into five levels, shown in Tab. III. Each level
represents a corresponding implication, shown in Tab. IV.
According to the evaluation results, levels of two
dimensions were determined by maximum membership
degree principle:
① PA1= 0.14 0.28 0.31 0.11 0.16 ，accident
probability belongs to level 3.
② PA2= 0.14 0.18 0.37 0.31 0.00  ，severity
of accidents belongs to level 3.
According to TABLE III, the potential accident level
of case portal crane is General hidden danger. As RA1
demonstrates, PB2= 0.10 0.10 0.22 0.10 0.48 
, which
means that equipment factors have a rather poor
performance. Accidents are likely to occur due to
equipment failure. The case crane requires improvement
and continual attention to avoid further degeneration.
TABLE III
SAFETY LEVEL OF SPECIAL EQUIPMENT
Severity of Accident
D. Calculation of Fuzzy Evaluation
Accident
Take layer C1, the physiological and psychological
factor for example, the fuzzy comprehensive evaluation
matrix R1 was calculated by substitute into the
membership functions:
0
0
0
0
1


0
1
0
0
R1=  0
1
0
0
0
0


0
0
1
0
0 

and，WC1= 0.3705，
0.3448，
0.1852，
0.0995
We can get fuzzy judging analysis sets according to the
formula Pui  A  R :


PC1= 0.5626，
0.4374，
0，
0,0
Other fuzzy judgment analysis sets was calculated as
same. Regard Bi as a comprehensive factor ， and use
PBi,i=1,2,3,4 to construct the evaluation matrix of
possibility of accidents RAi:
 PB1   0.12 0.47 0.29 0.13 0.00 

 

 PB 2   0.10 0.10 0.22 0.10 0.48 
R A1 = 

P   0.28 0.25 0.30 0.09 0.08 
 B3  

 P   0.12 0.00 0.66 0.08 0.15 

 （B 4  
and, WA1= (0.4668,0.2776,0.1603,0.0953)
Possibility
Level 1
Level 2
Level 3
Level 4
Level 1
Level 2
Level 3
Level 4
Level 5
Safety
Slight
Slight
General
Slight
Slight
Slight
General
General
Serious
Slight
Slight
General
General
Serious
Serious
Super-serious
General General General
Serious Serious Super-serious Super-serious
General
Level 5
TABLE IV
EVALUATION RISK LEVELS AND CORRESPONDING
IMPLICATIONS
Risk levels
Safety
Slight
General
Serious
Super-serious
Execution outcomes and implications
Excellent performance for equipment safety
Failure may occur, requiring continual attention
Accidents are likely to occur, requiring
improvement and continual attention to avoid
further degeneration
Safety statue of equipment is poor and accidents
are very likely to occur, requiring immediate
rectification and improvement with execution
feedback
Serious accident will occur if emergency measures
not be implemented immediately, and equipment
should not put into use until hidden risk has been
eliminated.
IV. DISCUSSION
Although the fuzzy evaluation scores was given by
relevant experts in this study, the subjectivity of people is
still a remarkable question. More objective risk
assessment results should be obtained by the analysis of
statistical data base. A further research on scoring
mechanism should be implemented.
What’s more, it is impractical to assure all the
evaluators have a good knowledge of math. Thus,
professional software should be developed to promote the
use of the proposed evaluation method in this study.
V. CONCLUSION
This article used the fuzzy comprehensive
evaluation method to assess the risk level of special
equipments. A systematic index system was developed
based on literature and experts’ knowledge. Risk level
was determined based on risk matrix and opinions from
experts in relevant fields. A case evaluation was
conducted and evaluation results indicate that the case
portal crane has a risk level of General hidden danger B
and should be rectified before turn in service.
ACKNOWLEDGMENT
This research is funded by the large-scale technology
projects of Fujian Special Equipment Inspection and
Research Institute, “Research on special equipment
hidden dangers of accidents classification and grading
methods and mechanism of scientific investigation and
management”, the National Nature Science Foundation of
China (71131006; 71020107027; 71192197), and the
Foxconn Technology Group’s Talent Selection Research
Program (11F81210101).
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