Same SIGNAL for some gate in two evaluations will imply the gate’s inputsin these two evaluations be same.
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62
H. Li et al.
(1)Weight calculation of Level 1 “zero harm” safe culture indicators and
consistency test
1st level indicator set, Un { U1 ,U2 ,U3 ,U4 } = {“Zero harm” safety concept
culture, “Zero harm” safety institution culture, “Zero harm” safety behavior culture,
“Zero harm” safety material culture}. Calculations are shown in Table 3.
Table 3. Weight calculation of Level 1 “zero harm” safe culture indicators and
consistency test.
Wi0
Om i
2
2.213
0.476
4.178
2
1
0.841
0.181
4.128
1/2
1
1/3
0.485
0.105
4.149
1
3
1
1.107
0.238
4.074
U1
U2
U3
U4
U1
U2
U3
U4
1
4
3
1/4
1
1/3
1/2
1
( 4.178 4.128 4.149 4.074 ) 4.132
4
Om ax
C.I .
Weight
Wi
U
Om ax n
C.R.
n 1
C.I .
R.I .
4.132 4
4 1
0.044
0.89
0.044 0.1
0.049 0.1
Because CR=0.049<0.1, the judgment matrix has a good consistency. Therefore,
calculated values of weights can be used.
(2) Weight calculation of Level 2 “zero harm” safe concept culture indicators and
consistency test
Level 2 indicator set: “Zero harm” safety concept culture U1 ^U11,U12 ,U13` =
{Enterprise “zero harm” safety values, “zero harm” safety concept, “zero harm”
thinking modes}. Calculation results are listed in the following Table 4.
Table 4. Weight calculation of Level 2 “zero harm” safe concept culture indicators
and consistency test.
Wi0
Om i
1/2
1.260
0.359
3.108
1
1/3
0.437
0.124
2.953
3
1
1.817
0.517
3.108
U21
U22
U 23
U21
U22
U 23
1
4
1/4
2
Om ax
Weight
Wi
U2
1
( 3.108 2.953 3.108 ) 3.056
3
An AHP Based Study Of Coal-Mine Zero Harm Safety Culture Evaluation
C.I .
C.R.
Om ax n
3.056 3
3 1
n 1
C.I .
R.I .
0.028
0.52
63
0.028 0.1
0.054 0.1
CR=0.0087<0.1 indicates that the judgment matrix passes the consistency test, so
calculations of weights can be used.
(3) Weight calculation of Level 2 “zero harm” safe institution culture indicators
and consistency test
Level 2 indicator set: “Zero harm” safety institution culture
U2 { U 21 ,U 22 ,U 23 } = {enterprise “zero harm” safety leadership system, “zero
harm” safety institutional system, “zero harm” safety organizational structure}.
Calculations are shown in Table 5.
Table 5. Weight calculation of Level 2 “zero harm” safe institution culture
indicators and consistency test.
U1
U11
U12
U 13
Weight
Wi
Wi0
Om i
U11
U12
U 13
1
3
2
1.817
0.545
3.018
1/3
1
1
0.693
0.210
3.020
1/2
1
1
0.794
0.240
3.017
Om ax
C.I .
C.R.
1
( 3.018 3.020 3.017 ) 3.018
3
Om ax n
n 1
C.I .
R.I .
3.018 3
3 1
0.009
0.52
0.009 0.1
0.017 0.1
CR=0.0087<0.1 indicates that the judgment matrix passes the consistency test, so
calculations of weights can be used.
(4) Weight calculation of Level 2 “zero harm” safe behavior culture indicators and
consistency test
Level 2 indicator set: “Zero harm” safety institution culture
U 3 { U31,U32 ,U33 } ={ Enterprise “zero harm” safety production style, “Zero
harm” safety production decision-making, field operation}. Calculation results are
listed in the following Table 6.
Table 6. Weight calculation of Level 2 “zero harm” safe behavior culture indicators
and consistency test.
U3
U 31
U32
U33
Weight
Wi0
Om i
64
H. Li et al.
Wi
U 31
U32
1
1/2
1/3
0.550
0.163
3.010
2
1
1/2
1
0.297
3.009
U33
3
2
1
1.817
0.540
3.009
Om ax
C.I .
C.R.
1
( 3.010 3.009 3.009 )
3
Om ax n
3.009 3
3 1
n 1
C.I .
R.I .
0.0045
0.52
3.009
0.0045 0.1
0.0087 0.1
CR=0.0087<0.1 indicates that the judgment matrix passes the consistency test, so
calculations of weights can be used.
(5) Weight calculation of Level 2 “zero harm” safe material culture indicators and
consistency test
Level
2
indicator
set:
“Zero
harm”
safety
material
culture
U 4 { U41 ,U42 ,U43 } ={ Enterprise “zero harm” safety material products,
Enterprise “zero harm” safety material technology, Enterprise “zero harm” safety
material environment}. Calculation results are shown in the following Table 6.
Table 7. Weight calculation of Level 2 “zero harm” safe material culture indicators
and consistency test.
Wi0
Om i
4
2
0.558
3.019
1
3
1.145
0.320
3.018
1/3
1
0.437
0.122
3.250
U 41
U42
U 43
U 41
U42
U 43
1
2
1/2
1/4
Om ax
C.I .
C.R.
1
( 3.019 3.018 3.250 )
3
Om ax n
n 1
C.I .
R.I .
3.096 3
3 1
0.048
0.52
Weight
Wi
U4
3.096
0.048 0.1
0.092 0.1
As CR=0.0087<0.1, it indicates that the judgment matrix passes the consistency
test, so calculations of weights can be used.
(2) Calculation of evaluation results
1) Calculation methods
An AHP Based Study Of Coal-Mine Zero Harm Safety Culture Evaluation
65
On the basis of using the AHP to determine weights of various factors, the FCE is
employed to grade “zero harm” safety culture of BLA as a coal-mine enterprise. The
FCE is a method using the fuzzy set theory to evaluate systems or programs. It is
hard to use traditional mathematical methods to solve problems with various
evaluation factors and fuzzy evaluation standards or natural state. However, the FCE
can well solve them. Before score assignment, work is done to set a total of six
( , , , , ,V )
evaluation ranks. The evaluation set is V= v1 v2 v3 v4 v5 6 =(quite
important, important, general, somewhat important, less important, and quite
unimportant). A corresponding score is assigned to each evaluation rank, as shown in
Table 8.
Table 8ˊ
ˊ Score assignments of different evaluation ranks.
Evaluation
Quite
A bit
High General
Low
Quite low
ranks
high
low
Interval value
80
60
90 100
70 80
60
Below 60
in Hundre
90
70
dmark system
Class
95
85
75
65
60
30
midvalue
The AHP is used to determine that weights of Level 2 indicators are W1 = (48, 18,
10, 24); W2 = (55, 21, 24); W3 = (16, 30, 54); W4 = (56, 32, 12). Meanwhile, a total
of 10 professors, assistant professors and lecturers specialized in safety engineering
from universities and relevant doctoral students and graduate students were gather o
form an expert team to mark the zero harm safety culture effects. Concrete grading
results are listed in Table 9-1ǃ9-2.
Table 9-1. Marking table for experts.
“Zero harm”
safety culture U
Evaluation factors
Evaluation scale
“Zero harm”
institution culture I
U1
U2
U3
U4
U21
U22
U23
90
80
70
60
4
3
2
1
1
5
4
0
5
2
1
2
3
4
2
1
2
3
5
0
6
2
2
0
2
5
1
1
60
0
0
0
0
0
0
1
30
0
0
0
0
0
0
0
66
H. Li et al.
Table 9-2. Marking table for experts.
“Zero harm”
concept culture C
“Zero harm”
behavior culture
B
“Zero harm”
material culture M
U11
U12
U13
U41
U42
U43
U31
U32
U33
4
2
2
2
0
5
3
2
3
4
1
1
4
6
0
0
6
3
1
0
5
2
2
1
1
5
3
1
3
2
2
3
6
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
For U1, 4 experts consider it to be quite important; 3 experts choose “important”;
2 experts choose “general”; and 1 expert choose “somewhat important”. Following
grading results can be obtained. U11 = 1/10 = 0.1; U12 = 4/10 = 0.4; U13 = 4/10 =
0.4; U14 = 1/10 = 0.1; U15 = 0, U16 = 0. These values are membership degrees of
corresponding evaluation scales. In the same way, membership degrees of other
factors can be calculated. Membership degree matrixes of other factors are as
follows.
ª0.2 0.3 0.5 0 0 0º
ª0.4 0.2 0.2 0.2 0 0º
»
« 0 0.5 0.3 0.2 0 0»
I= ô0.6 0.2 0.2 0
C=
0 0ằ
ô
ô
ằ
ôơ0.2 0.5 0.1 0.1 0.1 0ằẳ
ôơ0.3 0.4 0.1 0.1 0.1 0ằẳ
0 0 0
ê0.4 0.6 0
ô
M= 0.6 0.3 0.1 0 0 0ằ
ô
ằ
ôơ0.5 0.2 0.2 0.1 0 0ằẳ
ê0.1 0.5 0.3 0.1 0
0
0 ằằ
0 0.1ằẳ
B= ô0.3 0.2 0.2 0.3 0
ô
ôơ0.6 0.2 0.1
0
The same method can be employed to construct the membership degree matrix of
the factor in the target layer
ê0.4
ô0.1
U= ô
ô0.5
ô
ơ0.3
0.3
0.5
0.2
0.4
0.2 0.1 0
0.4 0 0
0.1 0.2 0
0.2 0.1 0
0
0ằằ
0ằ
ằ
0ẳ
In accordance with the above-mentioned evaluation steps, the comprehensive
evaluation vector of the factor U in the target layer is:
An AHP Based Study Of Coal-Mine Zero Harm Safety Culture Evaluation
ê0.4
ô0.1
T=W*R=0.48 0.18 0.1 0.24 0 0 ô
ô0.5
ô
ơ0.3
0.3
0.5
0.2
0.4
67
0.2 0.1 0
0.4 0 0
0.1 0.2 0
0.2 0.1 0
0º
0»» =(0.4 0.35
0»
»
0¼
0.23 0.092 0 0 )
Normalize T to get the final evaluation result (0.37 0.33 0.21 0.09 00).
Quantify evaluation ranks to calculate the overall score of the “zero harm safety
culture evaluation for BLT.
ê90
ô80ằ
ô ằ
U=0.37 0.33 0.21 0.09 0 0 ô70 ằ =79.8points
ô ằ
ô60ằ
ô60ằ
ô ằ
ôơ30ằẳ
On the basis of a calculation of the “zero harm” safety culture level of BLT as a
coal-mine enterprise, the calculation result (79.8 points) can help to determine the
development stage of “zero harm” safety culture of BLT, in order to provide useful
references to BLT to make plans for developing its “zero harm” safety culture.
Table 10 shows the division of “zero harm” safety culture levels of a coal-mine
enterprise
Table 10. Level division of “zero harm” safety culture a coal-mine enterprise.
“Zero harm” safety
culture levels
Development
stage
[ 95,100]
Level 5
Most developed
[85,95]
Level 4
More developed
[ 75,85]
Level 3
Mediumdeveloped
[60,75]
Level 2
Less developed
[0,65]
Level 1
Least developed
Valuation
Suggestions
“Zero harm” safety culture should
be preserved;
“Zero harm” safety culture should
be perfected;
“Zero harm” safety culture should
be further developed;
“Zero harm” safety culture should
be constructed
“Zero harm” safety culture requires
improvement;
4. Conclusion
The AHP is used to determine weights of “zero harm” safety culture of BLT, and the
FCE is chosen to mark the safety culture development of BLT. The total points for
“zero harm” safety culture of BLT are 79.8.
68
H. Li et al.
This score indicates that BLT is at the self-management stage, as an intermediate
development stage of “zero harm” safety culture.
BLT does not complete get rid of the passive restrained state. Therefore, BLT
should timely build a mechanism to make employees participate in discussion and
decision-making of safety issues, so that employees can realize the great importance
and value of safety for them, and individual employees and production groups can
voluntarily make commitment to and compliance with safety culture. In this way,
BLT can fully realize self-management, proceed in an orderly way, and finally move
towards the advanced stage of “zero harm” safety culture.
Acknowledgment
The work was supported by National Natural Science Foundation of China (7127116
9, 71273208).
References
1.
Kastenberg W E. Ethics, Risk and Safety Culture. Reflections on the Fukushima
Daiichi Nuclear Accident, pp.165-187ˈ2015.
2. MA YueˈFU GuiˈZANG Ya-liˊ Evaluation index system of enterprise
safety culture construction level.China SafetyScience Journalˈvol. 24(4) ˈ
pp.124 ˉ 129,2014.
3. Guldenmund F W. The nature of safety culture: a review of theory and
research.Safety Science,vol. 34(1),pp:215–257,2000.
4. Liu C, Liu J, Wang J X. Fuzzy Comprehensive Evaluation of Safety Culture in
Coal Mining Enterprises. Applied Mechanics & Materials, vol. 724, pp.373377,2015.
5. QIAN Li-jun LIˈShu-quanˊ Study on assessment model for aviation safety
culture based on rough sets and artificial neuralnetworks.China Safety Science
Journalˈ19( 10),pp. 132 ˉ 138,2009.
6. LIU Fangˊ Study on safety culture evaluation of construction enterprise,Ph.D.
thesis, Harbin: Harbin Institute ofTechnologyˈ2010ˊ
7. QIN Bo-taoˈLI Zeng-huaˊ Application of improved AHP method in safety
evaluation of mineˊ Xi˃an University of Science ˂ Technology Journalˈ
22( 2),pp. 126 ˉ 129ˊ2002.
8. Piyatumrong, et al. "A multi-objective approach for high quality tree-based
backbones in mobile ad hoc networks." International Journal of Space-Based
and Situated Computing 2.2(2012):83-103.
9. MLABao, Sarenna, and T. Fujii. "Learning-based p-persistent CSMA for
secondary users of cognitive radio networks." International Journal of SpaceBased and Situated Computing 3.2(2013):102-112.
10. Wen, Yean Fu, and C. L. Chang. "Load balancing consideration of both
transmission
and
process
responding
time
for
multi-task
assignment."International
Journal
of
Space-Based
and
Situated
Computing4.2(2014):100-113.
Analysis of Interval-Valued Reliability of Multi-State
System in Consideration of Epistemic Uncertainty
Gang Pan, Chao-xuan Shang, Yu-ying Liang, Jin-yan Cai, Dan-yang Li
Department of Electronic and Optic Engineering
Mechanical Engineering College
050003, Shijiazhuang
Email: pg605067394@163.com
Abstract. Since it is hard to obtain adequate performance data of highreliability component, resulting in epistemic uncertainty on component’
degradation law, system reliability cannot be accurately estimated. For the
purpose of accurate estimation of system reliability, assuming the component’
performance distribution parameter is the interval parameter, a component’
performance distribution model based on interval parameter variable is built,
the definition of interval continuous sequences of component’ state
performance and a computational method of the interval-valued state
probability are provided, the traditional universal generating function method is
improved, the interval-valued universal generating function and its algorithm
are defined, an assessment method of interval-valued reliability of multi-state
system in consideration of epistemic uncertainty is proposed, and verification
and illustration are conducted with simulation examples. This method
overcomes the shortcoming that an inaccurate reliability analysis model of the
component is built on account of epistemic uncertainty, which features great
universality and engineering application value.
1
Introduction
Systems are only in “normal working” and “complete failure” in the traditional
reliability analysis but, for some systems, traditional Binary State System (BSS)
assumption is unable to accurately describe some probable states in system operation.
These systems have multiple working (or failure) states except “normal working” and
“complete failure” or can operate under multiple performance levels, which can be
called Multi-State System (MSS) [1]. MSS model can precisely define component’
multiple state performance and more flexibly and exactly represent the influence of
component’ performance changes on system performance and reliability compared
with “BSS” model [2].
Research on MSS reliability has been widely concerned after it was raised in
1970s [3, 4]. From the perspective of theoretical methods, [1, 2, 5, 6] references have
a detailed description of basic concept, assessment method, and optimal design, etc.
of MSS reliability. Ref. [7] has an in-depth research on change and maintenance
decisions of incompletely maintained MSS. With regard to engineering application,
related theories of MSS reliability have been applied to electric power [8, 9], network
[10, 11], and machinery [2, 12, 13], etc.
© Springer International Publishing AG 2017
F. Xhafa et al. (eds.), Advances on P2P, Parallel, Grid, Cloud
and Internet Computing, Lecture Notes on Data Engineering
and Communications Technologies 1, DOI 10.1007/978-3-319-49109-7_7
69
70
G. Pan et al.
Components’ state performance and state probability are usually assumed as
accurate values and are given in traditional MSS theories. However, material and
components update speeds are accelerated along with technological development and
the improvement of industrial level, which enables components to present “integrated,
intellectualized, and complicated characteristics” and has an increasingly shorter
production cycle, and components reliability is tremendously improved in the
meantime. It is hard to get accurate and effective components or system failure data
for systems constituted by high-reliability components in normal conditions.
Therefore, there are many difficulties in estimating system’s accurate probability and
state performance by gaining accurate failure data. Some scholars promote traditional
MSS theories against the above-mentioned problems. Ding et al. [14, 15] have given a
general definition and a reliability analysis method of fuzzy MSS. Yan Minqiang et
al. [16] have proposed a computational method of fuzzy MSS reliability in
consideration of incomplete fault coverage against the problem that MSS performance
and probability distribution cannot be accurately gained and incompletely covered in
engineering application. Li et al. [17] have analyzed interval-valued reliability of
MSS by the use of interval analysis theory and universal generating function.
Sebastien et al. [18] have combined random set theory and universal generating
function method to analyze MSS reliability of epistemic uncertainty. Liu et al. [19]
have analyzed fuzzy MSS reliability by combining fuzzy Markov models and
universal generating function. In ref. [20], probability convolution and fuzzy
expansion are combined to propose an analytical method on MSS reliability based on
mixed universal generating function method against MSS reliability analysis under
aleatory uncertainty and epistemic uncertainty. In references [21-23], fuzzy
mathematical theory and Bayesian networks are combined to analyze MSS fuzzy
reliability from different perspectives.
There are usually two problems in the analysis of reliability of MSS constituted
by high-reliability components: (1) epistemic uncertainty on components performance
distribution appears because accurate performance degradation data of components
cannot be gained, which means parameters are inaccurate; (2) incomplete
understanding of performance degradation mechanism of systems or components
leads to inaccurate reliability analysis models and even great deviation. In addition,
the state performance and state probability of MSS are usually given in the research
on MSS reliability with epistemic uncertainty through the analysis of researches of
the afore-mentioned scholars, which does not conform to engineering application.
In view of the afore-said insufficiencies, an analytical method of interval-valued
reliability of MSS in consideration of epistemic uncertainty is proposed. First, a
components’ performance distribution model based on interval parameters is built;
second, the components’ state is divided in the form of interval continuous sequence
and components’ state interval probability is obtained according to the sequence in
order to more accurately describe components’ state information and define its
performance interval continuous sequence; finally, the traditional universal generating
function is improved, definition and algorithm of interval-valued universal generating
function are provided, and an analytical model of interval-valued reliability of MSS in
consideration of epistemic uncertainty is built.
Analysis of Interval-Valued Reliability of Multi-State System …
2
2.1
71
Paper Preparation
Performance analysis of performance degraded components
In engineering application, since accurate and effective data of high-reliability
performance-degraded components cannot be obtained within a short time, based on
which, the built performance degradation distribution model is usually inaccurate,
there may be great deviation in the analysis result. For that reason, the components’
performance distribution parameter can be regarded as an interval variable, then, the
performance distribution with the parameter as an interval variable is analyzed before
the following assumption is made:
(1) A continuous sequence of interval number is defined, [xi ] [ x i , x i ] I(R) is
assumed as the interval number, if the sequence is constituted by [x1 ],[x2 ], ,[xn ]
and meets [x1 ] d [x2 ] d d[[xn ] , it can be called a continuous sequence of interval
number (interval continuous sequence in short), noted as: êơ xI ẳ >[x1 ],[ xn ]@ ,
thereinto, i 1,2, , n .
(2) The components has only one performance parameter x, which corresponds
to one performance degradation process, and the degradation process is irreversible;
(3) At any time t, assuming components performance as x(t ) , which obeys
normal distribution with the mean value of Px (t ) and variance of V x2 (t ) , thereinto,
Px (t) and V x2 (t ) are random variables which respectively comply with uniform
distribution in [P(t )] and [V 2 (t )] , x(t ) is independent identical distribution.
(4) At any given time t , the distribution parameter of components performance
x(t ) is a random variable which obeys uniform distribution, so the performance
distribution function of the components is shown as follows˖
F (Y )
y
P (t ) V 2 (t )
³ ³P ³V
f
(t )
2
(t )
f ( x ux (t ),V x2 (t ))h(ux (t ))m(V x2 (t ))dux dV x2dx
(1)
Thereinto,
f ( x ux (t ),V x2 (t ))
§ ( x Px (t ))2 ã
exp ă
á
2
2SV x2 (t )
â 2V x (t ) ¹
1
1
° P (t ) P (t ) Px (t ) ux Px (t )
h(ux (t )) ® x
x
° 0
else
¯
1
V 2 (t ) V x2 (t ) V 2 (t )
°
m(V x2 (t )) ®V 2 (t ) V 2 (t )
°
else
0
¯
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72
G. Pan et al.
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quality before you send the files.
2.2
State probability analysis of performance-degraded components
When a components’ state performance is defined, the computational accuracy
of the universal generating function is increasingly improved with the increase of
components state number but the calculation amount will also be sharply increased, so
as to cause “curse of dimensionality” [1]. The state performance is divided in the form
of interval continuous sequences in order to remain the state number unchanged,
reduce error influence caused by epistemic uncertainty, and improve computational
accuracy as much as possible. Assuming the interval continuous sequence of the state
performance at t as êơ giI,ki ẳ êơ[gi,ki ],[ gi,ki ]ẳ and meets [ gi,ki ] [ x i,ki , xi,ki ] ,
[gi,ki ] [ yi,ki , yi, ki ] , and xi,ki yi,ki .
According to the analysis of assumption 4 in Section 2.1, the upper and lower
boundary s, p(t ) and p (t ) , of the interval probability of components’ state
performance at a given t are respectively:
p(t ) y (t )min
F ( yi (t), u,V )