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Same SIGNAL for some gate in two evaluations will imply the gate’s inputsin these two evaluations be same.

# 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

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

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

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

0»» =(0.4 0.35

»

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

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

(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

(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

¯

To ensure that the reproduction of your illustrations is of a reasonable quality, we

advise against the use of shading. The contrast should be as pronounced as possible.

72

G. Pan et al.

If screenshots are necessary, please make sure that you are happy with the print

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 )

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