Network Analysis on Safety Culture and Worker‘s Behaviour : A Forest of All Minimum Spanning Trees

Network Analysis on Safety Culture and Worker‘s

Behaviour : A Forest of All Minimum Spanning

Trees

Maman Abdurachman Djauhari

1

, Shamshuritawati Sharif

1,2

, Hariza Djauhari

3 1

Faculty of Science, Universiti Teknologi Malaysia, Skudai, Johor, Malaysia 2

College Arts and Sciences, Universiti Utara Malaysia, Sintok, Kedah, Malaysia 3

Coordinating Ministry for Economic Affairs, Indonesia

Abstract— In this paper safety culture and worker’s are considered, all together, as a complex system and statistically represented in the form of correlation network among their characteristics. We show that the current practice, based on a minimal spanning tree (MS T), to filter the information contained in the network is not robust. A robust filter based on the forest of all possible MS Ts is then proposed and used to analyze the network. For practical purpose, an algorithm will be provided to find the forest. The advantages of the proposed filter compared to the MS T-based filter will be illustrated first before we use it in the case of Malaysia manufacturing industry. S ome important results that will be useful for the management will be highlighted.

Index Term— adjacency matrix, centrality measures, correlation matrix, distance matrix, network topology.

I. INT RODUCT ION

Depart ment of Occupational Safety and Health (DOSH), Govern ment of Malaysia, is responsible in p roviding safety and healthy work environ ment for a ll e mp loyees and protect those who may be a ffected by its activities. A safety and health office r is appointed in every state office fo r coordinating and discharging the planned activities related to safety and health. This task is to ensure that the objectives of DOSH policy are fu lly met. Besides that, DOSH conducted three ma jor responsibilities, na mely, standard setting, enforcement, and promotion. A ll activit ies are periodically monitored fro m time to time in order to guarantee employers and employees in the country pay more attention to safety and health at work [1].

The DOSH policy comprises:

(i) To prepare and preserve a workplace with a safe and healthy working system;

(ii) To ensure that all staff a re p rovided with the relevant informat ion, instruction, training and supervision regarding methods to carry out their duties in a safe manner and without causing any risk to health; (iii) To investigate all accidents, diseases, poisonous and/or

dangerous occurrences, and to take action to ensure that these occurrences will not be repeated;

(iv) To provide basic welfare facilities to all workers; to revise and improve on this policy whenever necessary; and

These are an enforcement form of all the require ments of the legislations related to safety and health as stated in the Occupational Sa fety and Hea lth Act 1994 (Act 514), as we ll as regulations and codes of practice wh ich have been approved. The purpose of this act is to promote and encourage occupational safety and health awareness among worke rs and to create safety and health organization in a ll industrial sectors. In manufacturing industry, besides Act 514, DOSH also needs to enforce another important act, name ly, Factories and Machinery Act 1967 (Act 139) which covers manufacturing, min ing, quarrying and construction industries.

The aim of this paper is to have a better understanding to what e xtent the current pract ice of safety culture and worker‘s behaviour differs fro m DOSH policy. More specifically, to identify the most important factors that must be paid more attention by DOSH in order to reduce the number o f fatal accidents in manufacturing sector. For that purpose, safety culture and worker‘s behaviour will be considered as a comple x system and numerically represented in the form of a corre lation network a mong characteristics involved in this study. The current practice to analyze such network is generally consists of (i) info rmation filtering by using a min ima l spanning tree (MST), and (ii) interpretating the filtered information by using, for e xa mple , centrality measures.

the dot plot matrix, network topology, and centrality measures. Concluding re ma rks will close the presentation of this paper.

II. CURRENT SIT UAT ION

Manufacturing sector is one of the sexiest industrial sectors in Malaysia economic gro wth. It contributes around 10% [2]. Therefore , it provides economic opportunities for related industries and businesses. On the other hand, however, the number of accidents in manufacturing sector, including fata l acc idents, has been increased from time to time.

In 2008 – 2010, Malaysia‘s manufacturing sector has been contributing the highest number of accidents which result in non-permanent disabilit ies (NPD), permanent disabilities (PD) and death (D). Th is sector becomes the second sector where accident occurrences causing death is placed on the top behind the construction sector, in 2009 and 2010, as can be seen in Table I.

TABLE I

T he occupational accident by sector in 2008 – 2010

Source: DOSH (2011).

The occurrences of occupational accidents are believed due to direct, indirect and basic causes. Human factors are believed as the most important contributors to the accident occurrences. In this regards, Short [3] has mentioned that unsafe behaviour of the workers is the direct source of accident along with unsafe condition.

Safety culture and worker‘s behaviour, as observable human factors, are a manifestation of the organization reflected by its organizational culture. However, if safety culture is presumed as the underlying basic factor that permits direct cause of accidents to take place, worker‘s behaviour is the predominant factor in reducing the number and fatality of accidents.

Fro m Table I we learn that the current practice of safety culture and worker‘s behaviour differs considerably fro m DOSH e xpectation. More specifically, that table shows that the workp lace is neither safety nor healthy as required in DOSH po licy. It is to understand the deviation from DOSH e xpectation, and to find out the way to reduce accident occurrences, this research has been conducted.

III. MET HODOLOGY

In this research, front line workers a re the target group. They are requested to fill-in the questionnaire related to

safety culture and worker‘s behaviour. The questionnaire consists of nine factors of s afety culture, namely,

(i) Management Commitment

(ii) Communication

(iii) Priority of Safety

(iv) Safety Procedure and Policy

(v) Supportive Environment

(vi) Involvement

(vii) Personal priority and need of safety

(viii) Personal Appreciation towards Risk

(ix) Work Environment

and seven of worker‘s behaviour, i.e.,

(i) Reacting behaviour

(ii) Personal Protective Equipment

(iii) Specific Job Risk

(iv) Tools and equipments

(v) Safe Work Practice

(vi) Ergonomics

(vii) Communication

In total, there are 43 characteristics (questions) in this study; 18 characteristics are re lated to safety culture and 25 to worker‘s behaviour. See Appendix for the list and Djauhari [4]for the details of questionnaire construction.

Corre lation network approach is used to represent numerically the interre lationships among all characteristics. Once the data are collected fro m respondents, the network is then simp lified in the form of corre lation matrix. This matrix is the only source of information in any correlation network ana lysis. The current pract ice in this analysis is to filter the informat ion contained in the network by using a

minimal spanning tree (MST). See Mantegna[5] who

originally introduces MST-based filter in that analysis, Mantegna and Stanley [6] who popularize this filter, Miccichè et al. [7] for its application in price return and volatility, Siec zka and Holyst[8] in co mmodity ma rket, Pa rk and Yilmaz [9] for road network ana lysis, and Tabak et al. [10] for stock ma rket ana lysis. MST does not only serve as an information filter but also as a tool to simplify and visualize the co mple x netwo rk in the form of filtered network topology a mong all characteristics [11][12]. These show the important role of M ST as an informat ion filte r in network analysis. Ho wever, as we will show in the ne xt section, the use of MST-based filter might g ive misleading informat ion if there is more than one MST in the network; two diffe rent MSTs will differently filter the information in the network. To handle this drawback, instead of using a MST, we propose to use the forest of all M STs (o r, brie fly, the forest). Th is will ensure the robustness of the filtered information [13].

Monárrez-Espino and Caballe ro-Hoyos [14] for practica l examples.

A. Data collection and analysis

In our survey, the focus is on the front line worke rs, i.e., operators and technicians because they are the ma in target of DOSH policy. A nu mber of 136 workers we re participated in filling-in the questionnaire described previously. Data collected fro m those worke rs were used to construct the correlation matrix.

Let

X

_i and X_i denote the i-th characteristic and the average of

X

_i, respectively; i = 1, 2, … , n = 43. The correlation networks among those characteristics are numerically summarized in the form o f corre lation mat rix C. It is a symmet ric matrix of size

43 43



where the element in i-th row and j-th column is,

ij







2 2





2 2



i j i j

i i j j

X X X X

X X X X



 

the correlation coeffic ient of

X

_i and

X

j that serves to quantify the degree of their linear re lationship. By definit ion,



_ii



1

for a ll i and



_ij is between – 1 to 1 for all

i



j

. Thus, C is a nu merical summa ry representing the complex system of characteristics interrelationships.

The network C consists of 43 characteristics together with the (43-1)* 43/ 2 = 903 co rre lation coefficients. In general, see Mantegna [5], the standard practice to analy ze this network is

(i) transforming C into a d istance matrix D where its i-th row and j-th column is

d( , )i j = 2(1_ij) for all i, j = 1, 2, …, n, (1)

(ii) find a MST in D, which represents the filte red important information contained in D,

(iii) analyze the topological property of a ll characteristics based on MST. For this purpose, in this paper we use the centrality measures.

The centrality measures such as degree, betweenness, closeness, and eigenvector centralities[15 will be used to identify the most important factors followed by a Pareto analysis to identify the vital few in safety culture as well as worker‘s behaviour.

B. Robust information filtering

Minima l spanning tree (MST) re lated to the corre lat ion network beco mes an indispensible tool in network analysis to filter the most important informat ion. See, for e xa mple , Mantegna [5]for the original work, Tu mminello et al.[16] for its application in general co mp le x systems, Eo m et al. [17]in Shanghai and Shenzhen ma rket inde x, and , Eo m et al. [18] in a correlation network.

The role of MST in network analysis is as a tool to e xpla in the physical corre lation between the topological structure and classification of the nodes [19]. If the

topological structure of the nodes could be directly obtained fro m MST, the classification in the form o f an inde xed hierarchica l t ree is constructed based on its corresponding subdominant ultra metric (SDU). Howeve r, we will show below that the use of MST as an information filter might produce misleading informat ion if there is more than one MST in the network.

Consider the co mple x system in Fig. 1 consisting of five nodes P, Q, R, S, and T where the d istance between two different stocks is given in Table II.

TABLE II

T he Distance between stocks

P Q R S

Q 0.1

R 0.6 0.6

S 0.5 0.7 1.0

T 0.1 1.5 0.8 0.5

Fig. 1. Complex system of five stocks

To find a MST of that network, the two most suggested algorith ms in the literature are Kruskal‘s algorith m and Prim‘s. If the data structure in Table II is stored in Matlab version 7.8.0 (2009a), those algorith ms will g ive the MST in Fig. 2(a). If we store another data structure form, those algorith ms will g ive another MST. Actually, that co mple x system contains four MSTs as can be seen in Fig. 2(a) – 2(d).

Each M ST in Fig. 2 filters differently the information in the network co mpared to others. Two d iffe rent MSTs represent different filtered information. Thus, they define different topological property co mpared to each others. This shows that the use of a MST might provide misleading informat ion. In other words, the in formation filtered by using MST is not robust.

relation approach.

C. Algorithm to find the forest

We consider D fro m fu zzy relation vie wpoint. This will enable us to see more in-depth the properties of the distance d in (1). Let E the set of n characteristics. As a rea l non-negative function defined on E



E, for a ll i, j and k in E, d satisfies

0



d( , )i j <



and d( , )i j = 0 if and only if i = j, d( , )i j = d( , )i j , and d( , )i j



d( , )i k + d( , )k j

(a)

(b)

(c)

(d)

Fig. 2. All possible minimal spanning trees

Fro m fu zzy re lation viewpo int, these properties show that D is a symmetric and anti-refle xive fuzzy relat ion with d as the me mbe rship function. Consequently, the SDU of D is the min-ma x t ransitive c losure of D, [13] denoted by D*K for an integer K ; 2



K



n, where

(i) D*k = D * D*(k -1)is k times min-ma x transitive operation ‗*‘ of D; for k = 2, 3, …, K with D*1 = D

(ii) D*K = D*(K+ )m for all positive integers m. (iii) The me mbe rship function of D*k fo r all positive

integers k is d*k

 

i, j given by

 

*

d k i, j =



d( , ) d*( -1)( , )



1

n

k

i m m j

m

 



(iv) a



b = min{a, b} and a



b = ma x{a, b} for a ll real numbers a and b

By using D*K we construct the forest of all MSTs in D. Let M be a MST of D and ( =i i ,i ,...,i_{1 2 p}  j) be the chain fro m i to j in M . If we define the distance

d

between

i and j in M by

d( , )i j = 1

d( , ₁) =1

p

-i_k i_{k +} k

 ,

then, d is the SDU of d. See Djauhari [13]for the details. Therefore, there exists an integer m; 1



m < p, such that

 

*

d K i, j = d( , )i j = d(i_{m m+},i ₁).

Let



be a fuzzy re lation where its me mbership function is given by

( , )i j

 =

 

 

*

1; d( , ) d = 0 and

*

0; d( , ) d 0 or

K

i j i, j i j

K

i j i, j i = j

 _{ }

 

  



(2)

Based on the above results we propose the follo wing algorith m to find the forest. In this a lgorith m, D and



are considered as matrices of size (n n ).

Step 1: Let k = 2,

Step 2: Co mpute D*k where D* D*(k -1) is matrix mu ltip licat ion of D and D*(k -1) in the usual sense but mult iplication and su mmation o f t wo real numbers a and b are defined as ma x{a, b} and min{a, b}, respectively,

Step 3 : If D*k = D*(k -1), then the SDU of D is

D

*k

and go to Step 4. Otherwise, let k := k+1 and then go back to Step 2,

Step 4. Co mpute



as defined in (2). Then



is the adjacency matrix representing the forest of a ll MSTs in D.

To speed up the convergence of this algorithm we

compute D*2, D*4, D*8, … , instead of D*2, D*3,

*4

D , … . We stop at the K-th iteration if D*2 K

=

( 1) *2 D

K

-. Then, D*2 K

is the SDU of D and the nu mber of

iterations K satisfies 2K



n or K



ln( )

ln(2)

n

.

D. Some advantages of the proposed filter

Topological properties of correlation network derived fro m a MST as presented, for exa mp le, in [10] a re different fro m those issued fro m the forest e xcept if D contains one unique MST. Consequently, filtered informat ion issued from the forest and that from a MST are different. If MST is not unique, then its use will be misleading. This situation will not be encountered if we use the forest of all MSTs. As an exa mple, let us consider the topological properties in terms of degree centrality of each node. See Micciche et al.[7],and Borgatti [5]fo r the details about this measure. In correlation network analysis, degree centrality plays an important role. For e xa mple, in stock networks analysis, it is closely re lated to market inde x[18]. Stocks with high degree are more strongly correlated with ma rket inde x than those with low degree [17]. Suppose D contains more than one

MST. Let M be a MST with adjacent matrix



_M and F be

the forest of a ll MSTs. The degree of stock k with respect to M is the number of links adjacent to that stock or, equivalently, the sum of all ele ments in the k-th row o f



_M, i.e.,

( )k

_M = ( , )

=1

n

k j j





M . (3)

Here



_M

( , )

k j

is the ele ment in the k-th row and j-th column of



_M. Based on the forest F, the degree of stock

k is defined by

( )k

_F = max



 ( )k



 M

M F . (4)

Therefore, in general, _F( )k



_M( )k for a ll k = 1, 2, …, n.

As an illustration, suppose Kruskal‘s algorith m o r Prim‘s accidentally gives the MST in Fig. 2(d). Then, according to (3), the degree of P, Q, R, S, and T with respect to that MST are _M(P) = 2, _M(Q)= 2, _M(R) = 1,

(S)

_M = 1, and _M(T) = 2, respectively. These diffe r considerably fro m the degrees defined by the forest. According to (4); _F(P) = 4, _F(Q) = 2, _F(R) = 1,

(S)

_F = 1, and _F(T) = 2.

Similar phenomenon will a lso be encountered when we use the other centrality measures. This shows the advantages of the forest in terms of centrality measures.

IV. RESULT S AND DISCUSSION

In this section, the dot plot matrix issued from forest of a ll MST is performed to illustrate the benefit of this study. Later we show our result based on network topology and centrality measure.

A. Dot pot matrix

Fro m 136 surveyed workers, we obtain the correlation

matrix C a mong 43 characteristics. After having

transformed C into distance matrix D by using equation (1), the above algorithm g ives us the adjacency matrix associated to the forest of all MSTs. This matrix is presented in Fig. 3 in the fo rm of dot plot matrix. The b lank ce ll represents = 0 and black cell = 1.

That figure shows that the highest correlations a mong safety culture characteristics (region A) are concentrated along diagonal wh ile worker‘s behaviour characteristics (region C) are mo re dispersed. Moreover, some of worker‘s behaviour characteristics are a lso highly corre lated with some safety culture characteristics (reg ion B). This indicates that managing worker‘s behaviour is more co mplex compared to safety culture. More specifically,

(i) In safety culture (region A), the high correlat ions are generally a mong characteristics within factors. The correlations between factors are low.

(ii) In worke r‘s behaviour (region C), the high corre lations are not only a mong characteristics within factors but can also be found between factors.

(iii) The following worke r‘s behaviour characteristics CD1, CC2, and CA 3 representing ‗Reacting Behaviour‘, ‗Specific Job Risk‘, and ‗Tools and Equip ments‘ factors , respectively, are also highly corre lated with these safety culture characteristics ; BE2, BH1 and BI1 that represent ‗Supportive Environ ment‘, ‗Personal Appreciation Towards Risk‘, and ‗Work Env iron ment‘ factors. See region B of Fig. 3.

Fig. 3. Dot plot matrix issued from the forest of all MST s. The first advantage of the use of the forest of all MSTs compared to the use of a MST to filter the info rmation can be seen when we co mpare dot plot matrix in Fig. 3 with that issued from a MST in Fig. 4. In Fig.3 there are four additional black ce lls that cannot be found in Fig. 4. They are numbered 1 and 2 in region B (between safety culture and worker‘s behaviour characteristics), and 3 and 4 in region C (within wo rker‘s behaviour characteristics). This will be clarified in the next sections.

The second advantage is that the nu mber o f b lack ce lls in Fig. 3 is 46 which greater than that in Fig. 4 which is 42 (total number of characteristics minus 1). This means that the number of M STs in D is mo re than one. More prec isely, there are 16 M STs in D. Whichever MST is used, the informat ion is misleading. Therefore, the use of the forest of MSTs as a robust filter is mo re appropriate than a MST to filter the informat ion in D. Fo r this reason, in the rest of the paper, only the forest will be considered.

Fig. 4. Dot plot matrix based on a MST .

B. Network Topology

To elaborate the above results more c learly, in Fig. 5 we present the network topology that corresponds to the fo rest. In that figure we see the interconnectivity among all characteristics of both groups. Empty circles represent safety culture characteristics group and black circles are fo r worker‘s behaviour group. In general, the two groups are

clearly separated as mentioned earlier e xcept the fo llo wing two factors of safety culture,

(i) Personal appreciation towards risk (BH1 and BH2), and (ii) Work environment (BI1 and BI2).

These factors are more similar to ‗Reacting Behaviour‘ factor of wo rker‘s behaviour than to other factors within their own group. Furthermore, ‗Supportive Environ ment‘ factor (BE2) in safety culture group (e mpty circ les group) is more similar to ‗Tools and Equip ments‗ factor in worker‘s behaviour group (black c irc les group) than to factors of its own group.

Fig. 5. Network topology based on the forest of MST s.

C. Centrality measures

The importance of each particula r node can be nu merically analyzed by using the centrality measures such as degree, betweenness, closeness, and eigenvector centralities. See [8] for their applicat ion in co mmodity ma rket and [9] in road network. According to the forest, the score of each node for those centrality measures is given in Table III.

TABLE III Centrality measure

No.

i

d_i bi ci evi

1 BA1 0.024 0 0.142 0.019

2 BA2 0.071 0.138 0.165 0.053

3 BB1 0.048 0.048 0.143 0.022

4 BB2 0.024 0 0.142 0.019

5 BC1 0.024 0 0.125 0.008

6 BC2 0.071 0.138 0.165 0.053

7 BD1 0.095 0.373 0.191 0.108

8 BD2 0.024 0 0.161 0.039

9 BE1 0.024 0 0.186 0.159

10 BE2 0.095 0.411 0.227 0.443

11 BF1 0.071 0.463 0.213 0.155

12 BF2 0.048 0.377 0.220 0.215

13 BG1 0.048 0.048 0.143 0.022

14 BG2 0.024 0 0.125 0.008

15 BH1 0.048 0.048 0.122 0.017

16 BH2 0.024 0 0.109 0.006

17 BI1 0.048 0.048 0.127 0.010

18 BI2 0.024 0 0.113 0.003

1

3

A

C

A B

C

B

2

3

4

19 CA1 0.048 0.037 0.174 0.141

20 CA2 0.024 0 0.186 0.169

21 CA3 0.048 0.177 0.164 0.048

22 CA4 0.071 0.242 0.188 0.109

23 CA5 0.071 0.138 0.144 0.024

24 CA6 0.095 0.160 0.138 0.042

25 CB1 0.024 0 0.128 0.018

26 CB2 0.024 0 0.128 0.018

27 CB3 0.071 0.094 0.146 0.051

28 CB4 0.071 0.222 0.168 0.106

29 CB5 0.048 0.048 0.145 0.043

30 CB6 0.024 0 0.127 0.016

31 CC1 0.024 0 0.127 0.008

32 CC2 0.024 0 0.122 0.015

33 CD1 0.048 0.103 0.198 0.177

34 CD2 0.071 0.122 0.214 0.392

35 CD3 0.095 0.528 0.227 0.471

36 CD4 0.071 0.530 0.219 0.311

37 CE1 0.071 0.266 0.192 0.200

38 CE2 0.048 0.096 0.193 0.103

39 CF1 0.048 0.002 0.122 0.026

40 CF2 0.048 0.021 0.135 0.030

41 CF3 0.071 0.253 0.155 0.058

42 CG1 0.048 0.285 0.174 0.091

43 CG2 0.071 0.331 0.195 0.195

From those scores we summarize

(i) Based on degree centrality, BD1 and BE2 (blac k points), CA6, and CD3 (blank po ints) have the highest number of links (4 links). Each of the followings has 3 lin ks: BA 2, BC2, and BF1 (b lack points), CA4, CA5, CB3, CB4, CD2, CD4, CE1, CF3, CG2 (blank points). The rests are of 1 and 2 links only. The mo re the number of lin ks of a particular characteristic, the more the number of other characteristics influenced by that characteristic. For e xa mp le, according to this measure, BD1, BE2, CA6 and CD3 a re the most influentia l characteristics to the large nu mber o f other characteristics.

(ii) In terms of betweenness, CD3 and CD4 play the most important role in the network followed by, in order o f importance: (i) BE2 and BF1 as the second most important, (ii) BD1 and BF2 as the third most important, and (iii) CA4, CB4, CE1, CF3, and CG1 as the fourth most important. Thus, these characteristics should be well managed since the influence of the characteristics to each other will be passing through them more effectively than others.

(iii) According to closeness centrality measure, BE2 and CD3 have an e xce llent position co mpared to the others where the information flow in the network can faster reach the others. The second and third closest node to the others are (i) BF1, BF2, CD2, and CD4, and (ii) BA2, BC2, BD1, BD2, BE1, CA1, CA 2, CA3, CA4, CB4, CD1, CE1, CE2, CF3, CG1.

(iv) The last measure is the eigenvector centrality. According to this measure, CD3 receives the highest score followed by BE2 and CD2 at the second and third, respectively. Hence, CD3 is the node that influences the other high scored nodes. It is the most influential characteristic to the second BE2 and the third CD2.

It is important to note that these results are different fro m those given by MST-based filter. Since each measure plays diffe rent role, the factors that should be of high priority in reducing the number of fatality and paid more attention by DOSH depend on what measure is used. Due to this restriction, we p ropose to use also a Pa reto analysis on the top scored characteristics in each measure to find the vital few. Based on Pareto analysis, there are three among nine factors of safety culture and three among seven factors of worker‘s behaviour which are the v ital few. For safety culture, in order of importance, they are (a) ‗Supportive Environment‘, (b) ‗Safety Procedure and Policy‘, and (c) ‗Involvement‘. On the other hand, the vital few in worker‘s behaviour are, (a) ‗Tools and Equip ment‘, (b) ‗Safe Work Practice‘, and (c) ‗Communication‘.

V. CONCLUDING REMARKS

The forest of all MSTs is proposed to filter the impo rtant informat ion contained in correlation network o f safety culture and worker‘s behaviour in Malaysia manufacturing industry. We found that the network contains more than one MST. Therefore, whichever MST we use, the informat ion is misleading. This justifies the appropriateness of the use of the forest as a robust filter of information. A visual representation of the adjacent matrix re lated to the forest is given in the form o f dot plot matrix and the topological properties of the forest are analy zed nume rica lly by using centrality measures such as degree, closeness, betweeness, and eigenvector centrality. We a lso conduct a Pareto analysis on the top ten scored characteristics in each measure to find the vital v iew that could be paid attention by DOSH.

First, dot plot matrix indicates that managing worker‘s behaviour is more co mple x co mpared to safety culture. More specifically, in safety culture, high corre lation is generally a mong characteristics within and not between factors. On the other hand, in worker‘s behaviour, high correlation is not only among characteristics within factors but can also be found between factors. The two group of factors are clearly separated except ‗Personal Appreciation Towards Risk‘ and ‗Work Environ ment‘ factors in safety culture are of h igher correlat ion with ‗React ing Behaviour‘ factor of worker‘s behaviour than with other factors within their own group. Furthermore, ‗Supportive Environ ment‘ factor in the first group is of higher co rrelation with ‗Tools and Equip ments‗ factor in the second group than with other factors in the same group.

Second, the scores of each centrality measure lead to the follo wing conclusion. According to degree centrality,

Environment‘ factors of safety culture, and ‗Reacting Behaviour‘ and ‗Tools and Equ ip ment‘ factors of worker‘s behaviour are the most influential factors to other factors. In terms of betweenness, ‗Tools and Equip ment‘ factor o f worker‘s behaviour p lays the most important role followed by, in order of importance (a) ‗Supportive Environ ment‘ and ‗Involvement‘, (b) ‗Safety Procedure and Policy‘. The closeness centrality measure put ‗Supportive Environ ment‘ and ‗Tools and Equipment‘ as the closest factors to the others. Thus, the information flow in the network can faster reach other factors fro m the m. Based on eigenvector centrality, ‗Tools and Equip ment‘ is the only factor that lin ks to the other high scored factors. It is the most influential factor to the second most influential factor ‗Supportive Environment‘.

Third, according to a Pareto analysis the following vital fe w factors are to be paid more attention by DOSH. Fo r safety culture, in order o f importance, they are (a ) ‗Supportive Env iron ment‘, (b) ‗Safety Procedure and Policy‘, and (c) ‗Involvement‘. On the other hand, the vital few in worker‘s behaviour are, (a) ‗Tools and Equip ment‘, (b) ‗Safe Work Practice‘, and (c) ‗Communication‘.

ACKNOWLEDGMENT

We are very grateful to the Ministry of Higher Education, Govern ment of Ma laysia, fo r financia l support to conduct

this research under RUG vote nu mber

Q.J130000.7126.02H18. The authors would like to thank t he Ministry of Higher Education, Universit i Tekno logi Malaysia and Universiti Utara Malaysia for the sponsorship and the opportunity to do this research. Specia l thanks go to the Editor and anonymous referees for their helpfu l comments and suggestions.

REFERENCES

[1] (2011) Department of Occupational Safety and Health Malaysia. [Online]. Available: http://www.dosh.gov.my

[2] (2011) Malaysia Economic Report, Available:

http://www.treasury.gov.my.

[3] J. Short, The role of safety culture in preventing commercial motor vehicle crashes. Volum e 14 of Synthesis (Commercial Truck and Bus Safety Synthesis Program (U.S.)). Washington D. C. Transportation Research Board, 2007.

[4] H. Djauhari, ―Safety Culture at a manufacturing Industry in Johor Malaysia,‖ Master Dissertation. Universiti Teknologi Malaysia, Johor, Malaysia, 2010.

[5] R. N. Mantegna, ―Hierarchical Structure in Financial Markets,‖ European Physical Journal B, vol. 11, pp. 193-197, 1999. http://dx.doi.org/10.1007/s100510050929

[6] R. N. Mantegna, and H.E. Stanley, An Introduction to Econophysics: Correlations and Complexity in Finance. Cambridge University Press, Cambridge UK, 2000.

[7] S. Miccichè, G. Bonanno, F. Lillo, and R.N. Mantegna, ―Degree stability of a minimum spanning tree of price return and volatility,‖

Physica A, vol. 324, pp.66–73, 2003.

http://dx.doi.org/10.1016/S0378-4371(03)00002-5

[8] P. Sieczka, and J. A. Holyst, ―Correlations in commodity markets,‖

Physica A, vol. 388, pp.1621-1630, 2009.

http://dx.doi.org/10.1016/j.physa.2009.01.004.

[9] K. Park, and A. Yilmaz, ―A Social Network Analysis Approach to Analyze Road Networks,‖ ASPRS Annual Conference. San Diego, CA, 2010.

[10] B.M. Tabak, T .R. Serra, and D.O. Cajueiro, ―Topological properties of stock market networks: The case of Brazil, ‖ Physica A, vol. 389, pp. 3240-3249, 2010.

[11] V. Batagelj, and A. Mrvar, Density based approaches to network analysis: Analysis of Reuters terror news network, Ninth Annual ACM SIGKDD, Washington, D.C. 2003.

[12] V. Batagelj, and A. Mrvar, (2011) PAJEK: Program for Analysis and Visualization of Large Networks, version 2.02. [online]. Available: http://pajek.imfm.si/doku.php?id=download.

[13] M.A. Djauhari, ―A robust filter in stock networks analysis‖. Physica A: Statistical Mechanics and its Applications, vol. 391, no. 20, pp. 5049-5057, 2012.

[14] J. Monárrez-Espino, and J. R. Caballero-Hoyos. ― Stability of Centrality Measures in Social Network Analyses to Identify Long-Lasting Leaders from an Indigenous Boarding School of Northern Mexico,‖ Estudios sobre las Culturas Contemporaneas, vol. 16, no. 32, pp.155-171, 2010.

[15] S. P. Borgatti, ―Centrality and AIDS,‖ Connections, vol. 18, no. 1, pp.112-114, 1995.

[16] M.T umminello, T . Aste, T. D. Matteo, and R. N. Mantegna, A tool for filtering information in complex systems. Proceedings of the National Academy of Science USA, vol. 102, pp.10421 -10426, 2005.

[17] C. Eom, G. Oh, and S. Kim, 2006. Topological properties of the minimal spanning tree in Korean and American stock markets, Available: http://arXiv:physics/0612069v1

[18] C. Eom, G. Oh, and S. Kim, Statistical investigation on con nected structures of stock networks in a financial time series. Journal of the Korean Physical Society, vol. 53, no.6, pp. 3837-3841.2008. [19] R. Zhuang, B. Hu, and Z. Ye, Minimal spanning tree for

Appendix

Safety Culture and Worker‘s Behaviour Components and their Corresponding Variables

SAFETY C ULTURE

Manage me nt C ommitme nt

1 BA1 Management acts decisively whenever safet y matters occur

2 BA2 Management acts quickly to solve safety matters

C ommunication

3 BB1 My line superior always gives me information on safety 4 BB2 T here is good communication regarding

safety issues which influences my work

Priority of Safe ty

5 BC1 Management considers safety as important asproduction 6 BC2 I believe safety issues are put in high priority

Safe ty Proce dure and Policy

7 BD1 All health and safety rules and procedures need to be followed to get the job done safely

8 BD2 All health and safety rules are practical

Supportive Environme nt

9 BE1 I am encouraged to report unsafe condition 10 BE2 I can influence health and safety performance

Involve me nt

11 BF1 I am involved in informing management to important safety issues

12 BF2 I am involved with safety issues at work

Pe rsonal priority and ne e d of safe ty

13 BG1 Safety is my top priority when doing my work 14 BG2 It is important to do continuous emphasis on safety

Pe rsonal Appre ciation towards Risk

15 BH1 I believe I will not experience occupational accident here 16 BH2 T he chance of being involved in an accident here is low

Work Environme nt

17 BI1 Operational targets are always in accordance with safety measures

18 BI2 I am always given enough time to get my job done safely

Appendi x: S

afety Culture and Worker’s Behaviour Components and their Corresponding Variables

WO RKER’S BEHAVIO UR

Re acting be haviour

19 CA1 I always adjust my personal protective equipment before doing my job so that I can work safely

20 CA2 I never do shortcut in my job 21 CA3 I always change my position carefully when doing my job

22 CA4 I always stop my work first before attaching safety guards

23 CA5 I always do my job in order so that I can work safely 24 CA6 I never do horseplay during my job

Pe rsonal Prote ctive Equipme nt

25 CB1 I always use head gear

26 CB2 I always use eye protection and face shielding 27 CB3 I always use hearing protection

28 CB4 I always use respiratory protection 29 CB5 I always use arm and hand covering 30 CB6 I always use foot and leg protection

Spe cific Job Risk

31 CC1 I always follow safety policy and procedure 32 CC2 I never experience accidents due to my job

Tools and e quipme nts

33 CD1 I always use right tools and equipments for my job 34 CD2 I always use tools and equipments for my job correctly 35 CD3 Tools and equipment I use for my job are always be maintained well

36 CD4 I always participate to keep my workplace in a good housekeeping

Safe Work Practice

37 CE1 I understand how work safely in my job 38 CE2 I always work safely

Ergonomics

39 CF1 I never do many repetition in my job

40 CF2 I never do my work in long duration without rest 41 CF3 I never have awkward posture in my work

C ommunication