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Safety Science 47 (2009) 78–87

Stochastic modeling of accident risks associated withan underground coal mine in Turkey

Mehmet Sari a,*, A. Sevtap Selcuk b,1, Celal Karpuz c,2, H.Sebnem B. Duzgun c,3

a Engineering Faculty, Aksaray University, 68100 Aksaray, Turkeyb Department of Statistics, Middle East Technical University (METU), 06531 Ankara, Turkey

c Department of Mining Engineering, METU, 06531 Ankara, Turkey

Received 5 January 2007; received in revised form 14 December 2007; accepted 17 December 2007

Abstract

In this study, a methodology is proposed towards development of an uncertainty model that includes randomness in the occurrence ofdays-lost accidents in a coal mine. The accident/injury data consists of 1390 days-lost accident cases recorded at GLI-Tuncbilek under-ground lignite mine from January 1994 to December 2002. In the first step of proposed methodology, the frequency and the severity ofthe accidents have been modeled statistically by fitting appropriate distributions. The test done by BestFit software yields a chi-squarevalue of 21.53 (p = 0.089) with 14 degrees of freedom and estimates the parameter of lambda for Poisson distribution as 12.87 accidents/month. For the severity component, a lognormal distribution is fitted to days-lost data and chi-square goodness-of-fit test calculates avalue of 40.44 (p = 0.097) with 30 degrees of freedom. The parameters of lognormal distribution are estimated as a mean of 14.3 days andstandard deviation of 23.1 days, respectively. Then, two distributions are basically combined by Monte Carlo simulation in order to con-struct relative risk levels in yearly base referring to the final cumulative distribution. Finally, a simple forecasting modeling is carried outin order to quantitatively predict the expected risk levels by using decomposition technique in time series analysis. Stochastic model esti-mates that although, there would be substantial reduction in the expected number of accidents in the near future, the higher level of risksstill should be a concern for the mine management.� 2007 Elsevier Ltd. All rights reserved.

Keywords: Underground coal mining; Accident analysis; Distribution fitting; Poisson distribution; Stochastic risk modeling

1. Introduction

Coal mining, either surface or underground, has manyhazards that make it unique in the field of industrial healthand safety. The often soft, faulted and folded sedimentarystrata make wall or roof movement a risk to the safe andeconomic removal of the coal. Therefore, it has long been

0925-7535/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ssci.2007.12.004

* Corresponding author. Tel.: +90 382 2150953; fax: +90 382 2150592.E-mail addresses: mehmetsari@aksaray.edu.tr (M. Sari), sselcuk@

metu.edu.tr (A.S. Selcuk), karpuz@metu.edu.tr (C. Karpuz), duzgun@metu.edu.tr (H.Sebnem B. Duzgun).

1 Tel.: +90 312 2106853; fax: +90 312 2101592.2 Tel.: +90 312 2102665; fax: +90 312 2101265.3 Tel.: +90 312 2105415; fax: +90 312 2101265.

regarded as a relatively dangerous industry in every coun-try in the world for example; in the United States coal min-ing is considered to be one of the most hazardousoccupations (Hayduk and Ritzel, 1988; Leigh, 1988; Myerset al., 1998; Poplin et al., in press). Employees in coal min-ing are more likely to be killed or to incur a non-fatal injuryor illness, and their injuries are more likely to be severethan workers in private industry as a whole, according tothe US Bureau of Labor Statistics (US BLS, 2007). Therate of fatal injuries in the coal mining industry in 2006was 49.5 per 100,000 workers, nearly twelve times the ratefor all private industry. In Turkey, this sector is alsoresponsible for most of the occupational accidents and dis-eases. According to the Turkish Social Security Institution(SSK) annual statistics of 2005, the Turkish coal mining

M. Sari et al. / Safety Science 47 (2009) 78–87 79

industry ranks first in occupational diseases and permanentdisabilities, third in deaths and fifth in the occupationalaccidents (Anon, 2006).

Accidents are painful and costly to the workers and theirfamilies. They can be also a burden on the mining compa-nies because, in addition to the costs of personal injuries,they may incur far greater costs from damage to propertyor equipment, and production losses. It has been shownby Bhattacherjee et al. (1992) that the total cost of acci-dents on average resulted in a loss of 1 million USD peryear and an average loss of 5000 USD per accident in acase mine in the eastern USA. In a similar study carriedout for Turkish Coal Enterprises (Istanbulluoglu, 1999),the total cost of lost working days due to accidents in ayear is calculated as 4.3 million USD without consideringindirect losses. Therefore, one of the main concerns of min-ing companies is to cut the costs of accident while improv-ing mine safety.

Mining activities involve materials, equipment, humanresources and an environment where the potential risk ofcatastrophic losses is very high. Generally, losses resultedfrom mining accidents are examined without taking intoconsideration the uncertainty in the occurrence of hazardsand the analysis of those losses are mostly deterministic innature. For this reason, the stochastic assessment of acci-dent risks and the determination of proper risk controlmethods for mining applications has become a requirementfor decreasing the costs resulted from the occurrence ofhazards.

A deterministic risk assessment approach has been per-formed on the available days-lost data and risk levels werefirst identified for conventional and mechanized panels oftwo underground coal mines in earlier studies (Sari, 2002;Sari et al., 2004). In this study, an uncertainty analysismethodology is proposed as its steps are clearly identified.Risk due to accidents in the GLI-Tuncbilek coal mine isbasically evaluated by a stochastic analysis of several char-acteristics of past traumatic accident/injury experiencedata. In stochastic modeling of the GLI-Tuncbilek data,two random variables directly related with accident occur-rence are taken into consideration. The number of acci-dents per month denoted as frequency (H) and thenumber of days-lost per accident denoted as severity (S)constitute the basic components of the risk. The appropri-ate probability distributions of these variables enable theresearcher to establish the level of risk for any specified val-ues of H and S.

2. Risk assessment studies in the mining industry

The way in which risks are perceived is strongly corre-lated with the way they are calculated. Risks based on his-torical data are particularly easy to understand and areoften perceived as reliable (Wilson and Crouch, 1987). Itis, therefore, easy to illustrate a risk calculated from histor-ical data to identify some characteristics of risk estimation.When the severity of the loss is measured objectively, in

terms of something measurable, such as monetary unit,fatality or lost time, and the likelihood of the event canbe identified from relevant historical data, a quantitativerisk assessment can be conducted. When the severity andlikelihood cannot be specified exactly but can be estimatedbased on judgments or opinion, a qualitative or semi-quan-titative risk assessment can be conducted. A simple andpractical procedure to carry out qualitative risk assessmentfor the Australian mining industry was recently developedby Joy (2000), Joy (2004), Joy and Griffiths (2005).

2.1. Qualitative risk assessment

In mining risk assessment/management techniques werenot applied in a regular and systematic way. However,there are many studies on deterministic evaluation of coalmine accidents and safety. Some of the studies are underthe heading of job safety, worker health and job analysis(Hayduk and Ritzel, 1988; Leigh et al., 1991; Bozkurt,1993; Turin, 1995; Bajpayee et al., 2004). These kinds ofstudies in mining were generally aimed at evaluating dam-ages realized after accidents/incidents occurred and to takethe necessary precautions to prevent them happening. Inrecent years, accident analysis methods have been appliedsystematically to prevent accidents occurring (Graysonet al., 1992; Staley and Foster, 1996; Sari, 2002; Sariet al., 2004).

Another type of approach encountered in the literatureabout risk analysis can be grouped under the name of‘‘Practical Risk Assessment”. These types of studies aremostly applied in the case of the introduction of new sys-tems or changes in an existing operation. Usually, the iden-tification of potential hazards, probability of occurrenceand associated consequences of those hazards have beenassessed subjectively based on judgment, experience andexpert opinions in qualitative terms (Simpson and Moult,1995; Rowell, 1996; Staley, 1996; Van der Vyver, 1997;Davies, 1997; Joy, 2004). Since there was insufficient histor-ical accident data, only possible scenarios could be con-structed intuitively in a simple and logical manner whilerealistic and quantitative measurements on the determina-tion of risks would not be performed.

2.2. Quantitative risk assessment

The quantitative analysis of accident and injury data formeasuring safety performance and identifying safety prob-lems is usually done through two basic indices, AccidentFrequency Rate (AFR) and Accident Severity Rate(ASR), as follows (Brancoli, 1983):

AFR ¼ total number of accidents� 1; 000; 000

total number of man � hours workedð1Þ

ASR ¼ total number of days-lost� 1000

total number of man� hours workedð2Þ

AFR is an expression relating the number of specific acci-dents to a number of man–hours worked. The objective of

Monte Carlo Simulation

Accident Data Data Collection

Distribution Fitting

Frequency Severity

80 M. Sari et al. / Safety Science 47 (2009) 78–87

a severity rate is to give some indication of the loss in termsof incapacity resulting from occupational accidents. AFRis calculated by dividing the number of accidents (multi-plied by 1,000,000) occurring during the period coveredby the statistics by the number of man–hours worked byall persons exposed to the accident risk during the sameperiod. The severity rate should be calculated by dividingthe number of working days lost (multiplied by 1000) bythe number of hours of working time of all persons in-cluded. The US Mine Safety and Health Administration(Anon, 1990) adopted the same approach with changes inthe constants. The incidence rate is defined as the numberof injuries per 200,000 employee–hours and the severitymeasure is the number of lost workdays per 200,000employee–hours. The number 200,000 is used to stan-dardize for 100 full-time employees working 40 h/week -50 weeks/year.

It is possible to make sound comparisons using theseindices over a number of years for a sector or between dif-ferent sectors in a specific year to obtain an overview of thelevel of safety (Anon, 2006; MCA, 2006; Komljenovicet al., in press; Poplin et al., in press; US BLS, 2007). Infact, these numbers cannot include the uncertainty and var-iability inherent in the occurrence of accidents. Mining cannever have zero risk to occupational safety and health –there is always a degree of uncertainty with regard to thetype and extent of adverse impacts that could arise. Onthe other hand, Kerkering and McWilliams (1987), Cunyand Lejeune (1999), Quintana and Pawlowitz (1999), Duz-gun and Einstein (2004), Duzgun (2005) have appliedappropriate statistical distributions on accident data in dif-ferent industries. Results showed that it was possible tomeasure frequency of occurrences and severity of conse-quences in quantitative terms including the uncertaintyand variability revealed by the available data.

LowModerate

High

Severe

?

Risk Leveling

Risk Prediction

Decision Making

Risk = Frequency x Severity

Fig. 1. Flowchart for stochastic risk modeling of mine accident data.

3. Probabilistic modeling of accident data

Risk is defined as uncertainty concerning occurrence ofa loss (Rejda, 1998). Risk assessment consists of two dis-tinct phases: a qualitative identification, characterizingand ranking of hazards; and a quantitative risk evaluation,which includes estimating the likelihood (e.g. frequencies)and consequences of a hazard (Vose, 2000). According toRamani (1992), the term hazard is used to describe anunsafe situation in a mine and this may be an unsafe phys-ical condition or the unsafe acts of miners. There is now acommon agreement that risks should be evaluated in termsof frequency and severity, and most of the formulae used tosystematize quantitative assessments contain variables ofthese types (Cuny and Lejeune, 1999). The approaches ofthe studies carried out on the Turkish underground coalmines are mostly deterministic rather than probabilisticin nature (Buzkan and Buzkan, 1990; Bozkurt, 1993;Can, 1994; Istanbulluoglu, 1999; Sari et al., 2004; Ozfiratet al., 2006). Hence, the risk assessment approach pre-

sented in this paper considers probabilistic modeling,which is also combined with the risk leveling.

The risk analysis approach is one of the ways to examineevery aspect of an underground coal mine. In this respect,it is a method or a set of techniques, which identifies poten-tial losses and includes the consideration of the hazards,the severity of the consequences of exposures to the haz-ards, the level of risk and the control measures necessaryto reduce the risk to a level practically achievable.

The basic steps of stochastic risk analysis methodologydeveloped for this work are presented in Fig. 1 and consistof

i. Collection of mine accident data.ii. Evaluation of probability of accident occurrences.

iii. Determination of magnitude of accidents by estab-lishing possible consequences or severity.

Table 2Primary causes of accidents and frequency distribution

Accident type No of accidents % of accidents

Falls of ground 396 28.5Handling of tools and supports 330 23.7Struck by/falling object 235 16.9Powered haulage 51 3.7Movement of personnel 96 6.9Hand tools 50 3.6Machinery 112 8.1

M. Sari et al. / Safety Science 47 (2009) 78–87 81

iv. Compilation of probability and consequence (sever-ity) under a risk formulation using a Monte Carlosimulation.

v. Establishment of risk levels based on severity andprobability.

vi. Risk prediction by time series analysis.vii. Risk management and control methods for unaccept-

able risks.

Electricity 5 0.4All other causes 115 8.3

3.1. Collection of mine accident data

The GLI-Tuncbilek coal reserve, located on the mid-west of Turkey, is mined by two underground panelsnamely the Tuncbilek Mine and the Omerler Mine. Coalproduction was started in Tuncbilek Mine in 1940 with aretreat longwall mining method and sub-level caving. Thecoal seam with an inclination gently varying from 0 to 8has a thickness of 4–12 m. In a conventional system, theface area is supported by wooden posts and hydraulicshields lying perpendicular to the face. Two meters of thelower part of the coal seam are loosened by blasting thenexcavated by hand-held drills, while the remaining roofcoal is excavated behind by caving in to the face conveyor.In 1985 production began in the Omerler Mine using a con-ventional longwall mining method. In 1997, the mine man-agement underwent a revision and the current method of afully mechanized retreating longwall with sub-level cavinghas been started. In this method, bottom of coal is mined3 m high by a shearer/loader mounted on an armored faceconveyor with self advancing hydraulic powered roof sup-ports while the remaining roof coal is subsequently cavedin. Length of panels is 450–600 m as limited by the majorfaults. The length of longwall face is generally 90 m andincludes 58 units of lemniscate type shield supports. Aver-age coal production, employment, productivity and injuryrate values are tabulated in Table 1 for two different panelsin this mine.

According to Commission of the European Communi-ties, coal mine accidents may be classified as falls of groundlike roof, face, side, rib or pillar; movement of personnel,machinery; powered haulage; handling of tools and sup-ports; falling objects, explosives; explosions of firedamp;suffocation by natural gasses; underground combustionand fires; inrushes of water or material; electricity andother causes (Anon, 1975). The same standards in classifi-cation of coal mining accidents are also adopted in Turkey.By legislation, the appropriate authority must be notifiedfollowing a fatal accident or when a worker is injured

Table 1Performance figure of two panels in the GLI-Tuncbilek mine (Sari et al., 2004

Production (tonnes/year) Employment (man/y

Conventional 1994–1997 766,670 1449Conventional 1997–2002 307,000 667Mechanized 1997–2002 301,775 445

and is unable to carry on his/her work for a period of time(Anon, 2006).

The accident/injury data used in this study was initiallyobtained from Turkish Coal Enterprises (TKI), which isthe main state body responsible for lignite coal production,processing and marketing. This data comprised 1390 days-lost accident cases recorded at GLI-Tuncbilek under-ground mine from January 1994 to December 2002.Non-days lost injuries, incidents involving only equipmentdamage, occupational diseases, permanent disability andfatal cases were excluded in this study. The basic character-istics of the accident data were originally categorized asname, age, occupation of injured; the date, time, locationand type of accident; the parts of body injured and thenumber of days off work. A detailed analysis of accidentdata has already given in a previous study (Sari et al.,2004), but the primary causes of accidents and their relativeimportance is presented in Table 2.

3.2. Evaluation of probability of accident occurrences

If inputs in a process reveal uncertainty and variability,it will certainly be necessary to describe the nature of thisuncertainty and variability. The simplest and best way isto express this in the form of a probability distribution,which gives both the range of values that the variable couldtake and the likelihood of occurrence of each value withinthe range. Generally, the distribution and its parametersare previously unknown and need to be estimated fromthe available information about the random nature of theaccident data. The information is usually in the form of asample of observed values and there are according to Bury(1999) over 30 theoretical probability distributions that canadequately represent the data in various degrees of success.

The most basic distinguishing property between proba-bility distributions is whether they are continuous or

)

ear) Productivity (tonnes/man/year) Injury rate (injury/man/year)

529 0.16460 0.13678 0.08

0

5

10

15

20

25

0 –

2

2 –

4

4 –

6

6 –

8

8 –

10

10 –

12

12 –

14

14 –

16

16 –

18

18 –

20

20 –

22

22 –

24

24 –

26

26 –

28

28 –

30

Number of accidents/month

Freq

uenc

y

Observed frequency

Expected frequency

Fig. 2. Distribution of number of accidents for the GLI-Tuncbilek mine.

Table 3Chi-square goodness-of-fit test results for Poisson distribution

Number ofaccidents/month

Observedfrequency

Expectedfrequency

v2

0–2 0 0 –2–4 2 0.15 –4–6 5 1.30 10.536–8 9 5.50 2.238–10 18 13.50 1.5010–12 16 21.50 1.4112–14 17 23.90 1.9914–16 15 19.70 1.1216–18 9 12.50 0.9818–20 3 6.25 1.6920–22 3 2.55 0.0822–24 4 0.85 –24–26 3 0.30 –26–28 2 0 –28–30 2 0 –

Total 108 108 21.53

82 M. Sari et al. / Safety Science 47 (2009) 78–87

discrete. A discrete distribution may take one of a set ofidentifiable values each of which has a calculable probabil-ity of occurrence. A continuous distribution, on the otherhand, is used to represent a variable that can take any valuewithin a defined range (Vose, 2000). All distribution typesuse a set of arguments to specify a range of actual valuesand distribution of probabilities. A normal distribution,for example, uses a mean and standard deviation as itsarguments. The mean defines the value around which‘‘the bell curve” will be centered and the standard deviationdefines the spread of values around the mean. A compre-hensive description and use of probability distributionscan be found in the work of Bury (1999), Evans et al.(1993), Johnson et al. (1993, 1995).

Since adequate amount of data about coal mine acci-dents has been obtained from the GLI-Tuncbilek mine,the frequencies of accident records can be used in probabil-ity assessments. The plausible statistical distributions forthe number of accidents (H) can be detected by good-ness-of-fit test. The most commonly used statistical distri-butions for frequency of discrete data are Poisson,negative binomial and, in some special cases, binomial dis-tribution (Vose, 2000).

It is possible to test how well the distribution of samplevalues conforms to a theoretical distribution by the good-ness-of-fit or chi-square, v2 procedure. The expected fre-quency of occurrence within each interval of a theoreticaldistribution can be compared with the frequency of actualobservations that fall within the same intervals. If theactual number of observations in each interval deviates sig-nificantly from that expected it seems unlikely that the sam-ple was drawn from a Poisson distributed population(Daniel, 1978). The test statistics are calculated by theequation

v2 ¼Xk

j¼1

ðOj � EjÞ2

Ejð3Þ

where Oj is the number of actual observations within thejth class, and Ej is the number of observations expectedin that class. There are k classes or intervals.

In addition to visual inspection in Fig. 2, a detailed chi-square goodness-of-fit test was also carried out and Table 3outlines results of the v2 test on 1390 accident occurrencesfor the Poisson distribution. In the first column of Table 3,the number of accidents observed each month is dividedinto appropriate classes. The second column lists theobserved frequencies for each class, while the third columnlists the expected frequencies for each class as a result of thebest fitting Poisson function in Fig. 2. The fourth columnprovides the v2 term for each class calculated from Eq.(3) and the overall v2 statistics were calculated as 21.53,with 14 degrees of freedom (# of classes – 1). The resultof goodness-of-fit test suggests that it is a plausible approx-imation to represent the observed frequency distribution ofaccidents with a theoretical Poisson distribution. Similarly,the test done by BestFit software (Anon, 2001) yields a chi-

square value of 21.53 (p = 0.089) and estimates the para-meter k as 12.87 accidents/month. Poisson distribution isexpressed as

PðX ¼ xÞ ¼ e�kkx

x!x ¼ 0; 1; 2; � � � k P 0; ð4Þ

where, x denotes the number of occurrences per given timeand k is the average rate of occurrence per given time.

An important property of a Poisson process, the timebetween two accidents, T, is exponentially distributed.For the accident data, times to failures (time elapsedbetween two accidents) are evaluated and the statistical dis-tribution fitting the data is found to be a negative exponen-tial distribution with parameter estimate of b as 2.33 days(1 month/k) and goodness fit test produce a chi-squarevalue of 19.88 (p = 0.134) with 14 degrees of freedom.The density function of the exponential (negative exponen-tial) distribution with mean b is given as

f ðxÞ ¼ 1

be�x=b 0 6 x <1; b > 0: ð5Þ

M. Sari et al. / Safety Science 47 (2009) 78–87 83

These distributions are illustrated in Figs. 2 and 3, respec-tively. Poisson distribution allows the estimation of param-eter, k, for different time periods, once it is determined for aspecified one. If the mean accident frequency per month isestimated to be 12.87, the number of accidents per year willalso follow also a Poisson distribution with parameter ofk = 12 * 12.87 = 154.44.

0

10

20

30

40

50

60

70

80

Freq

uenc

y

Observed frequency

Expected frequency

3.3. Determination of magnitude of accidents by establishing

possible consequences or severity

The consequences of the accidents consist of fatalities,injuries, disabilities, equipment damage, shut down of thewhole system, production loss, etc. They may also consid-erably differ depending on the mine environment, theworkplace and the mineworkers’ characteristics. The vari-ety in the consequences requires a multi-dimensional con-sideration in modeling. The GLI-Tuncbilek mine has thecomplete records on the number of days a worker lost asa consequence of the accident. Therefore, the severity (S)is taken as the number of days-lost that is ranging from 1to 253 days with an average of 14.34 days and standarddeviation of 23.11.

In the literature, the severity distribution is usually mod-eled by normal, lognormal and Weibull distributions(Quintana and Pawlowitz, 1999). For the data set, BestFityields lognormal distribution supported by statistical sig-nificance test. The chi-square goodness-of-fit test calculatesa value of 40.44 (p = 0.097) with 30 degrees of freedom.The analyses carried out on the severity data by Hullet al. (1996), Cuny and Lejeune (1999) also showed lognor-mal distribution as a plausible choice. The parameters oflognormal distribution mean l and standard deviation rare estimated as 14.3 days and 23.1 days, respectively. Thisleads to the expression of the distribution of severity as

f ðxÞ ¼ 1

xrffiffiffiffiffiffi2pp exp � 1

2

ln x� lr

� �2" #

x P 0; l

> 0; r > 0 ð6Þ

0

50

100

150

200

250

300

350

1 3 5 7 9 11 13 15 17 19 21 23 25

Time between accidents (days)

Freq

uenc

y

Observed frequency

Expected frequency

Fig. 3. Distribution of time interval for the GLI-Tuncbilek mine.

Fig. 4 shows the fitted distribution for the number of days-lost data in GLI-Tuncbilek mine.

3.4. Compilation of probability and consequence (severity)

under a risk formulation

A simple risk matrix as given in Table 4 is constructedarbitrarily for days-lost data by combining two compo-nents in a risk formulation in which the one is replacedon the horizontal axis and the other on the vertical axis(Sari, 2002). In the risk matrix, frequency and severityscales are intuitively determined by referring to the cumu-lative distributions of these components estimated in previ-ous sections. Then, both of the cumulative distributions areequally divided into four probability intervals and anequivalent range of true observations on the x-axis is alsorecorded. It can be seen that the magnitudes of severityand frequency increase from bottom to top and from leftto the right. Finally, for each cell in the risk matrix, anappropriate risk score has been appointed quantitativelyby multiplying the lower and upper range of probabilityvalues on two components while assigning the highestvalue to the intersection cell. Qualitative risk levels are alsoassigned in cells ranging from very low to severe as thediagonal equality of risk scores is especially maintained.In Table 4, the proposed risk matrix is illustrated withtwo related components and appropriate risk scales forthe GLI-Tuncbilek mine.

50 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100Days-lost/accident

Fig. 4. Distribution of number of days-lost for the GLI-Tuncbilek mine.

Table 4The proposed risk matrix for the GLI-Tuncbilek mine

Accident/year

Cumulativeprobability

Days-lost/accident

0–4 4–8 8–16 16+

0.0–0.25 0.25–0.50 0.50–0.75 0.75–1.0

162+ 0.75–1.0 0.250 0.500 0.750 1.0Moderate High Very high Severe

154–162 0.50–0.75 0.1875 0.375 0.5625 0.750Low Moderate High Very high

146–154 0.25–0.50 0.125 0.250 0.375 0.500Very low Low Moderate High

0–146 0.0–0.25 0.0625 0.125 0.1875 0.250Very low Very low Low Moderate

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 500 1000 1500 2000 2500

Total days lost/year

Cum

ulat

ive

prob

abili

ty

Fig. 6. Cumulative distribution of yearly days-lost data for the GLI-Tuncbilek mine.

Table 5Relative risk levels for the GLI-Tuncbilek mine

Risk level Cumulative probability Total days-lost/year

Severe 0.750–1.000 2200+Very high 0.5625–0.750 1400–2200

84 M. Sari et al. / Safety Science 47 (2009) 78–87

Two risk components, quantified and modeled in termsof probability distributions, are simply combined in aMonte Carlo simulation in order to obtain a complete pic-ture of annual total days-lost due to accidents includinguncertainty and variability. @RISK, a system that pro-cesses these calculations in standard spreadsheet packages,explicitly includes the uncertainty present in the inputs togenerate outputs that show all possible alternatives (Anon,2001). Monte Carlo simulation can be loosely described asa simulation method where the simulation results are basedon a model where the input values are selected at randomfrom representative statistical distribution functions thatdescribe those inputs. The simulation is repeated n-timesand the results themselves now described a statistical distri-bution (Vose, 2000). Monte Carlo simulation methods areprimarily used in situations where there is uncertainty inthe inputs and where the calculated uncertainty of resultsaccurately reflects the uncertainty of the input data. Thedistribution in Fig. 5 is the product of input distributionof yearly accidents in the GLI-Tuncbilek mine, which isthe annual version of the previously obtained Poisson dis-tribution with a new parameter of k = 12.87 * 12 = 154.4accidents/year, and lognormal distribution modeling thedays-lost data as a result of each accident.

A new risk scale can be chosen for the mine risk levelafter figuring out total days-lost in a year of mine opera-tions due to traumatic accident occurrences. To set thesenew levels, the risks levels obtained quantitatively in therisk matrix can be located on the relevant probability scaleof new distribution’s cumulative graph as presented inFig. 6. Where it cuts the line, the value on the x-axis thatrepresents yearly total days-lost can be read and subse-quently it will correspond to a new risk level in the unitsof the total number of days-lost in a year which were pre-viously given as probability units. For example, in Table 4,for a moderate risk level, probability would range at a min-imum of 0.250 and a maximum of 0.375. If these numbersare located on the appropriate scale of the cumulativeprobability axis in Fig. 6, the equivalent value for the totaldays-lost would be 600 and 850 days, respectively, on the

0

0.0002

0.0004

0.0006

0.0008

0 1000 2000 3000 4000 5000

Total days lost / year

Prob

abili

ty

Fig. 5. Output of Monte Carlo simulation for the GLI-Tuncbilek mine.

x-axis. It means that if the GLI-Tuncbilek mine experi-ences a total of 700 days-lost in a year due to accidents,the relative risk level of the mine will be considered to bemoderate. Accordingly, other risk levels are establishedby following the same procedure and the final risk levelsare given in Table 5 for the GLI-Tuncbilek mine.

Table 6 presents the history of mines’ safety perfor-mance records in the past. According to the risk levels for-merly proposed, all the previous years have been subjectedto severe, very high and high levels of risk at the GLI-Tuncbilek mine. This deserves further attention; therefore,mine management is expected to put in force appropriaterisk management and control applications to reduce oreliminate, if possible, and if not, they must be controlledto the point that risks are as low as reasonably achievable,which is the aim of good risk management.

High 0.375–0.5625 850–1400Moderate 0.250–0.375 600–850Low 0.125–0.250 350–600Very low 0–0.125 0–350

Table 6Past safety records of the GLI-Tuncbilek mine

Year Number of accidents Total days-lost Risk level

1994 253 3535 Severe1995 209 3120 Severe1996 219 2791 Severe1997 150 2215 Severe1998 123 1620 Very high1999 115 1277 High2000 102 1740 Very high2001 125 2642 Severe2002 94 1315 High

yt = 20.91e

-0.0108t

R2 = 0.53

0

5

10

15

20

25

30

35

0 20 40 60 80 100 120Time, t

Num

ber

of a

ccid

ents

, Yt

Fig. 7. Plot of number of accidents per month in the GLI-Tuncbilek mine.

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

1 2 3 4 5 6 7 8 9 10 11 12

Period

Aut

ocor

rela

tion

Fig. 8. Autocorrelations of accident data at periods of L = 12.

M. Sari et al. / Safety Science 47 (2009) 78–87 85

4. Risk prediction by time series analysis

In the previous sections, the mine’s accident history wasevaluated and the condition of the mine in terms of incurredrisk level was based on the results of past records. It shouldbe kept in mind that risk analysis typically deals with futurephenomena and predictions of future events must be incor-porated into any decision-making process. In this section, astatistical approach towards the forecasting of mine risklevels expected in the future of mine’s life will be demon-strated by using time series technique in statistics.

A univariate time series model describes the behavior ofa variable in terms of past observations and assumes thatthe identified pattern will continue in the future. A simplemodel can essentially be developed to explain the underly-ing process generating the series, and be capable of fore-casting, interpreting and testing hypotheses concerningthe data. Contrary to linear regression, the observationsare assumed to be equally spaced and statistically depen-dent (Cryer, 1986). The number of accidents (frequency)is expressed in terms of a time series model, since there isa high possibility that an accident occurs with the conditionthat it has previously happened and will be occur again dueto the lack of equipment, manpower, and psychologicaland administrative reasons.

There are different modeling techniques applicable totime series data. The most widely used are moving average,decomposition, exponential smoothing and Box–Jenkinstechniques (Bowerman and O’connell, 1993). If time seriesdata shows a constant trend and also some regular devia-tions from the trend line depending on the time period (sea-son, month of year, day of week etc.), a simple andpractical method is the decomposition method. In thismethod, series are broken down into trend, cycle, seasonaland irregular components and then each component is ana-lyzed separately. In deterministic time series model at time,t, the obseved value (Yt) is expressed in forms of four com-ponents in a multiplicative model; trend (TRt), seasonal(SNt), cyclic (CLt) and irregular (random) (IRt) as

Y t ¼ TRt � SNt � CLt � IRt ð7ÞIn order to attain a stationary model, it is important toeliminate the model from its trend, seasonal and cyclicalcomponents. A model cleaned up from these componentswill yield a zero mean, constant variance and uncorrelatedresiduals denoted as a white noise series. One of the teststatistics in the model is the mean absolute percentage error(MAPE) of the series, which is the average absolute differ-ence between the estimated value and the actual value asthe percentage of the actual value (Vose, 2000).

A plot of the number of accidents per month from Jan-uary 1994 to December 2002 indicates that a downwardtrend exists in the series (Fig. 7). To eliminate the trendeffect, a trend line is estimated by LSE and found to be:

Y t ¼ 20:91 expð�0:0107tÞ ð8Þ

with R2 = 0.53.

The graph of the original data exhibits seasonal move-ments for specific periods of time as observed by significantcorrelations for some lag values of the autocorrelationchart shown in Fig. 8. For that reason, seasonality indicesare estimated by the moving average technique and theyare presented in Table 7. Here ‘‘12-period moving average”

is employed because the accident data is monthly (L = 12time periods or ‘‘seasons” per year). While higher indicesare observed in May, June and November every year dueto excessive monthly working days and the negative effectsof outside weather conditions, the remaining months havelower indices.

These two components (TRt � SNt) were eliminatedfrom the original data so that the stationarity of theremaining part (CLt � IRt) was subsequently attained.Since there are only nine years of data and most of the val-ues of CLt are close to 1, it is not possible to discern a well-defined cycle. Furthermore, in examining the values of IRt,no pattern was detected in the estimates of the irregularfactors. Fig. 9 shows that the plot of residual terms wasscattered randomly and the histogram of residuals refersto an approximate normal distribution as seen in Fig. 10.

Table 7Seasonal indexes for time series model

Month SNt

January 1.047February 0.921March 0.882April 0.971May 1.163June 1.101July 0.846August 0.885September 0.920October 0.957November 1.310December 0.998

0

1

2

Time. t

Res

idua

ls

0 20 40 60 80 100 120

Fig. 9. Plot of residuals (IRt) with time in the GLI-Tuncbilek mine.

0

2

4

6

8

10

12

14

16

18

20

0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9Residuals

Freq

uenc

y

Fig. 10. Histogram of residuals (IRt) in the GLI-Tuncbilek mine.

Table 8Estimated risk levels for the GLI-Tuncbilek mine (yearly)

Year Number of accidents Total days-lost Risk level

2003 73 1044 High2004 65 930 High2005 57 815 Moderate2006 50 715 Moderate2007 44 630 Moderate

86 M. Sari et al. / Safety Science 47 (2009) 78–87

The incorporation of the two estimated components inthe model presented in Eq. (7) results in the following timeseries equation:

Y t ¼ 20:91 expð�0:0107tÞ � SNt ð9ÞHere, Yt is the predicted number of accidents in period ‘‘t”that corresponds to the discrete time count of months,where the cohort t = 1 stands for January 1994. TheMAPE value for this model is calculated as 25.8%, whichgives information about the percentage of actual valuesthat are not covered by time series model. Here, smallerMAPE concludes better fit.

After the projection of accident occurrences in the nearfuture, it is straightforward to determine the expected risklevels for the mine. For this purpose, first, the total numberof accidents should be calculated from the time seriesmodel by inputting future time periods into Eq. (9) priorto totaling the estimated monthly numbers for each year.Then, the predicted yearly accident numbers should bemultiplied intuitively by a factor of average days lost peraccident (l = 14.3 days/accident). In the final step, the cor-responding risk level should be checked with the riskmatrix in Table 5. The results of the procedure are illus-trated in Table 8 as the predicted risk levels for the follow-ing years of the GLI-Tuncbilek mine. In the near future,this mine will be experience higher and moderate levels ofrisks due to accidents.

5. Conclusions

Accidents are mostly independent and random events;they possess some degree of uncertainty and variability inthe occurrences. Hence, they definitely require stochasticmodeling due to their inherent characteristics. In this study,two components of accident risk, level of hazard multipliedby probability of occurrence, have been modeled using adistributional approach including uncertainty dictated bythe available accident data. The developed risk assessmentmethodology is simple and general with its clearly identi-fied and outlined steps. Thus, it can be easily applied toany underground coal mine or extended to any other occu-pational area to assist in prioritizing of accident reductionefforts.

It was concluded from the time series analysis thatalthough the annual number of accidents, and as a conse-quence, the total days lost would gradually diminish; therisk levels in the mine would not completely change inthe coming 5 years. Therefore, those responsible for themanagement of mine should immediately develop andemploy an intervention program that will minimize therisks associated with accidents in their mines. Accordingly,the authors recommend some prevention measures that canbe found in most of the standards and guides including

1. CAN/CSA Q850-97, 2002. Risk Management: Guide-line for Decision Makers. Canadian Standard Associa-tion, Standard.

2. AS/NZS 4360, 2004. Standards Australia, StandardsNew Zealand. Risk Management, Homebush,Wellington.

M. Sari et al. / Safety Science 47 (2009) 78–87 87

3. MIL-STD-882D, 2000. Military Standard, StandardPractice for System Safety, Department of Defense.

Acknowledgements

The authors wish to thank all of the GLI-TuncbilekMine managers and engineers for providing necessary acci-dent data and their kind hospitality during mine visits. Thisstudy was financially supported by a research grant fromthe State Planning Organization (DPT) under project num-ber AFP-03-05-DPT.99.K120540.

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