Research Journal of Environmental and Earth Sciences 4(2): 162-165, 2012
ISSN: 2041-1492
© Maxwell Scientific Organization, 2012
Submitted: September 07, 2011
Accepted: September 25, 2011
Published: February 01, 2012
Time Series Model of Occupational Injuries Analysis in
Ghanaian Mines-A Case Study
S.J. Aidoo and P.A. Eshun
University of Mines and Technology, Tarkwa, Ghana
Abstract: This study has modeled occupational injuries at Gold Fields Ghana Limited (GFGL), Tarkwa Mine
using time series analysis. Data was collected from the Safety and Environment Department from January 2007
to December 2010. Testing for stationarity condition using line graph from Statistical Package for Social
Sciences (SPSS) 17.0 edition failed, hence the use of Box-Jenkins method of differencing which tested positive
after the first difference. ARIMA (1,1,1) model was then applied in modeling the stationary data and model
diagnostic was done to ensure its appropriateness. The model was further used to forecast the occurrence of
injuries at GFGL for two year period spanning from January 2011 to December 2012. The results show that
occupational injuries for GFGL are going to have a slight upward and downward movement from January 2011
to May 2011, after which there will be stability (almost zero) from June 2011 to December 2012.
Key words: Differencing, forecasting, mining, safety, stationarity
INTRODUCTION
MATERIALS AND METHODS
The main aim of any mining company is to mine an
orebody in a given environment as safely, efficiently and
economically as possible. Unfortunately, mining activities
are generally associated with dangerous working
conditions which result in accidents and injuries. The
consequence is the loss of production time, the victim’s
incapacity to work and the loss of special skills to the
mining companies.
As a result of such losses, most mining companies
worldwide are placing high premium on safety (accident
control and prevention). However, as posited by
Donoghue (2004), although substantial progress has been
made in the control of occupational injuries there remains
more room for further reduction of injury cases in the
mining industries. Gold Fields Ghana Limited (GFGL),
the highest gold producing company in Ghana, for
example, places more emphasis on minimizing
occupational injuries so as to increase production levels
and also to protect the wellbeing of the workforce. It is
also the aim of the mine to comply with international
standards such as OHSAS 18001 in assessing safety at the
workplace.
In this study, a time series model based on the
stationarity condition is used to forecast occupational
injuries at Gold Fields Ghana Limited, Tarkwa Mine, to
serve as a tool for managerial decision in reducing injuries
on the mine.
Brief information about the study area: Gold Fields
Ghana Limited, Tarkwa Mine, is located in Tarkwa which
is on longitude 2º00! and latitude 5º15!. Tarkwa is about
90 km by road from Takoradi, the Western Regional
capital and about 300 km west of Accra, the national
capital. The concession covers an area of 294 km2
extending from the town of Tarkwa in the south, for a
distance approximately 25 km to Huni Valley at its northeast limit and is averagely 152.41 m above sea level
(Kesse, 1985). The topography of Tarkwa area is
generally described as a remarkable series of ridges and
valleys parallel to one another and is the true reflection of
the pitching folding structures of the Banket series of the
Tarkwaian system. The orebody consists of a series of
sedimentary banket quartz reef units (conglomerates) of
the Tarkwain System that are similar to those mined in the
Witwatersrand Basin of South Africa. The company is
currently mining multiple-reef from open pits and there is
potential for underground mining in the future (Gold
Fields Limited, 2011).
Method of data collection and analysis: The data was
sampled from January 2007 to December 2010 incident
statements and investigation reports at the Safety and
Environment Department of Gold Fields Ghana Limited
(GFGL), Tarkwa Mine. Interviews and discussions were
also conducted to gain deeper insight on some of the
Corresponding Author: P.A. Eshun, University of Mines and Technology, Tarkwa, Ghana
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Res. J . Environ. and Earth Sci. 4(2): 162-165, 2012
Table 1: Occurrence of injuries at Gold Fields Ghana Limited, Tarkwa Mine
Jan
Feb
Mar
Apr
May
Jun
2007
3
3
3
3
9
5
2008
11
4
5
7
7
10
2009
2
1
8
5
2
8
2010
4
4
15
6
3
2
Jul
4
6
3
2
Aug
1
8
9
5
Table 2: ARIMA (1, 1, 1) and ARIMA (2,1,1) model statistics
Model fit statistics
----------------------------------------------------------------------------No. of
Stationary
Normalized
R2
RMSE
MAPE
BIC
Modal
preditores
R2
DIFF
0
0.712
0.161
4.101
1.097E2 3.072
(Occupational_Injuries,1) -Model_1 ARIMA (1,1,1)
DIFF
0
0.730
0.213
4.019
1.138E2 3.115
(Occupational _ Injuries,1)-Model_2 ARIMA (2,1,1)
12
Nov
7
9
7
5
Dec
7
13
7
3
Ljung-Q(18)
-------------------------------------Statistics
22.322
df
16
Sig
0.133
No. of
outliers
0
21.411
15
0.124
0
0.5
10
8
ACF
Occupational injuries
Oct
3
7
10
5
Coefficient
Upper confidence limit
Lower confidence limit
1.0
14
Sep
5
5
3
8
6
0.0
-0.5
4
2
-1.0
0
Jan 2007
Mar 2007
May 2007
Jul 2007
Sep2007
Nov 2007
Jan 2008
Mar 2008
May 2008
Jul 2008
Sep 2008
Nov2008
Jan 2009
Mar 2009
May2009
Jul 2009
Sep 2009
Nov2009
Jan 2010
Mar2010
May 2010
Jul 2010
Sep 2010
Nov 2010
1
2
3
5 6
7 8 9 10 11 12 13 14 15 16
LAG Number
Fig. 3: Graph of Auto Correlation Function (afc) verses lags
Date
Fig. 1:
Non-stationarity graphs of occupational injuries
versus months
0.5
Partial ACF
15
DIFF (Occupatinal_injuries,1)
Coefficient
Upper confidence limit
Lower confidence limit
1.0
10
5
0
0.0
-0.5
-5
-1.0
-10
1
Jan 2007
Mar 2007
May 2007
Jul 2007
Sep 2007
Nov 2007
Jan 2008
Mar 2008
May 2008
Jul 2008
Sep 2008
Nov 2008
Jan 2009
Mar 2009
May 2009
Jul 2009
Sep 2009
Nov 2009
Jan 2010
Mar 2010
May 2010
Jul 2010
Sep 2010
Nov 2010
-15
5 6
7 8 9 10 11 12 13 14 15 16
Lag Number
Fig. 4: Graph of partial auto correlation
independent variable. Occupational injury is dependent
over time, hence occupational injury is the dependent
variable and time is the independent variable. The time
component is in months.
Fig. 1 shows a line graph of occupational injury
against time as obtained from SPSS 17.0. The mean of the
graph is not constant over time and hence non-stationary.
Furthermore, the deterministic trend is not appropriate
because the spikes are increasing and it is not returning to
zero. The nature of the spikes suggests that the linearity is
not intrinsic to the process and will not persist in the
future.
Date
Fig. 2:
2 3
First difference stationarity graph of occupational
injuries versus months
issues in the reports. Table 1 presents the rate of
occurrence of injuries for the period under study. The data
was analysed using time series analysis tools in Statistical
Package for Social Sciences (SPSS) 17.0 edition
software.
Preliminary analysis (data exploration): The data has
two components, the dependent variable and the
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Res. J . Environ. and Earth Sci. 4(2): 162-165, 2012
Residual ACF
0.2
The non-stationary pattern in a time series data needs
to be removed in order that other correlation structure
present in the series can be seen before proceeding with
model building.
According to Box and Jenkins (1976), when a data is
not stationary differencing can be used. Fig. 2 shows a
first difference line graph of occupational injury against
time. From Fig. 2, the difference observed data fluctuates
around a constant mean independent of time and variance
of the fluctuation, hence stationary.
0.0
-0.2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
-0.4
Lag Number
RESULTS AND ANALYSIS
Fig. 5: Graph of residual ACFfunction (PACF) verses lag
Model identification: To find provisional orders of AutoRegressive (AR) and Moving Average (MA) models for
the first difference stationary data, the following are
examined in Fig. 3 and 4, respectively:
0.2
Residual PACF
0.1
0.0
-0.1
C
C
-0.2
-0.3
-0.4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Both Fig. 3 and 4 indicate lags less than 1, meaning
the first order autocorrelation coefficient is significant.
Therefore, an AR (1) or MA (1) or ARIMA (1) can be
started with. In this paper ARIMA for the first and second
orders were investigated.
Lag Number
Fig. 6:Graph of residual PACF verses lag
15
Observed
Forecast
Model estimation: Table 2 presents model estimations
for ARIMA (1,1,1) and ARIMA (2,1,1). It can be
concluded that ARIMA (1,1,1) is a better model fit
statistics since it has a lesser value of normalized
Bayesian Information Criteria (BIC) and lower mean
absolute percentage error as compared to ARIMA (2,1,1).
Considering the ARIMA (1,1,1) model parameters in
Table 3, it is shown that |N1| < 1 and |21| < 1, which are
the stationarity conditions for both AR (1) and MA (1)
respectively. Furthermore, it is shown that AR (1) is
significant at 0.007 levels which is less than 0.05. This
shows that AR (1) is sufficient condition for the
estimation of the parameter.
10
Occupa_1-Model_1
Number
5
0
-5
-10
may 2010
aug 2010
nov 2010
feb 2011
may 2011
aug 2011
nov 2011
feb 2012
may 2012
aug 2012
nov 2012
feb 2007
may 2007
aug 2007
nov 2007
feb 2008
may 2008
aug 2008
nov 2008
feb 2009
may 2009
aug 2009
nov 2009
feb 2010
-15
Date
Fig. 7: The observed and forecasted model
Table 3: ARIMA(1,1,1) model parameter
DIFF (Occupational DIFF (Occupational
_Injuries)-Model-1 _Injuries)-Model-1
Estimate
SE
Constant
-0.013
0.032
------------AR
Lag 1
-0.422
0.148
Difference
1
-------------MA
Lag
10.984
0.710
The sample Auto-Correlation Function (ACF); and
The sample Partial Auto-Correlation Function
(PACF).
Model diagnostic: Model diagnostic is concerned with
testing the goodness of fit of a model and if the model is
poor suggest appropriate recommendations. The graphs of
the autocorrelation and the partial autocorrelation in Fig.
5 and Fig. 6 respectively show that the points are scattered
in a random manner hence it could be concluded that the
model fit was appropriate.
No transformation
t
Sig.
- 0.426
0.672
2.850
0.007
1.386
0.173
Forecasted model: After the model diagnostic, the model
was fitted for two years as presented in Fig. 7. From the
model, it was found out that occupational injury is going
to have small upward and downward movement from
January 2011 to May 2011, after which occupational
The non-stationary pattern in a time series data needs
to be removed in order that other correlation structure
present in the series can be seen before proceeding with
model building.
164
Res. J . Environ. and Earth Sci. 4(2): 162-165, 2012
C
injuries will decrease slightly from May 2011 to
December, 2012. The slightly constant nature can be
explained that if the current safety measures implemented
are maintained or improved upon there will be a
remarkable decrease in injuries for the forecasted period.
C
Observations: It was observed from field interactions
that safety awareness has drastically increased among
greater number of the workforce. However, some workers
still have lackadaisical attitude to the safety measures
put in place by management. It was further observed
that the causes of accidents on the mines are mostly due
to ground fall, machinery, electrocution, vehicular
accident and slip fall. The body parts most susceptible to
injuries are the hand, legs and head for the period
considered.
C
REFERENCES
Box, G.E.P. and G. Jenkins, 1976. Time Series Analysis:
Forecasting and Control. Holden-Day Inc, USA.
Donoghue, A.M., 2004. Occupational health hazard in
mining. Occupational Med., (54)5: 283-289.
Gold Fields Limited, 2011. Review of International
Operations-Tarkwa Mine. Retrieved from:
http://www.goldfields.co.za/ops-int-tarkwa.php,
(Accessed on: June 2011).
Kesse, G.O., 1985. The Mineral and Rock Resources of
Ghana. A.A. Balkema Publishers, Rotterdam,
Netherlands.
RECOMMENDATION
Based on the study, the following recommendations are
made:
C
Safety talks must be held frequently and must be
geared towards attitudinal change since a greater
percentage of the causes of accidents are by unsafe or
substandard acts.
The use of personal protective equipment must be
enforced to protect the vital parts of the body
susceptible to injuries.
Management should continue with is effort of
enforcing safety regulations to drive injuries to
decreasing numbers as depicted by the forecast.
Management should pay more attention to areas such
as the mining operations, workshops and repair bays
where most of the risky activities take place.
165