INTRODUCTION
Based on an assessment by International Labor Office, 180,000 individuals
die in the work accidents in the industries per year, while 110 million
people are injured (Famoye, 2004; Hautzinge, 1987). On the other hand,
construction phase in industries is a dynamic process that is naturally
and intrinsically dangerous and as it becomes more complicated, the accidents
rate increases. According to OSHA International Organization, the number
of accidents led to death at these industries is more than 2000 death
per year in average (James and Fullman, 1994; John and Marvin, 2000).
In average, of each six construction labors, one is suffering from job
damages and illnesses per year and of each 16 individuals, one becomes
seriously damaged. In average, the construction labors miss about 1.2
days per year of their work as a result of damages in the work (Lars Harms,
2001).
The construction phase of oil, gas and petrochemical projects is facing
to a large spectrum of challenges; one of those challenges is the frequent
accidents. From the starting date of these projects (around four years
ago), many accidents have been occurred and a significant number of accidents
(50) led to death and many others ended with disability damages. Applying
the accidents study pyramid to such a subject will show the great importance
of the subject. As an example, by using the Tye/Pearson pyramid (19741975)
where per each accident leading to death or serious incidents in the world,
thirty accidents were minor, fifty accidents needed first aids, eighty
accidents led to damages to facilities and properties and four hundred
were semiaccident. With a simple calculation, one might note that during
this period, per each minimum 50 accidents leading to death, there have
been 1500 minor accidents, 2500 accidents needing first aids, 4000 accidents
damaging facilities and properties and 20000 semiaccident incidents.
These values and numbers show the fact that construction is a highrisk
region. Then it is needed to develop a proper strategy to lower the rate
of accidents in those projects. However, knowing the factors and causes
of those accidents are more important than calculating the total number
of accidents leading to death. This information could be used in the expansion
and development of a plan to improve the safety level in construction
phase through decreasing accident rate. On the other hand, with respect
to the important fact that occurrence of large accidents in this industry
(which is unique in Iran as well) might disconnect the production chain
in many other industries and cause huge loss. Therefore, we should make
a careful evaluation of the nature of energies and the risks involved
in them in order to take suitable controlling approaches. The major goals
of this research are:
• 
Study and identification of major and effective factors
in the occurrence of accidents leading to death and disability in
the system subject of study; 
• 
To present a mathematical model to estimate increase in work environment
as a result of any of the predicted factors (regression analytical
method) 
In this research, it is tried to carry out a comprehensive study of risk
assessment and by studying and identifying the main and effective accidents
that lead to death and disability in the system subject of study, develop
a mathematical model for assessing increase in work environment as a result
of each one of the predicted factors.
Concerning the factors that affect different accidents by regression
analytical method, considerable empirical studies have been performed,
followings are some of them Famoy (2004) studied the effects of environmental
factors, driving habits and medical cares in car accidents in Alabama
by using regression models (Ludwig, 1985).
Hautzinger (1987) studied safety in traffic by using regression analysis
(National Safety Council, 1992).
• 
Wegni and Ross (2004) studied volume of hospital accidents
and emergency accidents caused by air pollution in Europe. 
The results of the research, with using regression analysis, showed that
despite high air pollutions and affecting the health of society, one could
not measure the accidents caused by air pollution in micro level, easily
(Steve, 2004).
MATERIALS AND METHODS
Model is an abstract terminal (mathematical, physical or graphical) that
follows special regulations and standards. The model is the reflection
of a fact. In another expression, it should be said that the model represents
a system or process that could predicted the behavior of that system or
process. Therefore, models are used for understanding the behavior of
actual terminal and show a theory in the way that covers important variables
for describing phenomena and instead, ignores factors with low importance
in the expression of those phenomena.
One should note that without considering the model, one could not obtain
useful and reliable method to prevent accidents; therefore, to achieve
useful methods in preventing accident, it is desirable to consider models
on the quality of accident (Trevor, 1988).
In this research count model has been employed since the dependent variable
(FNOAC) takes integer values that represent the number of events that
occur over a fixed time interval. To estimate the count model EViews has
been employed, because EViews provides support for the estimation of several
models of count data. In addition to the standard Poisson and negative
binomial Maximum Likelihood (ML) specifications, EViews provides a number
of QuasiMaximum Likelihood (QML) estimators for count data. In the case
of count data, Poisson mode is a common model used to estimate the parameters
of the model.
For the Poisson model, the conditional density of y_{i} given
is:
where y_{i} is a nonnegative integer valued random variable.
The maximum likelihood estimator (MLE) of the parameter β is obtained
by maximizing the log likelihood function:
Provided the conditional mean function is correctly specified and the
conditional distribution of y is Poisson, the MLE
is consistent, efficient and asymptotically normally distributed, with
variance matrix consistently estimated by:
where:
The most important restriction is the equality of the (conditional) mean
and variance:
If the meanvariance equality does not hold, the model is misspecified.
To test this equality deviance and Pearson ChiSquare divided by the degrees
of freedom are used in the Poisson regression. Values greater than 1 indicate
overdispersion, that is, the true variance is bigger than the mean and
values smaller than 1 indicate underdispersion, i.e. the true variance
is smaller than the mean. Evidence of underdispersion or overdispersion
indicates inadequate fit of the Poisson model. We can test for overdispersion
with a likelihood ratio test based on Poisson and negative binomial distributions.
This test, tests equality of the mean and the variance imposed by the
Poisson distribution against the alternative that the variance exceeds
the mean. For the negative binomial distribution, the variance = mean+k
mean2 (k> = 0, the negative binomial distribution reduces to Poisson
when k = 0). The null hypothesis is:
H0: k = 0 and the alternative hypothesis is: H1: k>0.
To carry out the test, we use the LR (likelihood ratio) test, that is,
compute LR statistic as 2(LL (Poisson)LL (negative binomial).The asymptotic
distribution of the LR statistic has probability mass of one half at zero
and one halfChisq distribution with one df. 1 To test the null hypothesis
at the significance level 2α, use the critical value of Chisq distribution
corresponding to significance level 2α, that is reject H_{0}
if LR statistic>χ^{2}_{(12α, 1 df).}
The calculated LR statistic (26.72) is greater than the critical value
of χ^{2} (2.71). This indicates overdispersion and inadequate
fit of the Poisson model. When there is overdispersion in the data, one
common alternative to the Poisson model is to estimate the parameters
of the model using maximum likelihood of a negative binomial specification.
The log likelihood for the negative binomial distribution is given by:
where η^{2} is a variance parameter to be jointly estimated
with the conditional mean parameters β.
The following table presents the results obtained from estimating the
parameters of the model using maximum likelihood of a negative binomial
specification. The Robust Covariance of the estimation has been computed by the Huber/White
method using NewtonRaphson optimization algorithm to correct standard
errors for overdispersion.
Table 1: 
Estimation results of negative binomial (QML) model 

The response variable is the number of deadly accidents (i.e., accidents
lead to death or major injury (FNOAC)), from which we explore its relationship
with the total accidents (TACS), human errors (UNA), insecure conditions
(UNC) and either using nonstandard equipments or applying improper management
(MNGEQUO). Therefore, in Table 1, FNOAC is the response
variable in the negative binomial regression and underneath FNOAC are
the predictor variables and the intercept (C).
The result show that the estimated model is as follow.
As shown in the Table 1, the resulting adjusted Rsquared
value is 0.82 may indicate a very close fit to the data. It seems that
about 82% of variation in FNOAC is explained by the model.
The LR test statistic is used for the omnibus test that at least one
predictor variable regression coefficient is not equal to zero in the
model. The small pvalue from the LR test (p = 0.048)leads us to conclude
that at least one of the regression coefficients in the model is not equal
to zero.
All coefficients have the expected signs and are statistically significant
at 5% plevel.
TACS is the negative binomialregression estimate for a one unit increase
in number of total accidents, given the other variables are held constant
in the model. If the number of total accidents increases by one unit,
the difference in the logs of expected counts would be expected to increase
by 0.0025 unit, while holding the other variables in the model constant.
It means that for each number increase in the total accident the expected
number of deadly accident increase by a factor of 0.0025. UNA and UNC
as well as MNGEQUP are other negative binomialregression estimates for
a one unit increase in number of human errors and the number of insecure
conditions as well as the number of nonstandard equipments and management
faults. For each unit increase in the human errors the expected number
of deadly accident increases by a factor of 0.1137. Similarly, for each
unit increase in the insecure conditions the expected number of deadly
accident increases by a factor of 0.2982. By the same token, for each
unit increase in either nonstandard equipment or management fault the
expected number of deadly accident increases by a factor of 0.0259.
C is also a negative binomialregression estimate for a one unit increase
when all variables in the model are evaluated at zero. Therefore, if there
are no such predictors, the log of the expected count for deadly accidents
is 0.0023.
RESULTS AND DISCUSSION
Results of assessing the abovementioned model could answer following
questions:
• 
Do the unsafe conditions and unsafe functions (disregarding
standards before, during and after work) have any effects on the percentage
of work environment accidents? If this factor is effective, how much
is the percent of increase in job accidents leading to death because
of increase in the percentage of unsafe conditions and unsafe functions? 
• 
Do the undesirable managerial factors have any effects on the percentage
of accidents in work environment? If this factor is effective, what
is the percent of increase in job accidents leading to death as a
result of increase in the undesirable managerial factors? 
• 
Does the use of standard and sound facilities, materials and machinery
have any effects on the percentage of accidents in work environment?
If this factor is effective, what is the percentage of increase in
job accidents leading to death, as a result of increase in this factor? 
• 
Are there any other variables rather than predicted independent
variables that might play any role in job accidents leading to death? 
The result show that the estimated model is as follow.
As shown in the above table, the resulting adjusted Rsquared value is
0.82 may indicate a very close fit to the data. It seems that about 82%
of variation in FNOAC is explained by the model.
The LR test statistic is used for the omnibus test that at least one
predictor variable regression coefficient is not equal to zero in the
model. The small pvalue from the LR test (p = 0.048)leads us to conclude
that at least one of the regression coefficients in the model is not equal
to zero.
All coefficients have the expected signs and are statistically significant
at 5% plevel.
TACS is the negative binomialregression estimate for a one unit increase in
number of total accidents, given the other variables are held constant in the
model. If the number of total accidents increases by one unit, the difference
in the logs of expected counts would be expected to increase by 0.0025 unit,
while holding the other variables in the model constant. It means that for each
number increase in the total accident the expected number of deadly accident
increase by a factor of 0.0025. UNA and UNC as well as MNGEQUP are other negative
binomialregression estimates for a one unit increase in number of human errors
and the number of insecure conditions as well as the number of nonstandard equipments
and management faults. For each unit increase in the human errors the expected
number of deadly accident increases by a factor of 0.1137. Similarly, for each
unit increase in the insecure conditions the expected number of deadly accident
increases by a factor of 0.2982. By the same token, for each unit increase in
either nonstandard equipment or management fault the expected number of deadly
accident increases by a factor of 0.0259.
C is also a negative binomialregression estimate for a one unit increase
when all variables in the model are evaluated at zero. Therefore, if there
are no such predictors, the log of the expected count for deadly accidents
is 0.0023.
CONCLUSIONS
Work accidents in the World are very high, to the extent that 180,000
individuals die in the work accidents in the industries each year and
10 million people are injured. The rate of such accidents in the industrial
construction phase is naturally and intrinsically mostly high. The number
of accidents led to death at these industries is more than 2000 death
per year in average. Because of this, it became necessary to examine the
determinants affecting the work accidents in such industries. In this
study, a countdata regression has been applied to estimate and analyze
the effects of determinant factors affecting the accidents leading to
death, through negative binomial regression. To this end the 2750 accidents
in the Construction Phase in Oil, Gas and Petrochemical Projects of Assaloyeh
as a case study has been studied. The period of the study is 20032005.
Along with total accidents, unsafe conditions, human errors, management
faults and using nonstandard equipments, were considered as the main independent
variables affecting the work accidents leading to death, as the dependent
variable. EViews software has been employed to estimate several models
of count data. The findings of the study show that for each number increase
in the unsafe conditions, human errors and either nonstandard equipments
or management faults, the expected number of deadly accident increases
by a factor of 0.2982 and 0.1137 as well as 0.0259, respectively. If the
number of total accidents increases by one unit, the difference in the
logs of expected counts would be expected to increase by 0.0025 unit,
ceteris paribus. Apart from such predictors, the log of the expected count
for deadly accidents is 0.0023.
ACKNOWLEDGMENT
One who does not thank others, can not thank God, to follow these divine
Koranic words, I take this opportunity to extend my best appreciations
to the mangers of the Pars Energy Special Economic Zone; particularly
Engineer Rasoul Yarahmadi, Manager of Health, Safety and Environment (HSE)
Department who provided me with necessary equipment to carry out my research.