Research Paper

Available online at www.sciencedirect.com

Computers & Industrial Engineering 54 (2008) 34–44

www.elsevier.com/locate/dsw

A quantitative model for aviation safety risk assessment

Huan-Jyh Shyur *

Department of Information Management, Tamkang University, 151 Ying-Chuan Road, Tamsui, Taipei, Taiwan

Received 2 August 2006; received in revised form 14 June 2007; accepted 14 June 2007 Available online 21 June 2007

Abstract

The objective of this research is to develop an analytic method that uses data on both accident and safety indicators to quantify the aviation risk which are caused by human errors. A specified proportional hazard model considering the base- line hazard function as a quadratic spline function has investigated and demonstrated its applicability in aviation risk assessment. The use of the proposed model allows investigation of non-linear effects of aviation safety factors and flexible assessment of aviation risk. A subset of data gathered from the Fight Safety Management Information System (FSMIS) developed by the office of the Taiwan Civil Aeronautics Administration (CAA) was applied to accomplish this study. The results demonstrate that the proposed model is a more promising approach with the potential of becoming very useful in practice and leading to further generalization of aviation risk analysis. � 2007 Elsevier Ltd. All rights reserved.

Keywords: Risk assessment; Aviation safety; Human error; Proportional hazard model

1. Introduction

As the worldwide air transportation traffic volume grows rapidly, safety in aviation becomes a burning problem over many countries today. Aviation accident may result in human injury or even death. It influences the reputation and the economy of the air transportation industry of a country. According to the analysis of Mineata (1997), when today’s accident rate is applied to the traffic forecast for 2015, the result would be the crashing of an airliner somewhere in the world almost every week. Braithwaite, Caves, and Faulkner (1998) stated that in order to achieve safety and reduce accident rate, we must quantify risk and balance it with appropriate safety measures.

In order to ensure the public safety and maintain a safe aviation environment, developing an analytic method that moves beyond the essential identification of risk factors to assess the safety performance and dis- cover the potential hazards of airlines is indispensable. McFadden and Towell (1999) mentioned, while appre- ciating the value of accident investigations in identifying the cause and initiating corrective actions to prevent future errors, that a fundamental shift in the emphasis to ‘‘proactive safety’’ would be necessary. To achieve

0360-8352/$ - see front matter � 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.cie.2007.06.032

* Tel.: +88 6226215656 2881. E-mail address: [email protected]

H.-J. Shyur / Computers & Industrial Engineering 54 (2008) 34–44 35

‘‘proactive safety’’, an idea risk assessment tool should be developed enabling an analyst to examine a wide variety of accidents quickly, systematically, and probabilistically and assisting a risk manager in priority set- ting and policy decision making. However, only few attempts have been made so far at how to analyze the aviation risk systematically and quantitatively.

Risk assessment is a structured science-based process to estimate the likelihood and severity of risk with attendant uncertainty (Coleman & Marks, 1999). The most obvious approach to study aviation risk focused on analyzing the accident data. For example, Janic (2000) and Lee (2006) treated the pattern of accidents as a Possion process to assess the probability of future events by using a sample of global accident records. This approach neglects the ordinary safety performance of the airlines, which may influence the aviation safety environment directly. Civil aviation is a complex mosaic of many varied, yet interrelated human, technical, environmental, and organizational factors that affects safety and sys- tem performance. Aviation accidents result from multiple contributing factors. Logan (1999) mentioned that operational safety data such as aircraft reliability, flight data records, employee safety reports, enforcement information, inspector investigations or oversight information were also essential to aviation risk analysis.

The Airline Safety Assessment System, currently under development by the Taiwan Civil Aeronautics Administration (CAA), will contain indicators of air carrier safety performance that can identify potential problem areas for inspectors. The objective of this research is to develop an analytic method that uses data on both accident and safety performance to quantify the aviation risk. Our approach takes into account the more complex relationships among relevant aviation risk contributing factors. In this study, risk involves a measure of probability of the occurrence of a hazardous event caused by human error. A specified propor- tional hazard model considering the baseline hazard function as a quadratic spline function has investigated and demonstrated its applicability in aviation risk assessment. A subset of data gathered from the Fight Safety Management Information System (FSMIS) developed by the office of the Taiwan Civil Aeronautics Admin- istration (CAA) was remodeled to accomplish this study. The results demonstrate that the proposed model is a more promising approach with the potential of becoming very useful in practice and leading to further gen- eralization of aviation risk analysis.

Statistics indicate that more than 70% of aviation accidents are related to human errors and 56% of world- wide hull lose accidents are caused by flight crew errors (McFadden, 1993; Boeing Commercial Airplane Group, 2005). It has also been claimed that all accidents have some forms of human error attached to their causes (Braithwaite et al., 1998). Estimation of the human error related risk in a given time interval that a particular airline would be expected to have, upon adjusting for the airline’s corresponding safety performance indicators, could help to identify situations in need of heightened level of surveillance by the safety inspectors.

2. Research methodology

There are two proposed approaches for assessing the aviation risk and safety: The first one is looking at the number of accidents and fatalities continuously for offering an indicator on the improvement of the sector’s safety. The second approach statistically models the occurrence of air accidents over time by assuming the accident events following Poisson process (Janic, 2000). Such a process is based on the following assumptions:

• An event can occur at random and at any time. • The numbers of events, which occur in non-overlapping intervals are independent. • The probability of an event occurring for a small interval Dt is proportional to Dt and can be estimated by

kDt where, k is the hazard or failure rate.

According to the assumptions, the time interval between any two consecutive events will follow an expo- nential distribution, which is a fundamental model in parametric survival analysis. The probability of the occurrence of at least one accident in time t can be written as

PðT 6 tÞ¼ 1 � PðT > tÞ¼ 1 � e�kt; ð1Þ

36 H.-J. Shyur / Computers & Industrial Engineering 54 (2008) 34–44

where T is the random variable representing the time between any two consecutive events and k is a constant. If there are safety related factors upon which accident inter arrival time may depend, it becomes of interest to consider generalizations of the model to take account of the dependent information. The above model ignores the possible influence of safety factors to event inter arrival time.

Regression models for survival analysis have been extensively studied in the past 30 years. They allow the hazard rate to be a function of the observed explanatory variables (or covariates). Generally, regression mod- els can be generally categorized in two classes. The first one is called the parametric statistical model, which assumes the shapes of time to event distributions are known. McFadden (2003) used logistic regression model to predict pilot-error accident and incident rates on an airline-by-airline basis. However, when the survival time data involve complex distributional shapes that are not well-known or when the number of observations is small making it difficult to test, the second model type of survival analysis – semi-parametric or non-para- metric statistical model appears to be an attractive method to the parametric ones. The model is ‘‘distribution- free’’ since no assumptions need to be made about the shapes of time to event distributions. For example, Cox’s proportional hazards (PH) model (Cox, 1972) is one of the most famous semi-parametric or non-para- metric statistical models for time-to-event data with explanatory variables. It is widely applied in the medical field. Recently, the model is also gaining acceptance in many sectors, including reliability engineering, trans- portation, and finance.

A log linear PH model is expressed as

kðtjzÞ¼ k0ðtÞ � ezb ð2Þ

where k(tjz) is the hazard rate at time t and covariate vector z, k0(t) which is the modified multiplicatively by covariates is referred to as the baseline hazard function, and b is the regression coefficients vector. A PH model is a class of models with the property that different individuals have hazard functions that are proportional to each other. That is, the ratio k(tjz1)/k(tjz2) of the hazard functions for two individuals with different covariate vectors z1 and z2 does not vary with time. In other words, k(tjz1) is directly proportional to k(tjz2).

There are two unknown components in Eq. (2): the vector of regression coefficients and the baseline hazard function k0 (t). Cox (1972) uses an attractive approach, in which a likelihood function that does not depend upon k0(t) is obtained for. This function is referred to as a partial likelihood function and is expressed as

LðbÞ Yn i¼1

expbziP l2SðtiÞ

expbzl ð3Þ

where, n is the number of observed failure times and S(ti) is the risk set at time ti. This function can be max- imized to give an estimate of b in the absence of any knowledge on k0(t). The motivation for the likelihood function is that given S(t) and given that a failure occurs at t, the probability that the component i (i 2S(t)) fails is

kðtjziÞP l2SðtÞ

kðtjzlÞ ¼

k0ðtÞ � expbziP l2SðtÞ

k0ðtÞ � expbzl ¼

expbziP l2SðtÞ

expbzl : ð4Þ

Gill (1984) gave a discussion on how martingale approach could be used to give a firm mathematical basis to Cox proportional hazard model.

If we assume k0(t) = k0, (2) will reduce to an exponential regression model. It is a special case of the pro- portional hazard model where the base line hazard is specified by a single parameter. The conditional density function of t given z is

fðt; zÞ¼ k0ezb e�k0 e zb t; ð5Þ

and the conditional probability of the occurrence of at least one accident in time t for covariate z is given by

PðT 6 tÞ¼ 1 � e� R t

0 kðsjzÞds ¼ 1 � e�k0 e

zbt ð6Þ

The maximum likelihood theory is used to evaluate the unknown parameters of the above models. Consider n independent observations distributed according to (2). Let ti be the observed event inter arrival time with the

H.-J. Shyur / Computers & Industrial Engineering 54 (2008) 34–44 37

corresponding covariate vector zi = (z1i, z2i ,..., zsi) for the ith observation. The natural logarithm of the like- lihood function for this model is given by

ln Lðk0; bÞ¼ ln Y

i

k0e zib e�k0 e

zi b ti

! ¼ n � lnðk0Þþ

X i

zib � k0 X

i

ezibti ð7Þ

This function can be maximized to give an estimate of k0 and b by setting the first derivative of lnL(k0, b), with respect to k0 and b, equal to zero and by solving the resulting equations. Here,

o ln Lðk0; bÞ ok0

¼ n k0 � X

i

ezibti ¼ 0 ð8Þ

o ln Lðk0; bÞ obj

¼ X

zjið1 � ezi btiÞ¼ 0 ð9Þ

The standard likelihood approach outlined above does not adequately take the advantage of the particular structure of this model. However, for the specified proportional hazard model, it can determine all the un- knowns at once.

The Weibull distribution can be generated to the regression situation essentially in the same way, when a nonlinear expression for the baseline hazard rate function is used. The hazard rate function under this condi- tion is

kðtjzÞ¼ hcðtÞc�1ezb; ð10Þ

where both h and c are positive and are referred to as the scale parameter and the shape parameter of the dis- tribution, respectively. In our study, the baseline hazard function k0 (t) is specified by a quadratic spline func- tion to estimate the unknown underlying distribution. We use the Heaviside function, where, U+ = U if U = 0 and U+ = 0 if U < 0 to create a spline function. The formula is given by

k0ðtÞ¼ X2 n¼0

cnt n þ

Xl m¼1

hmðt � smÞ 2 þ ð11Þ

where l is the number of knots, sm is the location of knots, hm is the added linear effect following knots, and cn is the coefficient of the underlying base polynomial. Splines are presented as a non-parametric function esti- mating technique (Wegmen & Wright, 1983). A spline function of degree m is a piecewise m-degree polynomial with pieces joining at defined points, which are called ‘‘knots’’. A detailed discussion of spline functions is gi- ven in our previous paper (Shyur, Elsayed, & Luxhoj, 1999). To estimate the parameters of the spline function and the coefficients of the covariates, a general likelihood function is used. Since the baseline hazard rates are always non-negative, we must ensure that the results of the estimation will satisfy the constraints. The details of the proposed model will be provided at a later point in this paper.

3. Data description

A subset of data gathered from the Flight Safety Management Information System (FSMIS) developed by the Taiwan Civil Aeronautics Administration (CAA) office was remodeled to accomplish this study. The FSMIS is an analytical tool intended to support CAA inspection activities, which contains data related to the surveillance records of air operators, maintenance facilities, and manufacture of aircraft parts and acci- dents/incidents investigation reports.

Any member of a set of human actions that exceeds some limit of acceptability will cause human error (Latorella & Prabhu, 2000). The main goal of this research is to develop a model to provide relative risk prob- ability inference and trend analysis among different kinds of human errors, which may cause any major avi- ation events. Here, a major event is defined as a flight event, which may lead any person to suffer death or serious injury, or the aircraft to receive substantial damage. The risk of this kind of event is much more essen- tial to be managed. For this reason, the analysis focuses only on the major event, but not all kinds of accidents and incidents. We analyze the aviation safety risk using a sample of 61 major accident records for the period

38 H.-J. Shyur / Computers & Industrial Engineering 54 (2008) 34–44

from January 2003 to December 2004. The provided database contains a general cause category for each acci- dent/incident. The aviation accidents/incidents that were coded as (1) improper maintenance, (2) operator deficiency, (3) crew induced, (4) operation and maintenance, (5) inadequate maintenance, and (6) crew, ground crew, and ground handle system were analyzed in this paper. All the events are related to human error. According to the accident/incident records, the time between every two consecutive events for each cause cat- egory and airline can be simply calculated.

Based on the FSMIS database, numerous safety performance indicators for signaling the potential problem areas considered for inspection are currently defined by CAA (Shyur, 2006). These indicators assist in diag- nosing an airline’s ‘‘profile’’ compared with others in the same peer class and provide insights as to whether an airline is more or less likely to undertake unsafe practices. The airline safety performances influence the whole aviation safety environment directly and assist in diagnosing the profile of an airline. So the safety per- formances are explored as the effecting factors or explanatory factors of the aviation risk. Three integrated major corresponding performance indicators are considered in this study – airworthiness surveillance (AS), operations surveillance (OS), and frequency of general events (FE). Surveillance is one of the most significant duties of the CAA office in its larger responsibility of assuring air transportation safety. According to the safety report published by FAA (Federal Aviation Administration, 1997), the information on factors that could affect airline safety practices can be found in the inspection and surveillance reports on air carrier operations.

The CAA monitors the airworthiness-related activities performed within an air carrier using various sur- veillance techniques. The airworthiness surveillance activities conducted are based on the risks associated with the scope and depth of airworthiness authority assigned to the airline, and are performed against the CAA approved airworthiness process manual of that carrier. The CAA is also responsible for monitoring all phases of air carrier operations including: training programs and records; base and station facilities; airports and route systems. One of the limitations of the FSMIS surveillance database is that it does not use a quantitative way to measure the surveillance result.

The recorded surveillance report in FSMIS contains a result category for each check item, for instance, S represents that the check item has satisfied the certain requirements and F means there are some findings in this item, etc. For quantifying the surveillance result, each code was assigned a weighted score according to its order of severity. A ratio scale approach, the Analytic Hierarch Process (AHP), was conducted to make the decision. AHP was proposed by Saaty as a method of solving socio-economic decision making problems and has found its widest applications in multi-criteria decision making (Satty, 1980). Using the weighted scores, the surveillance indicators were measured by the percentage of unfavorable surveillance records asso- ciated with a given smoothed time period. The exact calculation formula is

Unfavorable rate ¼

PN i¼1 ðwi � niÞ

W � N ð12Þ

where W: predefined maximum weighted score, N: total number of inspections during time T, wi: weighted score for the result i of individual inspection item, i is the result code, ni: result i of individual inspection item during time T. Table 1 contains a sample of the summary of input data from FSMIS for air carrier A. For data security,

only 10 records are shown.

4. Application of the methodology

Our approach takes into account the more complex relationships among relevant aviation risk factors. Using the models presented, risk has been assessed as the probability of occurrence of a specific type of human error related aviation accident. The potential human error related risk could be identified and monitored timely. The results can provide better references to the civil aviation communities to manage the aviation- safety risk, thus corrective action can be taken to reduce the occurrence of aviation accidents.

Table 1 Sample FSMIS ‘‘Organized’’ data

Air carrier A

Major event cause

Improper maintenance

Event no. Time elapsed before next event (days)

Airworthiness performance

Operation performance

Frequency of general accidents per thousand landings

1 196 0.01556 0.00203 2.116995 2 10 0.01613 0.00358 1.770303 3 68 0.01284 0.0054 2.971014 4 78 0.00756 0.00117 1.461988 5 311 0.01735 0.00245 2.705822 6 3 0.00649 0 0.605938 7 14 0.00629 0.00399 0.807918 8 28 0.01055 0.0012 0.420698 9 29 0.02442 0.00374 0.386453

10 20 0.01144 0.00118 0.420062

H.-J. Shyur / Computers & Industrial Engineering 54 (2008) 34–44 39

4.1. Model development

Consider n independent category k events distributed according to (2). Let T ki refers to the time between the ith and (i�1)th events. The covariates ðz1i ; z2i ; z3i Þ represent the unfavorable rates of AS, OS, and FE measured in the ith time interval. Since the time interval is not a constant, the event frequency is normalized by thou- sands of flight landings. The likelihood for this model is given by

Lk ¼ Yn i¼1

fðT ki ; ziÞ¼ Yn i¼1

k0ðT ki Þe zi�bk exp �ezib

k Z T ki

0

k0ðtÞdt !

ð13Þ

where, zi � bk ¼ z1i b k 1 þ z2i b

k 2 þ z3i b

k 3, for i = 1–n. The log-likelihood function provides more flexibility in the

parameter estimation for the spline function, k0(t), in the extreme tails and in estimating the coefficients of the covariates. The natural logarithm of the likelihood function used in this paper is

l ¼ ln L ¼ Xn i¼1 ðzi � bk þ ln k0ðT ki Þ� e

zi�bk Z T ki

0

k0ðtÞdtÞ: ð14Þ

Because the baseline hazard rates are always nonnegative, we must make sure that the resulting estimate will satisfy this constraint. To approximate the maximum value of the log-likelihood, the Generalized Reduced Gradient (GRG) algorithm (Lasdon, Waren, Jain, & Ratner, 1978) has been applied to obtain the optimized solution. The GRG solves a sequence of reduced problems by a gradient method to prevent a more complex searching problem. The algorithm has been shown to be efficient and reliable when solving small to moderate nonlinear programming problems. To estimate the spline function, Etezadi-Amoli and Ciampi (1987) suggest starting with zero knots and constant hazard. The number of knots is increased, adding one knot at a time, until no improvement in the fit is obtained.

To estimate the baseline spline functions, k0(t), models with a different number of knots are created. Results show that one knot spline functions can provide good approximations of the hazard functions for all analyzed data sets. The created models related to air carrier A are shown in Table 2. Three covariates are introduced to 2 sets of accident/incident data for air carrier ‘‘A’’ since this carrier contains only two types of major events in the analyzed time period. The standard errors (SE) of the estimates of the proposed model coefficients are pro- vided in the parentheses. We use the information matrix only to determine standard errors for regression parameters. In this case, we found that the log-likelihood is quite insensitive to the changes in the position of the knots. The situation will be reflected by ‘‘ridges’’ in the likelihood surface and a nearly singular Hessian matrix (Ciampi & Etezadi-Amoli, 1984). Therefore, we kept the position of the knots fixed when calculating the information matrix of b1, b2, and b3.

Table 2 Results of proposed risk assessment model for air carrier ‘‘A’’

Parameters Major event cause

Improper maintenance induced Crew induced

c0 0.049868021 0.0067334 c1 �0.000260578 0.0000094 c2 �0.000092883 *0 h1 0.000102162 *0 s1 5.38 15.35 b1 (SE) 0.00440092(0.0028) 20.703049(0.76) b2 (SE) 0.00139579(0.00035) 0.000013(0.0000087) b3 (SE) 0.00973966(0.00065) *0 Log-likelihood �48.54 �29.43

40 H.-J. Shyur / Computers & Industrial Engineering 54 (2008) 34–44

According to the results, it appears that the estimated hazards increase as the unfavorable rate of airwor- thiness surveillance and operation surveillance increase, with coefficient estimates of b1 = 0.0044 and b2 = 0.0014 for the improper maintenance induced event, and b1 = 4.4477 and b2 = 0.0096 for the crew induced event. In this case, it can also be noted that the estimated effect of airworthiness performance is stron- ger than the operation performance since b1 > b2. Moreover, it can assess the probability of an occurrence of any kind of major event by providing the values of air carrier performances (covariates). The corresponding mathematical function of risk assessment is

Risk ¼ PðT 6 tÞ¼ 1 � e� R t

0 kðsjzÞds ¼ 1 � e�e

zb R t

0 k0ðsÞds ð15Þ

Fig. 1 illustrates the probabilities of the occurrence of at least one major event within the time period t for an air carrier ‘‘A’’ when the same safety performances existing in the current will continue to exist in the future. In this case, we set AS = 0.01144, OS = 0.00118, and FE = 0.420062. According to the risk assessment function, the probabilities rise over time until the next event. For example, the probability of at least one major event caused by improper maintenance is about 0.372 by 10 days, 0.654 by 30 days, and 0.752 by 60 days. The prob- abilistic risk inferred by the models can be further used to facilitate the organization to identify relative haz- ardous human error. For example, as Fig. 1 indicates, the extent of risk can be compared in the order: improper maintenance > crew induced > others. Therefore, the inspection plan or prevention action should be taken to strengthen the routine monitoring for the two types of human error risk especially for the impro- per maintenance problem in order to prevent the occurrence of the corresponding events.

0

0.2

0.4

0.6

0.8

1

The time until the main event (days)

P ro

ba bi

li ty

o f

on e

m ai

n ev

en t w

it hi

n th

e ti

m e

t

Improper Maintenance Crew Induced

0 10 20 30 40 50 60 70 80 90

Fig. 1. Risk assessment for air carrier A.

H.-J. Shyur / Computers & Industrial Engineering 54 (2008) 34–44 41

In our developed model, the covariates are measured as unfavorable inspection rate and the frequency of general event, so the risk increases if the performance of the related effecting operations is not right. On the contrary, if there is improvement in performance, then the aviation risk can be reduced. Briefly, the results of the relationship of the covariates and the human error induced risk can direct the inspectors to focus on more related or important aviation operations inspection in order to control the hazardous risk in the future.

4.2. Comparing models

Although we wish to summarize our risk assessment with a single model, there are usually other choices to be made. Kullback and Leibler (1951) addressed such issues and developed a measure, the Kullback–Leibler information, to represent the information loss when approximating reality. Akaike (1974) proposed using Kullback–Leibler information for model selection. He established a relationship between the maximum like- lihood and the Kullback–Leibler information. In essence, he developed an information criterion to estimate the Kullback–Leibler information, Akaike’s information criterion (AIC), which is defined as

Table Result

Param

Scale p Shape b1 b2 b3 Log-lik

Table Akaike

AIC

Impro Crew i

AIC ¼�2ðlog�likelihoodÞþ 2k ð16Þ

where, k is the number of estimated parameters included in the model. For a given data set, the log-likelihood of the model reflects the overall fit of the model. The AIC penalizes for the addition of parameters, and thus selects a model that fits well but with a minimum number of parameters. The model with the lowest AIC being the best model among all models specified for the data at hand, when it is compared to the AIC of a series of models specified a priori.

In this paper, two semi-parametric methods for estimating the function form of aviation safety risk assess- ment have been investigated to compare with the proposed approach. One is the exponential regression and the other is the Weibull regression model. Using the identical data sets, the maximum likelihood approach was also conducted to evaluate the unknown parameters for the alternative models. Table 3 shows the estimation results. The AIC statistics are presented in Table 4.

In general, the proposed models tend to provide better fit in both the given data sets with the advantage of being ‘‘distribution-free’’. Comparing all the alternative models including the Poisson process technique, a graphical analysis of the risk estimation curves for each of the models under two different levels of safety per- formance for air carrier ‘‘A’’ was performed. The risk assessment models consider safety performance indica- tors as the contributing factors of aviation events. Figs. 2–5 show that the proposed model better represents the effects of safety performances on aviation risk no matter what type of human error related risk has been

3 s of semi-parametric models for air carrier ‘‘A’’

eters Improper maintenance induced Crew induced

Exponential regression Weibull regression Exponential regression Weibull regression

arameter 0.01321 0.033877 0.007153 0.009374 parameter N/A 0.805614 N/A 0.941930

�0 �0 23.442 24.40633 0.00024 0.131236 0.013409 0.452157 �0 �0 �0 �0

elihood �53.26 �52.79 �33.46 �33.44

4 ’s information criterion of the hazard regression models

Proposed model Exponential regression Weibull regression

per maintenance induced 113.08 114.52 115.58 nduced 74.86 74.92 76.88

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50 60 70 80 90

Time

R is

k

Proposed model Poisson processPoisson process

Exponential Regression Weibull Regression

Fig. 2. Risk assessment for improper maintenance induced event with low AS and OS (AS = 0.01144, OS = 0.00118, and FE = 0.420062).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50 60 70 80 90

Time

R is

k

Proposed model Poisson process

Exponential Regression Weibull Regression

Fig. 3. Risk assessment for improper maintenance induced event with high AS and OS (AS = 0.5, OS = 0.5, and FE = 0.420062).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50 60 70 80 90

Time

R is

k

Proposed model Poisson process

Exponential Regression Weibull Regression

Fig. 4. Risk assessment for crew induced event with low AS and OS (AS = 0.01144, OS = 0.00118, and FE = 0.420062).

42 H.-J. Shyur / Computers & Industrial Engineering 54 (2008) 34–44

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50 60 70 80 90 Time

R is

k

Proposed model Poisson process

Exponential Regression Weibull Regression

Fig. 5. Risk assessment for crew induced event with high AS and OS (AS = 0.1, OS = 0.1, and FE = 0.420062).

H.-J. Shyur / Computers & Industrial Engineering 54 (2008) 34–44 43

studied. Similar results were also appeared when we studied the accident and safety data of the other five air carriers.

5. Conclusions

In the past, only accident or fatality data were investigated and used to measure the risk or/and safety level of airlines. This is just a reactive way to manage the aviation risk. However, commercial aviation is a complex mosaic of many varied, yet interrelated human, technical, environmental, and organizational factors that affect safety and system performance. The possible influencing factors should be included while assessing risk. The application of the hazard regression models to the analysis of aviation risk has not been previously reported in the research literature.

This paper proposed a new quantitative methodology for the assessment of risk in civil aviation. The spline function is used to present the baseline hazard function. Our proposed approach allows finding fundamental cause of human error related accidents through the analysis of operational safety data. The modified propor- tional hazards model takes into account the relationships among relevant aviation risk factors. Furthermore, the dependence of the aviation risk on operational performance of airlines can also be measured. Finally, the results of the case study demonstrate that the proposed model is a more promising regression model with the potential of becoming very useful in practice.

Acknowledgements

The author would like to thank the Taiwan CAA for their assistance in problem formulation and data collection.

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