Risk modeling of hazardous materials rail movement to include a terrorist incident.

ABSTRACT

The enactment of the Hazardous Materials Transportation Uniform Standards Act of 1990 placed added emphasis on the need to assess the risks and benefits associated with the transportation of hazardous materials by all modes. Rail transportation is playing an increasing role in the growing movement of hazardous materials. The events of September 11, 2001 and the real possibility of future attacks have raised the concern level for rail transportation of hazardous materials and the safety of people and property in the event of a terrorist rail incident. Add to this the ever present possibility of an unrelated rail accident involving hazardous materials especially given the growing volume of hazardous materials.

This paper presents a preliminary risk probability model of a train accident or terrorist incident involving hazardous materials by identifying relevant variables and their applicability to rail movement risk analysis. Although the risk of release due to a rail accident or incident is estimated to be small, it is not impossible. Risk of a low-probability high-consequence accident involving a significant release of hazardous materials must be given adequate consideration.

A delineation of a concept of risk assessment and linking that concept to rail transportation quantitative risk analysis is the initial basis for this paper. It is followed by a review analysis of relevant hazardous materials transportation risk models. Based on these existing models, the paper outlines the elements of a risk based modeling analysis to include types and causes of rail accidents. The paper then defines an initial methodology for carrying out a risk assessment of rail transportation of hazardous materials to include risk of terrorist attack. To accomplish any risk assessment of hazardous substances movement during rail transportation, one must consider the complexity and magnitude of chemicals moving through the rail network. The multiplicity of chemical and physical characteristics of substances, location of manufacturing facility in relation to final destination and volume of cargo tend to further enhance the dimensions and complicate the issue.

Keywords: Rail Hazardous Materials Movement, Rail Freight Terrorist Attacks, Rail Risk Models.

1. INTRODUCTION

Railroads are an essential component of our transportation economy. Some 40% of all intercity freight goes by rail, including 67% of the coal used by electric utilities to produce power and 20% of the chemicals (USDOT, 2005; AAR, 2005a). There are thousands of chemicals in use today and many more are being introduced all of the time. Railroads carry an even higher percentage of those chemicals essential to the public health and standard of living for the United States. Chlorine, for example, used to purify the nation's water supplies has significant rail movements (AAR, 2005b).

Vast quantities of these hazardous substances are being moved by rail alone. Due to the nature of most chemicals, they can pose hazards of explosion, toxic release, and fire. The transportation of these hazardous materials is an important problem due to their pervasiveness. Hazardous materials, or dangerous goods, include explosives, gases, flammable liquids and solids, oxidizing substances, poisonous and infectious substances, radioactive materials, corrosive substances, and hazardous wastes. The fact that the volume of hazardous materials moving by rail more than doubled since 1980 indicates that rail has become an integral part of the tremendous increase in the transport of hazardous materials. Nearly 155 million tons of chemicals are being transported by rail in North America each year which constitutes 1.75 million rail cars of hazardous materials (D'Amico, 2001).

The risk associated with a release of these materials during transportation is what differentiates rail shipments of hazardous materials from rail shipments of other materials. Hazardous materials can be extremely harmful to the environment and to human health since exposure to their toxic chemical ingredients could lead to the injury or death of humans, plants, and animals. The events which have traditionally given rise to hazard during rail transportation are container failure or the impact due to collisions. However, on October 24, 2002 the FBI issued a warning, based on information obtained from al-Qaida prisoners, which said terrorists may try to destroy bridges or key sections of railroad infrastructure and tracks. In its warning, the FBI said captured al-Qaida photographs of U.S. railroad engines, cars and crossings increased the agency's concern about the threat. The 140,000 mile network of rail tracks, bridges, and terminals, more than three times the Interstate Highway System, presents a huge security challenge. Much of the network is in isolated areas where fencing is neither practicable nor effective. Intelligence officials continue to believe that aI-Qaida plans to attack targets such as railroads that would be readily recognized as representing U.S. economic interests. In sum, security has placed a new dimension of concern on the rail system across the country. Terrorism must now be added to the risk equation.

Models dealing with hazardous materials rail transportation problems must deal with uncertainties when assessing risks, because data are often sparse and of questionable quality. Uncertainties also arise because researchers frequently encounter estimating very small probabilities associated with events which may have never occurred such as terrorist attacks. Thus, a model which explicitly recognizes uncertainty is preferable to one which does not. However, building stochastic models is significantly more difficult than building deterministic ones, and the bulk of work to date has been of the deterministic variety (List, et al., 1991).

The purpose of this paper is to add to the knowledge base to help public entities anticipate, identify, plan for, and respond to uncertain events and outcomes of an accident or terrorist incident on a U.S. freight railroad that may interfere with their ability to continue operations and fulfill their missions. It should serve as a resource for the practical enhancement and control of risk management of these entities. Specifically, the analysis will serve to identify and evaluate for these entities what a rail transportation risk analysis is, what it can do, how to communicate the risk analysis to all concerned.

2. RISK ASSESSMENT

Risk has to do with the probability and the consequence of an undesirable event. The terms risk and hazard are often used synonymously, but are quite different in reality. Hazard is the inherent characteristic of a material, condition, or activity that has the potential to cause harm to people, property, or the environment. Although some authors define risk as only one of these terms, it is more common to define risk as the product of both the probability of and the consequence of the undesirable event (Covello and Merkhofer, 1993). This is an "expected consequence" definition, and it is the definition of "traditional risk" definition used in the U.S. Department of Transportation 1989 guidelines for transporting hazardous materials.

Probability is often defined as a number between zero and one that expresses a degree of belief concerning the possible occurrence of an event. Probability usually refers to a conditional probability which is a probability for an event that has been preceded by another specified event. Consequence is considered to be the direct effect, usually undesirable, of an event such as a rail accident involving hazardous materials. The consequence component of risk analysis begins with the release of hazardous material from the container. The consequence scenario may involve a three-step procedure: (1) the release amount and mode of release; (2) the extent to which people are exposed to the source term; and (3) assessment of the health effect.

An undesirable event that results in the release of a hazardous substance is usually called an incident. An initiating event is the first in a sequence of events that may lead to an undesirable consequence. In transportation risk analysis, the initiating event usually is considered a reportable accident that is of the severity to require notification of regulatory agencies. Although there can be many undesirable consequences of an incident (such as damage to wildlife, economic losses, and injuries) the prime concern is with fatalities. It is common to assume that the undesirable consequence is proportional to the size of the population in the neighborhood of the incident, where the size of the neighborhood depends on the substance carried. Furthermore, the probability of an incident occurring depends on the substance carried and the route.

Risk assessment can be viewed as the determination of risk acceptability, often by comparison with other risks. Risk analysis is to be utilized as the computation of risks. Taking action to reduce risks is risk management. Risk assessment should quantify the transportation risk, identify sources of greatest risk, and examine specific issues in risk reduction. It should identify risks associated with accidents or terrorists' attacks on rail transportation of hazardous materials and help determine the levels of risk that are acceptable, affordable and comparable with other terrorist risks present in our country. Most of this depends on probabilistic estimates of a release given an incident.

More specifically, risk assessment involves estimating the frequency and consequences of undesirable events, then evaluating the associated risk in quantitative terms. The process of risk assessment serves to organize thinking about risks, permitting judgments in a systematic way. It also helps identify risks that might not have been thought of otherwise and it motivates improvements in data collection by pointing out data base deficiencies. The results of risk assessment provide knowledge essential to informed decisionmaking.

2.1 The Public and Risk Assessment

The techniques of risk assessment address two fundamental questions: 1) what is the actual level of risk? And, 2) what level of risk is acceptable to those affected? The first issue is addressed by quantitative results. Qualitative judgments are important to the second question. The public creates its own unscientific risk assessments. Though the safety record of hazardous material being transported is excellent, public attention focuses simply on any incident involving hazardous materials. The effect is heightened public awareness of the risks associated with transporting hazardous materials. Public concern is greatest regarding risks that are involuntary, uncontrolled, unfamiliar, immediate, manmade and catastrophic. Hazardous materials transportation possesses these attributes. The question of risk acceptability is complicated by the fact that the public may have risk perceptions that differ substantially from the actual risks. The difference between the statistical risks and perceptions of risks associated with nuclear transportation is substantial. Risk equity, the appropriate distribution of risks among different members of society, is another complicating factor.

3. REVIEW OF TRANSPORT RISK MODELS

The transport of hazardous materials by rail is an important strategic and tactical decision problem. Risk modeling plays a significant role in the strategic and tactical decision processes surrounding rail hazardous materials transport. Risks associated with this activity make transport planning difficult. Although most existing analytical approaches for hazardous materials rail transport account for risk, there is no agreement among researchers on how to model the associated risks. This suggests that particular attention must be paid to the modeling of risks in rail hazardous materials transport.

Most risk modeling analyses have revolved around one or all of the following criteria (Erkut and Verter, 1998):

1) Shortest travel distance

2) Minimum population exposure

3) Minimum societal risk

4) Minimum DOT risk

5) Minimum accident probability

6) Minimum incident probability.

The shortest travel distance might not always be a good choice for transporting hazardous materials. Number 2 ignores incident probabilities and finds the path that exposes the fewest number of people to the hazardous materials. Number 3 is the traditional definition of risk. It uses the following formula to find the risk: Societal risk = (length of the exposure area per miles) X (accident rate probability per mile) X (conditional release probability given an accident) X (population/worker density in the neighborhood of the exposure area-persons per sq. mile) X (pi-impact radius in miles-sq). Thus, the societal risk is the expected number of people to be impacted; an important consideration.

The 4th criterion is the definition of risk suggested by the U.S. Department of Transportation (1989). This definition is similar to the definition of societal risk with two differences: it ignores conditional release probabilities, and it computes population impacted by using a rectangle instead of a circle. Number 5 finds the path that minimizes the accident probability, ignoring all other information. The last criterion concentrates on incident probabilities and finds the path that minimizes the probability of a hazardous materials accident involving a release.

Some models used have depended on the type of material involved. Some of the popular models are CASRAM, Chemical Accident Stochastic Risk Assessment Model (Argonne National Laboratories, 2005), FIREPLUME, to predict consequences of toxic chemicals released from a vehicle fire that burns the hazardous material cargo (Argonne National Laboratories, 2005), SPILL, to estimate transient (including two-phased) release from a pressurized vessel (Oakridge National Laboratories, 2005), HEGADAS, to estimate the consequences of steady state or transient release of dense vapor, and to help to predict near-field and far-field consequences (Oakridge National Laboratories, 2005). It may be noted that these models have been used by United States Department of Transportation for carrying out risk assessment studies (Argonne National Laboratories, 2005; Oakridge National Laboratories, 2005).

One method of summarizing a risk analysis uses a risk profile. The risk profile gives the probability that consequences will exceed a given level. It is a multiple-measure method because it explicitly represents varying probabilities of different levels of consequences, rather than producing a single measure such as "expected fatalities."

Attention to special transportation facilities, such as bridges and tunnels, is present in several studies. For example, one study focused on six major types of potential events: corrosive or toxic liquid release, flammable liquid release, liquefied gas release, toxic gas release, asphyxiate gas release, and condensed phase explosion. For each type of event, probabilities of exceeding 1, 10 and 100 fatalities were estimated, as a means of creating a series of points along a risk profile (Consideine, 1986).

The U.S. Department of Transportation (USDOT) established a set of guidelines to be used in assessing the risks of transporting hazardous materials over specified routes. These guidelines have been used in several studies involving a variety of materials and sites. For example, Hobeika et al. (1986) applied them to the movement of spent nuclear fuel between two power stations in Virginia. Kessler (1986) performed a similar analysis for a wider variety of hazardous materials moving through the Dallas-Fort Worth metropolitan area in Texas.

The work done for high-level nuclear wastes (spent fuel assemblies from commercial reactors) provides an example of risk analysis which includes a substantial effort on assessing risks that are associated with normal operations, rather than focusing only on incident-related risk. Cashwell et al. (1986) provided an extensive report on risk analysis for transporting nuclear wastes, based on use of models developed at Sandia National Laboratories. This modeling takes a routing selection as input, and then assesses the level of risk to both workers and the public from movements along the route.

Rhyne (1994) expressed the overall risk as obtained by summing over all scenarios:

[R.sub.i] = f ([F.sub.i],[C.sub.i])

The scenario frequency computation usually is divided into three components: the accident frequency; the conditional probability of a release, given an accident; and the conditional probability of various consequence terms. The accident frequency starts with a value for accidents per mile and usually ends with accidents per year or accidents per some unit of material delivered so that all analyses can be put on a common basis. The conditional probability of release may be subdivided into several components in the predictive approach or simply evaluated at this top level in the historical approach. The consequence analysis usually introduces some conditional probabilities into the frequency term, such as the probability that a certain meteorological condition exists, given that the accident has occurred. The terms in the mathematical formulation may vary with the specific analysis. The usual procedure for a quantitative transportation risk analysis is to divide the transport route into segments (also called links) along which the important parameters can be reasonably approximated by a single average value. A detailed expression for risk then can be further defined:

[R.sub.i] = f([F.sub.1a] x [M.sub.a] x [P.sub.2abx] [P.sub.3abc] x [P.sub.4ad] x [P.sub.5ae] x [N.sub.ad] x [A.sub.abc x [X.sub.ace]) where:

[F.sub.1a] = frequency of an accident per mile of rail track type and conditions, vehicle type, and traffic conditions

[M.sub.a] = number of miles, or miles per year, in link a

[P.sub.2ab] = probability that the accident in link a results in accident forces of type b (e.g., mechanical or thermal forces)

[P.sub.3abc] = probability that release class c occurs, given that the accident force type b occurs in link a, which depends on the force magnitude and the container's capability to resist the force

[P.sub.4ad] = probability that population distribution class d occurs in link a

[P.sub.5ae] = probability that meteorological condition e occurs in link a

[N.sub.ad] = number of persons per unit area in population class d in link a

[A.sub.abc] = release amount for release class c, given that force type b occurs in link a

[X.sub.ace] = area that experiences the specified health effect from a unit release of the hazardous material for meteorological condition e for release class c

The overall risk is obtained by summing all scenarios for each rail link or for the entire route:

R = [SIGMA][Ri.sub.i]

Ang and Briscoe (1989) suggested a general framework for risk analysis in transportation, drawing heavily on the experience in the nuclear power industry. One of the key ideas in this approach is to break the problem into three separate stages: (1) determining the probability of an undesirable event (e.g., an accident involving release of hazardous material); (2) determining the level of potential population and properly exposure, given the nature of the event; and (3) estimating the magnitude of the consequences (i.e., fatalities, injuries and property damage), given the level of exposure. Although most hazardous materials incidents involve property damage only, it is the small but finite probability of a major disaster with multiple fatalities that attracts most of the attention in a risk analysis.

In concept, at least, each stage of the process described above produces one or more consequences. These three types of distributions can then be combined to produce a resulting distribution of potential consequences from a specified activity. In practice, however, the process is seldom carried all the way through. A frequent shortcut is to compute only the expected value of each of the distributions, producing an "expected loss" as the measure of risk. In other cases, the sole focus is on the second stage, and population exposure to an assumed "worst case" event is used as the measure of risk, without regard for the likelihood of such an event, or the probability of various outcomes, given exposure.

Saccomanno and Chan (198.5) examined three strategies for routing of hazardous material shipments. These were: (1) minimize risk exposure, (2) minimize accident likelihood and (3) minimize operating costs. Abkowitz and Chan (1988) evaluated the use of five criteria for routing analysis: (1) minimize shipping distance, (2) minimize travel time, (3) minimize release-causing accident likelihood, (4) minimize population exposure, and (5) minimize the product of accident likelihood and population. The first two criteria minimize economic cost, and the latter three maximize safety. He found that routes that minimize risk may be so circuitous that they can be economically unfeasible, or at least impractical. His recommendation was that a routing analysis considers combinations of factors and use different weighting factors to evaluate trade-offs.

Many risk models in the hazardous materials transport literature have used the concept of a danger zone. The assumption is that residents and workers inside a circle centered at the incident site, with a given impact radius, will experience the same undesirable consequence, and residents/workers outside this circle will experience no undesirable consequence. Although most researchers agree on the need to include risks in route selection for hazardous materials transport; they do not agree on how transport risk should be modeled.

The ways of measuring risk vary widely. Other prominent models include: traditional risk, population exposure, incident probability, perceived risk, and conditional risk. Some analysts use population exposure. Others multiply population exposure by the amount of material being shipped. Still others try to estimate the expected fatalities, injuries, environmental impacts, and dollar damages. When these latter measures are used, accident probabilities must be multiplied by conditional probabilities that other events will occur in succession (e.g. a catastrophic release given that an accident has occurred). The conditional risk model can be viewed as a multiplicative multi-attribute model, where the first attribute is traditional risk and the second attribute is incident probability. Equity is often measured by the largest risk impact per unit population (e.g. fatalities per thousand persons) or the difference between the largest and smallest of these.

4. RISK-BASED MODELING OF RAIL HAZARDOUS MATERIALS MOVEMENT

The consequences of railroad incidents that involve hazardous materials and the probability that these will occur are important components of a risk assessment method. A probabilistic consequence analysis is germane because a railroad incident can occur at any point on a rail line used to move hazardous materials. In fact, a variety of population distribution and accident occurrence rates usually exist along a given rail route. Analyses of accidents or incidents along rail routes need to be accomplished using combinations of the potential accident consequences and the probabilities of their occurrence. Given that consequences are usually expressed in terms such as fatalities, injuries, or property damage, the expected value of the risks is obtained by multiplying each consequence event that can occur by its frequency of occurrence and summing overall consequence levels. To perform an analysis, routes need to be identified and divided into segments for better accuracy of results. The segmentation can be based on changes in population densities or accident rates.

A general method to calculate risks from the transportation of hazardous materials through a populated zone can be summarized as:

RISK = (Unit Risk Factor) X (Number of Shipments) X (M/Shipment)

The unit risk factor is a measure of the increment of risk to the reference population for each mile of transport. Variables are the mode, population zone (urban, suburban, or rural), and hazard type. They are calculated for both workers and the general population. Unit risk factors can also be calculated for both normal transportation conditions and accidents/incidents.

Major characteristics of an analysis include: what type(s) of materials and transportation options are considered, the measure(s) of risk used, the analytic approach, and the nature of the conclusions drawn. Estimates of the probabilities of various types of incidents depend on: (1) estimates of accident rates, and now terrorist attacks, involving rail cars carrying hazardous materials, and (2) estimates of the probability of release of material (or of the probabilities of releasing various amounts of material) in an incident of a given type. For any particular application, it is desirable to have an estimate of the probability that a rail car of the type being considered will be involved in an incident with a consequent release of hazardous material, in a specific location and under a given set of environmental conditions. However, the available data generally do not support such detailed estimates.

Available accident/incident data show numbers of reported accidents and/or spill incidents over specified time periods. When coupled with some measure of exposure (e.g., truck-miles or railroad car-miles), these data may possibly be used to estimate accident/incident rates, which are commonly used in place of probabilities. But, there are three principal difficulties in creating specific estimates: (1) selecting from the set of reported accidents/incidents those which represent relevant events for the estimate to be constructed; (2) determining an appropriate measure of exposure which is consistent with the definitions of the events of interest; and (3) recognizing the uncertainty in the estimates as a result of both the small numbers of accidents/incidents in specific categories, and the probability.

5. TRANSPORATION QUANTITATIVE RISK ANALYSIS

A comprehensive approach to risk assessment of hazardous materials rail transportation not only addresses consequences and probability but should also provide an analysis that considers the following:

* Transportation routes-Although rail transportation under Federal Railroad Administration (FRA) regulations is considered "safe" for any route; some routes are safer than others. Regulatory and public interest groups may demand that the safest route be used. Routing of hazardous materials is an important decision problem that is of interest to hazardous materials producers and consumers, hazardous materials carriers, local governments, insurance companies, and the people exposed to the risks from the shipments. Risks imposed on the residents and workers near transport routes can be reduced by explicitly taking the risk of the shipments into account in the planning and the selection of routes.

Basically, a routing analysis should be based on three criteria:

1. Minimizing the rate of accidents resulting in a release of hazardous material;

2. Minimizing the rail route population exposure; and

3. Minimizing the length of the rail route.

Using risk assessment methodology over rail routes is essential since selection of rail routes is usually based solely on economic considerations such as the shortest route between two points. Consideration must be given to the availability of en-route facilities for managing emergencies. Other factors like avoiding population centers or tunnels when there are alternative rail routes must also be considered when deciding on a particular route.

* Package release statistics-The amount of material released depends on the severity of the accident and the container package.

* Commodity Shipping Patterns-An analysis of transportation of hazardous chemicals requires information on commodity shipping patterns which should indicate the quantity of chemicals and distances over which they must be shipped.

* Accident Statistics-Accident statistics involving hazardous substances transported on rail routes and states must be considered (i.e., accident rates per ton/mile).

* Public Relations-It is imperative to make consistent and defensible decisions to advert adverse public and/or regulatory reaction to rail hazardous materials shipments. The public is concerned because even though major accidents occur infrequently, one accident or incident has the potential to cause substantial human and property damage. Relying on "worst case scenarios" only can have a detrimental effect on the public's perception of feasibility of rail transport of hazardous materials. It is important that consideration be given to the potential effects of all types of incidents such as low-frequency accidents.

* Liability Control-The entity should be able to evaluate potential financial exposure should an incident occur.

* Acceptable level of Risk-Acceptable level of risk can be established by considering accident data and frequency of occurrence. By comparing this data with other accident causes the risk acceptable to society for transporting hazardous chemicals can be derived.

* Risk Management-

Entities can reduce exposure to incidents/accidents if they have the information from risk analysis. They are enabled to make cost-effective decisions with the objective being the most risk reduction at the least cost.

The following sequence of quantitative risk analysis provides a summary basis for making consistent and viable decisions. It allows for the evaluation of the effectiveness of existing controls and procedures and provides insight on how to cost-effectively reduce the risk.

1. Hazard Analysis (Define and Identify)

2. Accident and/or Incident Origination

3. Probability Analysis (Conditional Probabilities)

4. Consequence Analysis (Human, Animal and Material)

5. Risk Evaluation (Including evaluation of potential risk reduction alternatives)

6. TYPES AND CAUSES OF RAILROAD ACCIDENTS

The most common train accident is a derailment, in which a car separates from the preceding car and leaves the track. A number of the cars behind the lead car follow that lead car. At the initial separation, the brake system for all cars is activated, and both segments of the train are stopped; thus, the derailed cars leave the track at successively lower speeds. The lead car is decelerated by impact with the terrain, and the following cars may impact a previously derailed car and potentially override it. The result is usually a jumble of cars lying parallel, across, and at odd angles to each other along a section of track. If a fire occurs, about 10 cars in the vicinity usually are affected. Train analyses are more complicated than truck analyses because the probability that the derailed segment includes the hazardous material of interest must be considered.

The second most common train accident is a collision. In a collision, the cars nearest the impact experience the highest velocity change, but the differential velocity change is rapidly reduced away from the point of impact. Typically, collision velocity changes for affected cars are greater than derailment velocity changes for affected cars.

The major factors incorporated into modeling the risk associated with hazardous materials rail movements have traditionally been the types and causes of railroad accidents. The Federal Railroad Administration lists 11 classifications of accident types, which can be divided into five major groups (Federal Railroad Administration 2005):

1. Derailment: occurs when on-track equipment leaves the rail for a reason other than collision, explosion, rail-highway crossing impact, etc.

2. Collision: occurs when two trains, parts of trains, locomotives or track equipment impact each other; includes head-on, rear-end, side, raking, broken train, and railroad crossing.

3. Rail-highway (R/H Crossing) crossing collision: an impact at grade between railroad on-track equipment and highway vehicles, farm vehicles, bicycles or pedestrians.

4. Fire/Explosion (Fire/Exp): an accident caused by detonation, combustion or violent release of material carried or transported by rail.

5. Other: any event not otherwise classified; also includes switching collisions when all consists involved are parts of the switching movement.

The distribution of accidents by type is based on the assumption that accident types do not mix. This is not necessarily correct. If it is assumed that collisions, either train-train or train-auto, could cause subsequent derailment, the percentage of rail accidents involving derailments would be even greater. It should be noted that (a) rail-highway crossing accidents accounted for the vast majority of rail accidents between 1979 and 1991; and (b) the vast majority of fatalities in freight train accidents result from grade-crossing accidents and low-damage accidents in which trespassers are hit.

The FRA lists 4 classes of accident causes (Federal Railroad Administration 2005):

1. Track, Roadbed and Structures (Track/Bed): accidents caused by defects in the track, roadbed or track structures.

2. Mechanical and Electrical Failures (Mech/Elec): accidents caused by malfunction of some part of a train; generally these are mechanical failures related to axles, wheels or journals.

3. Train Operation--Human Factors (Human): accidents caused by human error, including rules violations and improper train handling.

4. Miscellaneous (Misc.): accidents caused by events not covered by the above categories, including rail-highway.

7. A RISK PROBABILITY MODEL FOR RAIL MOVEMENT OF HAZARDOUS MATERIALS

The probability model postulated is a multivariate logit model that estimates the probability of occurrence of an event as a function of several variables (called "exogenous" variables) thought to influence the probability of occurrence. The relationship between the exogenous variables and the probability is the nonlinear logistic function:

P[Y=1|f(x)] = 1/(1+exp{f(x)}),

Where f(x) is a function of the vector x=([x.sub.1], ... [x.sub.n]) of n variables influencing the probability of occurrence.

The coefficients of the function f(x) are estimated using a regression technique, and are then substituted in the expression above to yield a formula for the probability that an event will occur conditional upon the value of the (n) exogenous variables. The technique can be applied to compute the probability that a car on a train with given characteristics will be damaged or derailed, and to compute the probability that the car will release its contents.

The n variables used are of two types; quantitative variables (like speed weight, ...) which can be included in the expression of f(x) without transformation, and qualitative variables (like weather conditions, visibility, etc.) which must be represented by "dummy variables" whose number depend upon how many values the qualitative variables can take. For example, if weather conditions can take four possible values (clear, foggy, raining and snowing) then three dummy variables must be created. The rapid buildup of dummy variables is computationally very expensive, which is why several categories defined by the Federal Railroad Administration have been combined. Exogenous variables considered in the model include:

[A.sub.s]= Age & condition of static equipment.

[A.sub.d]= Age & condition of moving equipment.

D = Number of cars damaged or derailed.

[D.sub.k]= Number of cars damaged or derailed in position k.

[D.sub.r]= Number of cars damaged or derailed that release hazardous material.

[D.sub.x]= Number of cars damaged or derailed with hazardous material.

k = car position in the train (# of cars from the engine consist).

L = Number of cars in the train (L<200).

[N.sub.L]= Number of trains of length L per year.

[N.sub.x]= Number of cars with hazardous materials in the train.

Q = Existence of accident prevention equipment (yes or no).

S = Directional traffic (one way or two way track).

T = Total million tons of each train.

[T.sub.s]= Total million ton miles per year per line segment.

[T.sub.e]= Terrorist attack

V = Train speed.

[V.sub.m]= Maximum speed of rail traffic for each line segment (proxy for track class)

W= Weather conditions (Clear, cloudy, raining or snowing, foggy)

Z= Time of day (Dawn, day, dusk, night)

The probabilities estimated with the logit model are:

P[R|x] = probability that a given train (whose attributes are described by the vector x) will release hazardous material.

P[[D.sub.k]|x] = probability that a car in position k will be damaged or derail on a given train.

P[[R.sub.k]|[D.sub.k],x]= probability that a car damaged or derailed in position k will release hazardous material on a given train.

The probability of a release of hazardous material on a train with characteristics given by the vector of attributes (x) is given by the sum of the probability that one or more car carrying hazardous material will be damaged or derail, multiplied by the probability that a car damaged or derailed in position k will release hazardous material. The probability of that the car in position k will release hazardous material is given by:

P[[R.sub.k]|X] = P[[R.sub.k]|[D.sub.k],X]P[[D.sub.k]|x]

and the probability of having a given train releasing hazardous material is given by;

P[R|x] = [k=L.summation over (k=1)] P[[R.sub.k]|x]

The Federal Railroad Administration accident data base used for the estimations covers a period of nearly 10 years, and contains almost 100,000 observations (Federal Railroad Administration 1991). It is expected that the number of usable observations will greatly exceed the number of variables, and that the degrees of freedom of the regressions will be very large. If that is not the case, it might be necessary to group the cars and identify the car position as "cars 1 to 5", "cars 6 to 10", etc.

The probabilities needed to perform the analysis are computed as shown in the following section.

7.1 Estimation of P[[D.sub.k]|x]

Let [P.sub.k] denote a point estimate of the unconditional probability that car in position k will be damaged or derailed (P[[D.sub.k]]). It is obtained by taking the ratio of the number of cars in position k that were damaged or derailed annually, divided by the annual number of trains of length greater or equal to k. We therefore have:

P[[D.sub.k]] [approximately equal to] [P.sub.k]= [D.sub.k]/[N.sub.h], h = k, k+1, ... 200

and the logistic equation is:

Log[[P.sub.k]/(1-[P.sub.k])]=[a.sub.0]{[a.sub.1]+[a.sub.2]V+[a.sub.3] [V.sup.2]+[a.sub.4][T.sub.s]+[a.sub.s]L+ ...}+e

Where [a.sub.0[= 0 if L<k, otherwise [a.sub.0] = 1 and the expression in brackets is a linear or quadratic function of the variables thought to influence the probability P[[D.sub.k]. The parameters [a.sub.i] are estimated with the maximum likelihood technique using all non zero observations, to generate the following table:

Car

Position -- Parameters --

        [a.sub.1]      [a.sub.2]      [a.sub.3]      [a.sub.4]     ...

1       [a.sub.11]     [a.sub.12]     [a.sub.13]     [a.sub.14]    ...
2       [a.sub.21]     [a.sub.22]     [a.sub.23]     [a.sub.24]    ...
:       :              :              :              :
200     [a.sub.2001]   [a.sub.2002]   [a.sub.2003]   [a.sub.2004]  ...

The coefficients are then used to compute P[[D.sub.k]|x], the probability that car in position k will be damaged or derailed given the characteristics of the train given by the vector of attributes x (such as speed and length of the train, class and usage of the line, terrorist incident, and any other variables that might affect the probability that a car will be damaged or derail). The probability is given by:

P[[D.sub.k]|x)= 1/[1+exp{[a.sub.0]([a.sub.1]+[a.sub.2]V+ [a.sub.3][V.sup.2]+[a.sub.4][T.sub.s]+ ...)}]

7.2 Estimation of P([R.sub.k]|x)

In a major research effort for the NRC, Lawrence Livermore National Laboratories (1987) attempted to estimate the annual expected number of spent fuel casks involved in accidents in regular train service. Their estimate was 0.82, (1.7 x [10.sub.-6] accidents per car-mile times 735 miles per trip, times 652 shipments per year). It estimated that the fraction of these casks suffering a release would be 0.6% due to mechanical forces and less than 0.1% due to the thermal effects of a fire. The annual probability of a release due to either cause is 8.8 x [10.sup.-6]

Since there has been no radioactive release in any of the accidents involving radioactive material, using accident reports to estimate the probability of having a release would yield a probability of zero. That is clearly unsatisfactory because casks were involved in very few of the accidents, and these accidents do not represent the extreme conditions the casks could be subjected to in the most severe accident. There are several instances when a derailed or damaged car has released non-radioactive hazardous materials. If there are enough observations, the probability of having a damaged or derailed care release hazardous material can be computed in a manner similar to the estimation set forth in 7.1.

Two methods available to estimate P[[R.sub.k]|[D.sub.k],x] are the proxy and the inertia.

(1) Proxy approach:

Since the casks are designed to be more resilient than any of the cars currently used, cars resembling the cask cars can be used as a proxy for the cask cars. An upper bound for the probability that a car with hazardous materials in position k will release its contents is then given by P[[R.sub.k]|[D.sub.k],x], using only observations in the data set involving proxy cars damaged or derailed. If enough data for the proxy cars are available, that probability is estimated using another logit analysis:

[P.sub.j] = point estimate of P[[R.sub.k]|[D.sub.k]] = [R.sub.k]|[D.sub.k],

and the regression equation is:

Log[P/(1-[P.sub.j])]=[b.sub.0]([b.sub.1]+[b.sub.2]V+[b.sub.3] [V.sup.2]+[b.sub.4][T.sub.s]+[b.sub.5]L+ ...)+e

Where [b.sub.0] = 0 if L<k, otherwise [b.sub.0]= 1. If too few data are available, that probability can be approximated by the ratio of the number of cars of the given type that released their contents in an accident divided by the total number of cars of the given type that were damaged or derailed in the accident ([R.sub.x]/[D.sub.x]). That approximation implies that the probability of a car releasing the material is independent of the speed, position and other variables characterizing the train.

Like in the previous section, the parameters [b.sub.i] are estimated using the maximum likelihood technique using all non zero observations to generate a table of b parameters. The parameters are then used to compute the probability that car damaged or derailed in position k will release the material, given the train attributes given in the vector x. The probability P([R.sub.k]|[D.sub.k],x) is given by:

P[[R.sub.k]|[D.sub.k],x]=1/[1+exp([b.sub.0]([b.sub.1]+b [.sub.2]V+[b.sub.3][V.sup.2]+ ...)]

Under the normal assumptions of the logit distribution, the error term of the estimate for P[[R.sup.k]|[D.sub.k],x] is normally distributed, with mean zero and variance [v.sub.k] = [[[n.sub.k][P.sub.k](1-[P.sub.k])].sup.-1], where [n.sub.k] is the number of observations used in the regression, and [P.sub.k] denotes P[[R.sub.k]|[D.sub.k],x]. The inverse of the variance can be used as a measure of risk, and the risk associated with a given train is given by:

[l.sub.a] = [k=L.summation over.(k=1)] [v.sub.k]P[[R.sub.k]|[D.sub.k],x]P[[D.sub.k]|x].

(2) Inertia approach:

Several theories have been proposed to explain how the weight and length of the train influence the magnitude of the accident. Their common core is that the magnitude of the accident is positively related to the inertia of the cars behind the first derailed car. To test it, the weight of each car is needed. For lack of better data, we make the crude assumption that the weight of the train (T) is uniformly distributed among all cars. Hence, using the notation defined above, the inertia of the cars behind the first derailed car (in position j) can be approximated by the product of the total weight of those cars T(L-j)/L times their speed V. The theory is tested using the number of cars derailed (D) as a proxy for the accident magnitude. The regression equation in the logarithmic form is:

Log[D] = [a.sub.0] + [a.sub.1]Log[L-j] + [a.sub.2]Log[L] + [a.sub.3]Log[T]+[a.sub.4]Log[V] + e.

If all the regression coefficients are significant, the theory is verified and the worse case scenario can be used as an index of risk associated with a train of a given length:

[l.sub.b](L|x) = max{[D.sub.k]P[[D.sub.k]|x]},

where k = 1,2 ... L, and [D.sub.k] is obtained from the regression equation ([D.sub.k] is a function of the car position (k), and of the length (L) weight (T) and speed (V) of the train). The index of risk [l.sub.b] is then minimized over the n-dimensional surface (where n is the total number of variables used in the model) to identify the attributes of the train minimizing risk.

Note that even though the indices [l.sub.a] and [l.sub.b] will not provide a complete risk profile, either one will allow the ranking of all possible train combinations considered including dedicated and non dedicated trains. In particular, the model will determine the length and speed of the train, and identify the location of the cars that will minimize the risk index. Also note that the approach described above applies only to the accident-induced risk of transporting hazardous material. The other components of a risk profile (accident-free risk and yard switching accident risk) can be computed separately.

Incorporating the exogenous variables outlined above into the probability estimates as defined here by use of the multivariate logit model will promote a better understanding of the risks consequences of railroad accidents or incidents involving hazardous materials. The probabilities of this model are estimated using data without terrorist action. Two kinds of actions can be considered: 1) an action that leads to a derailment, in which case the data is relevant; but the probability of a derailment is higher than the logit estimate, and 2) an action that directly affects the operations of the train (hijacking, sabotage of the consist, detonations of cars) for which there is no data.

8. CONCLUSIONS

The proposed model presents a first step. The need to insure secure rail hazardous materials movement is imperative. To further this goal, the model could be turned around to estimate the probability that a train containing hazardous materials would be the target of a terrorist attack based on the risks associated with the route (e.g. different routes for different risk levels) and contents of each train. A database containing more precise information (e.g. the position and contents of hazardous materials cars in the consist) is an essential component. Some subjective estimate of the probability of a terrorist attack also needs to be incorporated.

In general, the risk measures relating to routing of rail hazardous materials that should be considered are: 1) terrorists' acts; 2) hazardous material release probabilities; 3) impact on population and environment in the case of release; 4) consequences to population from non-accident risks, 5) length of route; 6) track conditions; 7) rail terminals involved, and; 5) accident rates. Modeling the risks associated with such a model of hazardous materials movement on rail routes is a challenge. To refine the model, gather appropriate data, input the data, and make the model operational are even more formidable challenges.

A comprehensive risk routing analysis model should address all of the above factors. For the risk measures, the risk probabilities need to be estimated to delineate and initiate data for the routing risk analysis model. The model adopted should be versatile enough to include the effect of special precautionary operating measures such as alternative routing to avoid or lessen the probability of an incident or accident. The long-range goal would be to analyze where risks can be reduced by operating procedures such as reintroducing a secured caboose for all hazardous materials movements or alternative routing for different risk levels and the cost-effectiveness of such changes.

9. SUMMARY

The Hazardous Materials Transportation Uniform Act of 1990 emphasized the need to assess the risks and benefits associated with the transportation of hazardous materials by rail. Given the new dimension of terrorism, rail transportation of hazardous materials has become an even greater problem and major concern. This model has attempted to address such issues by identifying the applicability of relevant variables to rail-route risk analysis. This paper has proposed a model useful in making rail movement decisions involving hazardous materials. Distances, train size, and car location play key roles in the risks. Hopefully, this initial model will contribute to the refinement of the modeling of risk assessment of consequences. It should help provide railroad managers and governmental policy makers with an enhanced method of assessing the routing of hazardous materials rail shipments and a means of determining the most appropriate method of rail transportation. The model together with the relevant variables which were discussed will hopefully aid the DOT and other federal agencies in the safety of rail hazardous materials transportation as Congress mandated in the Amendment to the Hazardous Material Transportation Uniform Safety Act of 1990.

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H. Barry Spraggins, University of Nevada, Reno, Reno, Nevada, USA

John Ozment, University of Arkansas, Fayetteville, Arkansas, USA

Phillip Fanchon, Cal Poly State University, San Luis Obispo, California, USA

Dr. H. Barry Spraggins earned his Ph.D. at the University of Minnesota in 1976. Currently he is a professor of managerial sciences at the University of Nevada, Reno.

Dr. John Ozment earned his Ph.D. at the University of Minnesota in 1984. Currently he is the Oren Harris Chair in Transportation at the Sam M. Walton College of Business Administration at the University of Arkansas.

Dr. Phillip Fanchon earned his Ph.D. in economics at UCSB in 1982. Currently he is Professor of Economics at Cal Poly State University in San Luis Obispo.