the concept of exposure

Accid. Anal. & Pre~'. Vol. 5, pp. 95-II0. Pergamon Press 1973. Printed in Great Britain.

T H E C O N C E P T O F E X P O S U R E

ROGER CHAPMAN Road Safety and Traffic Authority, 801 Glenferrie Road, Hawthorn, Victoria 3122, Australia

(Received 21 August 1972)

I N T R O D U C T I O N

FOR AT LEAST 30 years scientists and engineers carrying out research into road safety have attempted to take account of the amount of exposure to accidents which was present in their studies. It is instructive for anyone contemplating undertaking similar research to know how earlier research workers defined and measured the exposure relevant to their enquiry and what success they had with its use.

In this paper the concept of exposure to road accidents is developed, from its general to its particular use, with references to the work of many road safety investigators. (Alterna- tively the paper can be regarded as a fairly complete review of exposure literature.) The subject is presented in the following order: Concept of Exposure; Exposure for Large Areas, Groups, or Times; Induced Exposure Measures; Exposure as Opportunities; Specific Exposure at Locations, to Persons, or in Time. An alphabetical list of references concludes the paper.

THE CONCEPT OF EXPOSURE

Underlying most statistical analyses of accident frequencies is the notion of exposure. It has long been recognized that it is important to consider exposure, to define what is meant by the term, and to try to measure it. The term has come to have a number of slightly different meanings in accident research, the meaning adopted for a particular analysis often depending on the aim and data of that analysis. It is important that the measure of exposure used be the one most relevant, it if is possible to obtain it, and that it be specified to enable readers and other researchers to compare results and methods. The concept of exposure is in fact a general one; it is a concept by which the researcher tries to take account of the amount of opportunity for accidents which the driver or the traffic system experiences.

It is convenient, instructive, and almost essential to consider to what extent people are exposed to situations which may result in an accident. Harry de Silva (1942) talks of "exposure, or the number and relative danger of the hazards he (the driver) encounters". He speaks of a general exposure to different hazards in terms of where, when, and how a person drives. Later, Skillman (1965) suggested a method by which drivers may reduce the number of situations in which they find themselves which may have resulted in an accident. This method involves a driver counting the number of times he becomes vulnerable to a collision, and trying to reduce this number by what has become popularly known as "defensive driving". Skillman's vulnerabilities are a measure of the exposure of de Silva, since they are dependent on when and where the driving occurs, and in what manner it is performed. Each is a measure of the risk which a particular driver undergoes, In a recent book on accident- proneness (Shaw and Sichel, 1971) the authors quote at length from de Silva, pointing out the relevance of his ideas today.

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96 ROGER CHAPMAN

In discussing radiation risks Sowby (1965) refers to other hazardous occupations in which humans take part. With respect to road traffic he comments that transportation risks are usually compared on the basis of deaths per passenger mile, and remarks that this is unsatisfactory for a comparison of transportation with other risks in which the distance factor is absent. He therefore compares many sorts of risk using risk per hr of exposure in a population of one thousand millions, that is to say, the number of deaths per hr per thousand million persons undertaking the activity in question.

Stewart (1960) poses the question "driving exposure--what is it and how is it measured ?" He suggests various meanings for the term, and then analyses data to find a measure. He is unable to show that annual mileage per person is significantly related to accident occurrence or traffic citations; no mileage data were given so it has not been possible to find evidence why this might be so. Stewart refers to an earlier paper by Boek (1956), who did find total mileage and accidents to be associated. It is not uncommon in accident research to read reports of conflicting evidence; each report could be correct for its own data.

A recent report from the United States (Operations Research, Inc., 1971)pays strong attention to exposure, viewing it as "a systematic process affecting the crash system that is essentially a function of the continual interaction of driving behavior with the ever- changing environment". The authors of this report regard exposure as "obviously something more than the gross vehicle mileage for all drivers under all driving conditions, the usual proxy measure". The elements of exposure they consider should be included are; (i) characteristics of drivers and vehicles, (ii) characteristics of the road system and intensity of system use, (iii) environmental conditions (weather, day/night etc).

Many authors believe that exposure holds the key to the interpretation of accident situations (for example Blunden, 1972). Blunden suggests that there has been too much concen- tration of effort in the past on the liability factor, and strongly urges that more emphasis be placed on the study of exposure.

E X P O S U R E F O R L A R G E A R E A S , G R O U P S , O R T I M E S

For national road safety publicity or for the purposes of international comparisons it has been regarded as adequate to compare the number of injury accidents (or number of casualties) against some gross estimate of the amount of road travel in a country. For example, the most commonly used figure against which accident numbers are compared is that of vehicle- mileage (Smeed and Bennett, 1949 ; see also Garwood, 1962). This endeavours to take account of how much traffic uses the road network and how far this traffic travels in the network. It is a useful measure, giving a guide as to how efficiently, interms of a measure of safety, the traffic system is operating, It does not, however, enable a researcher to use a probability approach-- to do this he must adopt different measures of exposure, as wilI be described in a following section.

Smeed (1955) uses the rate of personal injury accidents per million motor vehicle miles for some analyses, and finds that in general this rate is lower on rural roads than on more built-up roads. Reasons may be thought of to explain this, such as that in built-up areas there are more pedestrians, more intersections and hence more cross and more turning traffic. These explanations introduce a measure of exposure in terms of opportunities, which is to some extent missing from the rate Smeed uses. Even so, in analyses such as he tackled, in which it would be difficult to obtain detailed exposures, an indication of the relationship between accidents and traffic is found which is not altogether misleading.

One aspect of road accidents which has caught the eye of researchers and the public is

The concept of exposure 97

that of young or inexperienced drivers. In this aspect exposure (and the lack of knowledge of it) has played an important part. Klein (1966) says " I t is quite conceivable that once techniques are developed for the accurate measurements of exposure the teen-aged driver will be found to have no more accidents than any other drivers. I f this occurs the 'problem of the teen-age driver' will disappear or will be essentially the 'problem of the driver ' ." Little research has found that younger drivers have only their share of accidents--many, even those studies in which care has been taken to allow for differing exposures, find young persons have more accidents relative to their elders or more experienced drivers. In a German study Munsch (1966) finds evidence to suggest that at a given amount of experience, younger drivers may be safer than older ones. This could reflect cultural differences. Foldvary (1969 a,b) (using his own data from postal questionnaires) finds that the number of accidents per hundred-million miles of performance decreases as the age of the driver increases. The shape of the curve can be regarded as a learning curve, in which accidents are a measure of errors made during learning. Lock (1966), Raymond (1967), and many others find similar results. The number of licensed drivers in each age or experience group, the average distance travelled by persons in those groups, and at what times of the day their driving is clone will affect the accident experience of a group of motorists. By stratifying or otherwise attempting to allow for such factors any remaining differences between group accident experience may be attributed to inherent characteristics of the groups. (see for example Johnson, 1972).

National statistics for the United States make use of the figure of accidents per million vehicle miles--the vehicle mileage is estimated from annual gasoline consumption. Kroj (1969) finds for the German Federal Republic some correlations between traffic mileage (from fuel consumption) and accidents, mainly to private cars, for the period 1960-1965. A remarkable set of correlation coefficients is obtained between fuel consumption figures and accidents: 0.38 on 72 pairs of raw data, --0"26 between accidents and 12 month moving fuel averages, and 0-87 between monthly percentages of fuel and accidents. The conclusion which is most reasonably drawn is that although monthly correlations are fair (that is the cyclicity of monthly fuel consumption is followed by the accident frequencies) the general trend (that is a smoothed correlation) is not.

By regressing accidents onto the independent variable of estimated daily traffic, Erlander Gustavsson and Larusson (1969) find that a large part of the day by day variation in the daily number of road accidents in rural areas may be explained by the amount of traffic. The traffic figures used were estimates of the number of millions of vehicle-kin travelled per day in Sweden, for a 4 month period in the summer of 1962. An extension of results of this type is expressed by Baker (1971): "The absolute number of fatalities and injuries has steadily increased, but so have population and amount of travel. As the population increases, the number of travelers and vehicle-miles of travel will increase for the same level of mobility for individuals. As a result, the degree of 'exposure' to accidents is increased, and a greater number of accidents would be expected if no improvement were made in the highway transport system."

In a report which led to a method of economic assessment of road improvements on Spanish highways, Calleja (1965) uses an index of danger equivalent to the number of accidents per hundred-million vehicle-kin per year. Of 11,000 km of open road excluding settle- ments of more than 5000 population only 400 km of road had more than 200 accidents per hundred-million vehicle-kin in a year. These road sections tended to be on the outskirts of the larger cities of Madrid, Seville and Barcelona. Calleja uses a damage-from-accident cost in pesetas per vehicle-km for a section of road with a high index of danger to show how much

A.A.P. 5/2--B

98 RO~ER CHAPMAN

would be saved if that index could be reduced to the average. This allows him to determine what level of expenditure could be permitted on those sections, assuming that the effectiveness of whatever safety measures were applied was the same.

A comparison of the time trend of the ratio motor deaths/vehicle in four countries shows a tendency for this ratio to reach a limit (Chapman 1968a).

The results one obtains in a study of accident rates may depend on the particular rates used. Greenberg (1971) compares five techniques and concludes that some models or rates were superior in understanding the data. In comparative studies at intersections Chapman (1971b) shows that for priority treatment four different ranking procedures give much the same selection, but that in correlating an accident rate with total traffic flow the conclusions are dependent on which rate is used.

The reports reviewed here cover a wide range. Some use a measure of travel to estimate exposure to accidents; others try to determine to what extent the numbers of accidents are related to the amount of traffic. The latter poses the following problem. If the number of accidents is found to be closely related to travel, the amount of traffic can be regarded as a measure of exposure. If no relation is found, does this invalidate the use of traffic as such a measure? The answer to this is negative; the variation which has not been explained by travel may be due to something which has not been measured. This problem is faulty experi- mental design, with no control of variables other than those under study.

INDUCED EXPOSURE MEASURES

It is not always possible to obtain a suitable estimate of the exposure experienced by the drivers or road sites. Since it is nearly always desirable to allow for differences in exposure it is useful to have a method which will permit this. Thorpe (1964) proposed a method which does not require directly measured exposure (as, for example by traffic flows) but which instead induces exposure from the accident data, provided that these data are of a certain type. Thorpe's method is modified by Cart (1969) and together they provides a useful analytical method for certain studies, especially those of a comparative nature. Their methods lead to a relative assessment of the accident experiences of various categories of drivers or vehicles, relative that is, to other drivers or vehicle types.

Thorpe makes five assumptions about the manner in which single and multiple vehicle collisions occur. Based on these he analyses data, essentially using the relative frequency of single vehicle collisions as a measure of exposure. Carr assumes much the same things as Thorpe, with one exception. In Carr's data the driver responsible for any collision was given, whereas Thorpe had to assume that responsibilities were similar between two vehicle and single vehicle accidents.

Both these methods provide a useful technique for comparing the relative accident risk of different groups of drivers, vehicles or other characteristics. If accident data can be split into two groups, responsible and not-responsible, then Carr's method is appropriate and easier to use. If not, but involvements in single and multi-vehicle accidents are available, then Thorpe's method is applicable.

Research on Road Safety (1963).

This volume contains a table (Table 4.3) with the ratio (Involved in all accidents)/(Invol- red in stationary accidents) for a number of age groups ; this has similarities with Thorpe's method. In Table 4.1 of the same book are the numbers of drivers blamed and not blamed in each age group, together with a relative induced risk ratio. Cart 's method is closely related


to this way of analysing data. In all cases the shape of the accident risk ratio vs age curves are similar.

Haight (1970) presents an idea, based on Thorpe's , for making "exposure correcting" transformations which are formulated in mathematical terms. He gives a hypothetical example, before discussing ways of ensuring the validity of the axioms or using data in such a form that the axioms could be relaxed.

Koornstra (1969 a,b) gives an even more general approach using multivariate analysis of categorical data, which should yield a powerful tool for this type of investigation.

EXPOSURE AS OPPORTUNITY

The purpose of studying traffic accidents and the way numbers of accidents relate to exposure is at least 2-fold. One purpose is to study the phenomenon and to find general or particular truths about i t - -another is to search for ways of helping to reduce the number of accidents and injuries. If it is not possible to reduce the absolute number of accidents it might at least be possible to reduce the ratio of the number of accidents to the number of opportunities. One immediate task of accident research could be to predict what would be expected if nothing in the system was changed. Then one could try to find out which factors could be changed to effect a decrease in accident frequency and to determine their cost and effectiveness.

For some purposes, analysis of accident data may not require knowledge of exposure. It seems likely, however, that more will be gained by having such knowledge. Sichel (in Shaw and Sichel, 1971) states that the researcher should have at his disposal, for each individual person the length of exposure to risk, measured in exposure units such as actual driving days or mileage.

It is possible to consider the traffic system as having opportunities for accidents to occur. These opportunities are occasions when cars cross each other's path, when they are following one another, or even when a vehicle is travelling by itself on a winding road. The number of opportunities could be measured for small locations or small time periods, but it is usually difficult to measure it for large areas or times. This difficulty is due to the size of the task of observing all parts of the system at all times. Sampling is necessary in small studies of particular locations or questions to selected drivers, and estimates of exposure must be made. For many purposes it is not necessary to know the absolute number of opportunities (from which one could determine the actual probability of an accident ensuing from an opportunity), but only an estimate of the ratio of accidents per opportunity. Most accident studies are of a comparative nature, for which ratios would suffice.

Exposure to traffic accidents in an area could be regarded in two ways, either as the exposure of an individual driver or the exposure to accidents of certain types at a given location in a given time. The summations of each exposure should lead to the same total possible number of opportunities. Either approach could be used; for road safety studies it is the latter approach which is most common. A number of accidents occur in a certain time and the researcher wishes to relate this number to the possible number of accidents, which is called exposure.

In the past five years several research workers (Chapman, 1967; Garrett and Tharp, 1969; Cameron, 1970; Blunden, 1972) have used various forms of the following definitibns:

(1) Exposure: the exposure is the number of opportunities for accidents of a certain type in a given time in a given area (i.e. it is the possible number of accidents of that type which could occur in that time in that area)

10o ROGER CHAPMAN

(2) Propensity: the propensity is the conditional probability that an accident occurs given the opportunity for one.

The two definitions are connected by a simple equation:the number of accidents is equal to the exposure multiplied by the propensity. This equation really defines a conditional probability, the propensity. When measures of exposure are given, the propensity becomes the accident rate, in one of its many forms.

Simple mathematical expressions and approximations for measures of exposure, possible distributions of propensity, and the effect of the propensity of exposure and other items such as flow, weather, darkness, and road design are treated by Chapman (1971a).

Some road safety workers try to reduce the frequency of accidents by reducing exposure or the propensity to accidents. Other workers try to reduce the number and severity of injuries. I f sufficient studies could be made it might be possible to determine values of the propensity under conditions of wet and dry, day and night, drivers with and without alcohoI, and to determine the likely benefits of non-skid surfaces, lighting, and abstention. Much has already been done in this area. (See, for example, Research on Road Safeo', 1963).

EXPOSURE MEASURES FOR SPECIFIC LOCATIONS, PERSONS, OR TIMES

Perhaps reflecting the practical nature of road safety research, most work on exposure has dealt with particular real situations, rather than with developing general theories for exposure. While coarse measures or broad descriptions of exposure are suitable for some purposes, including that of introducing the concept, the research worker often needs to know specifically about the exposure of the subject matter of his study. This could be particular persons, in which case he would like to know when, ~s here, how much, and under what conditions these persons drive. If he is studying a particular location he might wish to know which type of conflict situations between vehicles occur most often. For instances such as these it may be possible to define, though not always to measure, a suitable exposure index or group of indices.

Consider a road network: lengths of road and the intersections and junctions where the roads cross or meet. There are two ways of viewing accident exposure in the network, which could be approximated to yield a composite measure of exposure:

(i) the exposure to accidents by a particular person as he drives in the network and (ii) the exposure to accidents at a particular site as drivers pass it.

These are related if the sums are taken over a time period : the sum of the exposure in- curred by each driver should be equal to the sum of the exposure at each site. These sums can be called the exposure over the whole road network.

Types of accident

Several researchers try to approach traffic accident analysis in this manner. One of the first was Belmont (1953) who attempts to be rigorous in his analyses, and compares hypothetical models with accident data. He refers to an ENO (1947)publication which expresses a standard exposure theory of accidents as one in which single vehicle accidents are expected to vary directly with traffic flow, and multi-vehicle accidents are expected to vary with the square of the flow. Smeed (1955) reports that this might be expected from first principles, but observes that his data does not vary as expected. A later study (Chapman, 1971a) con- firms this observation and postulates that driver behaviour might change with the amount of traffic, pointing to the need for a more complex model.


Belmont, too, rejects the simple vehicle model because of poor agreement with data, and adds a further explanatory variable, that of speed. He achieves better results with this addition, although he relies on qualitative comments to do so.

Battey (1959) divides accidents into four groups, pedestrian vs vehicle, vehicle vs vehicle, non-collisions and others. After some discussion he says that an exposure measure is obtained by squaring the vehicle mileage. I f this were done the safety of the road system year by year would show a much greater improvement than it has done using the more popular measure of vehicle mileage alone. In an attempt to obtain a hazard index formula for use at railroad crossings Bezkorovainy (1967) relates accidents and vehicle volumes, obtaining an empirical relationship which leads him to use simply vehicle volumes as a measure of exposure.

Crowther and Shumate (1964) also relate classes of accidents and cIasses of exposures, but on rural highways: "To characterise the traffic states a series of variables, here referred to as exposures, are defined. These exposures are chosen in such a way that it is possible to classify each accident as arising from one specific kind of exposure. Also, by taking a sample of traffic, it is possible to determine the rates at which the exposures are generated . . . . Each accident was assigned to one of six classifications depending on the incident or traffic state from which it evolved, as follows: (a) passing (b) rear-end (c) meeting (d) crossing, entering, or leaving at junctions (e) single vehicle (f) others." In the analysis types (e) and (f) are omitted because of small numbers. The regression equations contain the dependent variable of accidents per mile per time period (of appropriate type (a), (b), (c), (d)) with independent variables reflecting exposure rates. These exposure rates are generally the number a specified item occurs per time or per mile-time, from a list of items such as volumes, headways, passings, and meetings. The independent variables are not all independent of each other, which the authors realise. The parameters which explain most of the variation in the dependent variable are traffic volume and headways, with number of passings and meetings per mile-sec of secondary importance. Instead of simply relating accidents of a certain type with the exposure category most likely to lead to that type, these authors allow all exposure measures to be used in the regression equations, but only those contributing significantly are retained.

Another way of typing accidents which is appropriate to exposure is that of classifying an accident according to the movements of the vehicle or vehicles. A simple taxonomy is: only one vehicle (single vehicle ~ SV); vehicles in the same direction (rear-end = RE); vehicles from opposite directions (head-on = HO); vehicles from different, not opposing directions (e.g. intersections). Accidents falling into the group SV normally involve skidding, overturning, or hitting a fixed object. They sometimes include accidents in which a parked car was hit, though the number of possible collisions of this type can be derived in a manner similar to that for intersection collisions. Accidents between vehicles and pedestrians can also be considered to be of the last type (see Chapman, 1967).

Head-on collisions could be viewed as single vehicle accidents in which the driver was unfortunate to hit an opposing vehicle. This assumption is not in keeping with the definition of exposure, yet is almost tacitly made by researchers who use accidents per vehicle mile as their rate. Also implicit in this is the assumptions of one responsible driver per accident, an assumption not often supported by accident reports. The number of vehicles per accident and the proportion of accidents which involve only one vehicle as functions of flow have been considered by Chapman (1969).

Hall (1969) comments that ideally the investigator desires populations which have the

102 ROGER CHAPMAN

same "exposure to risk", but that this concept is not yet well-defined or understood in accident research. It is true that exposure has not been given a single definition applicable to all analysis--part of its value lies in the broadness of the concept so that researchers can take account of it in a way most appropriate to their analysis.

Accident research is now attracting academic attention, and is no longer being carried out solely with results in mind. Students are becoming interested in basic knowledge. A thesis by Cameron (1969), of which the practical results and data analyses have been published (I970), investigates the concept and analysis of accident risks. Cameron approaches the subject as a statistician; as a result his analytical findings are easy to relate to data, where these are obtainable. He adopts the idea of potential accident events (as in Chapman, [967). He defines an accident event, A, and a potential accident event, P. (A can occur only if P has.) An individual is considered to be associated in some way with a sequence of E potential accident events (P~, P2 .... PE). The parameter E is the number of potential accident events with which the individual is associated, and is called the exposure. The author points out that his method assumes complete knowledge of the apportionment of exposure over the attributes under consideration. In practice this is seldom available and it is necessary to estimate the apportionment. Cameron does this, and applies his method to an analysis of pedestrian accident data.

Head-on collisions

A significant proport ion of the variation in the number of head-on collisions per section of road can be explained by taking account of exposure* in the form ABLt(1/v~ + 1leo) where A, B are the flows in each direction, L length of section, t length of time, and va, co the respective mean speeds in each direction. (Chapman, 1967).

The ratio of accidents per exposure for each road section can be regarded as the conditional probability that an accident occurs given the opportunity to do so. The average figure obtained for this probability was of the order of 4 × 10 -7, indicating how small a risk factor researchers and road engineers are dealing with. The variation which this probability shows between sections could be due to chance, it or could be due to differences in risk between sections, or both. Data for other years would be required for the same sections to determine which of these possibilities in the case. For some New Zealand data in each of four years it seems that between sites variation is much greater than within sites. This suggests that it is a difference in risk which causes the variation as well as chance.

Very little analytical work on head-on collisions of the type attempted here has been made. Belmont (1953) gives data for many road sections in the form of number of accidents per 108 vehicle-miles by type of accident against flow. The types are multi-car, rear-end, head-on, and single car. Some theoretical analyses of the probabilities of occurrence of various types are compared with his data.

His theory for head-on collisions may be summarized : the number of head-on collisions per vehicle-mile increases directly with traffic volume and with average speed. The chance of collision between any pair of opposing vehicles is approximately proportional to the square of their approach speeds. The latter result was found by studying three assumptions, and selec- ting the one which gave results qualitatively in accordance with the data. The assumptions he rejected were (i) that the probabili ty of a collision between any pair of opposing vehicles is

* Editor's Note: Koornstra points out that this formula is equivalent to his exposure/proneness model, with speed as the proneness index and f low-divided-by-speed as exposure.


independent of their speeds, which leads to the number of collisions per vehicle-mile being proportional to the inverse of speed and (ii) that the probability of collision is directly proportional to the approach speed, which leads to the number of collisions per vehicle-mile being independent of speed.

Rear-end collisions

Malo, Mika and Waldbridge (1960) produce a graph which shows an empirical relationship between "modal spacing" and each of flow and annual number of rear-end collisions on a U.S.A. urban expressway. The graph is represented by the equations:

N = 74.6-40.4 S S -= 1.88-7.42 × 10-Sq

where N = number of rear-end collisions per year S ----- most frequently occurring time separation between vehicles in seconds (modal

spacing) q = flow in three lanes per hr

From these two equations one obtains

N = 0.003q--1.42

Thus as flow increases and modal time-spacing decreases the expected average of rear-end collisions increases.

This analysis points to a linear relationship between headways and rear-end accident frequencies, but it may be useful only for high flows (which were considered). An analytical relationship derived from a model based upon the mechanics of rear-end collisions would possibly be more satisfactory.

A report from the Road Research Laboratory (Harms, 1968) contains data on accidents and flows on the M4 motorway by time of day, and information as to whether it was dark or wet at the time. Harms found that the number of bumper-bumper collisions per million vehicle miles is higher at night than during the day, and that the relationship between that number and hourly flow is a U-shaped one. Since the road length in his study was fixed, Harms was essentially using number of vehicles as his measure of exposure, which is the simplest measure appropriate to rear-end collisions. However, the manner in which the data were presented makes it difficult to check the validity of Harms ' conclusions.

At flows above which the speed of traffic decreases due to increased vehicular interaction, it is quite likely that a change in driver behaviour results in fewer rear-end collisions than would have been expected at those flows. In such a case the simple model is inadequate to cover the range of traffic conditions, and a more refined one, incorporating some aspects of driver behaviour, may give a better description of the phenomenon, but will be more difficult to obtain.

Intersection collisions

This has been the subject of most study by researchers, probably because many accidents occur at intersections, and perhaps also because it is an easier situation to analyse than most of the other types of collision.

Accidents and traffic at intersections have been studied in two ways. One way defines a function of the flows using the intersection as the exposure, and compares accident occurrences with this calculated exposure. (The defined measure of risk may merely be used to

104 ROGER CHAPMAN

compare different intersection layouts.) The other compares empirically accidents and flows for many locations, assuming that the risk at each location is the same, to find a function of the flows which compares best with the observed accident occurrences.

These two methods plus direct observation have led to four measures of exposure being suggested for collisions at intersections:

(a) the total traffic using an intersection (i.e. sum of all entering flo~s) (b) the product of cross flows at conflict points (c) the square root of the product of the cross flows (d) the observed number of conflicts at a location.

One of the themes at the Tenth International Study Week in Tramc and Safety Engineer- ing (Rotterdam, 1970) was Accident Risks and Capacity of Single-Level Intersections. The general report by Duff (1970) contains a discussion of the different ratios (accidents/some function of flows) used by contributory authors, but does not venture to recommend any particular one.

E.,:posure measure--sum of entering flows

Arguments against using mileage as a variable in measures of exposures at intersections are due to Mathewson and Brenner (1957) Breuning and Bone (1959). AII researchers agree that the amount of traffic and the paths it takes are more meaningful than distance at intersections. Grossman (1954) calculates the number of conflict zones in an intersection, adds together the flows which pass each zone, and sums over all zones; this sum is his measure of exposure. He uses this measure to compare different intersection layouts. Confict zones are studied in greater detail by Peleg (1964) who calculates the number of zones for the general case of an intersection with n approach roads. He continues his anaIysis (Peleg I967) and adopts an exposure measure similar to Grossman's. The use of conflict zones has been suggested earlier by Feuchtinger (1949), and developed by Rappaport (1957)--both papers are discussed by Schaechterle et al. (1970).

Raft (1953), and Thorson (1967) both relate accidents at intersections to the sum of the entering flows. McDonald (1953) uses accidents and minor crossroad traffic. Each finds that the number of accidents per vehicle decreases as the number of vehicles increases, but in all cases this increase in traffic is obtained by observing many locations. Those locations with higher flows may have had better design than those with lower flows, so none of these studies can claim to have shown conclusively the effect of flow on the ratio of accidents per vehicle. For uncontrolled intersections there does not seem to be a strong case for the use of the sum of entering traffic as a measure of exposure. McDonald and Thorson find that accident risks do not vary much between heavily trafficked intersections, even though the flows at them varied widely. Yet Babkov et al. (1970), Smith (1970), and Schaechterle et al. (1970) all compare the number of accidents at intersections with an estimate of the total vehicle flow.

Exposure measure--produ ct of conflicting flows

A measure which relates to the number of times vehicles conflict at an intersection is in keeping with the earlier definition of exposure. Such a measure takes into account the number of times vehicles from different directions wish to occupy the same area of road space simul- taneously.

Breuning and Bone (1959) derive a measure which is proportional to the product of the fows at any conflict point. Surti (1965) uses this measure to compare various intersections

The concept of exposure I05

and merging ramp layouts. For 4 intersections Surti (1969) relates accidents to calculated exposure measures and finds a high correlation. Underwood (1966)compares accidents with sums of flows and with products of flows, and advocates the latter. Chapman (1967) and Bennett and Blackmore (1970) argue for using the product of flows as an exposure measure, but the square root of the product of the flows may be a better predictor of accident occurrence.

Square root of the product of flows

McDonald (1953) reports a study of 1811 accidents at 150 divided highway (dual carriageway) intersections. He obtains the relation A = 0-000783 va°'~ssvc °633 between the number of accidents per year, A, and the average daily traffic entering from the divided highway, t'a, and the crossroad traffic, vc. Tanner (1953), in a study of 390 accidents at 232 rural 3-way junctions in Great Britain, obtains the relationships

AL = 0"0075 umO'SSUcO'36 and

A R ~-- 0"0045 l)mO'621)RO'56

where v,, is the average daily (16 hr) traffic on the main road in both directions, and the suffixes L and R refer to traffic and accidents on the left-hand and right-hand sides of the junction respectively. (Traffic moves on the left in Great Britain.)

Both McDonald and Tanner conclude that there would be fewer accidents if the number of access points in main roads was restricted. Little further work of this nature has been found until 1964, when the subject of accidents at intersections was one of the topics discussed at the Seventh International Study Week in Traffic Engineering, held in London.

Several papers (Summerfield and Bennett, 1964; Bennett, 1966a, b, 1969) discuss and confirm the relation found by Tanner (1953), but offer little that is new to the general subject of accident risks. Bennett (1966a)investigates the influence of islands in the main road on turning accidents from the main road, but analysis of further data (1966b) fails to confirm the preliminary findings.

Colgate and Tanner (1967) pursue the early work of Tanner (1953) confirming and extend- ing the general form of the previous findings. The authors study the effect of different junction layouts on the ratio of the number of accidents to the square root of the product of the flows.

Exposures at traffic lights

Because of the s top-go nature of the operation of traffic at signalized intersections the measures of exposure devised for uncontrolled locations are not directly applicable. Never- theless it is possible to obtain useful results empirically, as for example in the work of Webb (1955). Webb provides graphs (for urban, semi-urban, and rural sites) showing the average expected numbers of accidents per year according to the average daily main road and minor road traffic.

Pfundt (1964) assumes that traffic flows do not change much within a few years (and hence that exposure is constant) and shows from a before-and-after study of the installation of traffic signals that such an installation may reduce the right-angled collisions but increases rear-end collisions. An investigation of accident rates at signalized intersections by Thorpe (1968) relates the number of accidents to the square root of the product of entering traffic,

t06 ROGER CIta.P MAN

without justifying the use of such a measure for signalized intersections. In the discussion to Thorpe's paper, A. J. H. Clayton states that potential conflicts are proportional to the product of the flows, but experience shows that collisions are more nearly proportional to the traffic. At the Fifth Australian Road Research Board Conference Andreassend (1970) presented additional data, but was strongly criticised for not including before-and-after traffic movements, and for neglecting to note accident changes in neighbouring streets as a result of diverted traffic.

Exposure measure-counting conflicts

Perkins and Harris (1968) adopt a new method of measuring conflicts at intersections. They observe vehicles' brake lights and weaving manoeuvres. The number of these events was called the "number of conflicts". Without waiting for accidents to happen these researchers found that the effect of installing traffic signals was to reduce right-angled conflicts and to increase rear-end conflicts, a result which agrees with Pfundt (1964). Perkins and Harris's method is used in a simplified form by Chapman (1967).

The technique of Perkins and Harris was found to be flexible enough to be applied to both rural and urban intersections. Campbell and King (1970) are of the opinion that the traffic conflicts technique does detect accident potential and that it appears to be a good systematic method for studying and evaluating the accident potential of an intersection prior to development of an accident history.

A rural study by the Road Research Laboratory (Spicer 1971) gives more specific findings, namely that simple conflicts, defined as situations involving one or more vehicles taking evasive action, do not correlate well with reported injury accidents, but serious conflicts, defined as situations involving a vehicle in at least a sudden rapid deceleration or lane change to avoid collision, correlate well with reported injury accidents both in location and time of day.

The incidence of debris from vehicle collisions has been compared by Faulkner (1968) with the number of reported accidents. "The evidence sho~ved that the debris accident rates were about 10 times the reported injury accident rates, and that a fair prediction of injury accident rates could be made after observing accident debris for a few months. Several of the accidents reported to the Police during the debris survey period did not leave debris, e.g. a serious injury accident involving a cyclist".

A comparison of some exposure measures using analytica[ and empirical methods

In a comparative study of exposure measures at intersections Chapman (1971b) finds:

(i) that the accident rate at cross roads is higher than at T- or Y-junctions, twice so in urban areas, 5 times so in rural areas, irrespective of which rate is used: number of accidents per sum of, per product of, or per square root of product of entering flows and

(ii) that at intersections and junctions the rates "accident per sum of entering flows" and "accident per square root of product of entering flows" have little correlation with total traffic using the intersection, whereas the rate of accidents per product of entering flows tends to decrease as flow increases--all of which is not inconsistent with analytical expectations of the respective behaviour of these rates.

Before deciding to recommend remedial treatment at any location an engineer would take into account the costs involved, and the likely effectiveness of the accident reducing meassures. If a given measure reduces the accident rate by half for the same cost at any location


then he should deal with those locations with the highest numbers of accidents per year, irrespective of their rates. It is possible, however, that a location which has a high number of accidents per year yet a low accident/exposure ratio will require safety measures costing more than would be necessary at some other locations, to obtain similar saving in accidents (see Jorgensen, 1966; Jorgensen and Laughland, 1967; Hakkert , 1969; Chapman, 1971b).

Research into the safety of u rban road junct ions is the subject of a special report by an OECD Road Research Group (OECD, 1971). This group was formed to "assess the effectiveness of road safety measures presently used and to evaluate current techniques and methods of research". A useful chapter is devoted to methods used to assess safety, in which the conflict concept is debated, and a bibl iography of 78 items is appended. The conclusions of the group are in two pa r t s - - the first contains recommendat ions for immediate action based on existing knowledge (e.g. reduce and define access-points to abut t ing land), the second includes topics which are new or less well known but which deserve the at tent ion of governments and authorit ies (e.g. great caut ion must be used in interpreting traffic accident statistics since the level of accident report ing is highly variable.)

Acknowledgement--The work upon which this paper is based was completed while the author was at the Research Group in Traffic Studies, London. Jim Youngman (N.Z. Ministry of Transport) made helpful comments at the draft stage.

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BEZKOROVAINV, G. (1967) Optimum hazard index formula for railroad crossing protection. Traff] Engng 38 (3), 14-21.

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613. CA.~,n'BELL, R. E. and KL','G, L. E. (1970) Rural intersection investigation for the purpose of evaluating the

General Motors Traffic-Conflicts technique. H R B Spec. Rep. 107, 60--69. CARR, B. R. (1969) A statistical analysis of rural Ontario traffic accidents using induced exposure data.

Accid. Anal. & Prey. 1 (4), 343-357. CHAPMAN, R. A. (1967) Traffic collision exposure. New Zealand Roading Syrup. 184-198.

108 ROGER CHAPMAN

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Inst. o f Traffic Engrs (USA) 149-160.

Abstract--In this paper the concept of exposure to road accidents is developed, from its general to its particular use, with references to the work of many road safety investigators; the paper can be regarded as a fairly complete review of exposure literature. The subject is presented in the following order: Concept of Exposure; Exposure for Large Areas, Groups, or Times; Induced Exposure Measures; Exposure as Opportunities; Specific Exposure at Locations, to Persons, or in Time.

R~sumd--Dans ce mdmoire on d6veloppe l'idee g6nerale de l'exposition aux accidents de la route, des son usage g6n6ral 5. son usage particulier, avec rdfdrence aux travaux des nombreux investigateurs de la sdcurit,~ des routes; le mdmoire peut ~?tre consid&d cornme une rdvision assez complete de la tittdrature de l'exposition. Le sujet est present6 dans l'ordre suivant: L'idde gdndrale de l'Exposition; l'Exposition pour les Grandes Etendues, les Groupes ou les Temps; les Mesures prises dans les Expositions Provoquees; l'Exposition comme Opportunit6; les Expositions Sp6cifiques aux Locations, Personnes ou dans le Temps.

110 ROGER CHAP~4AN

Zusammenfassung--In diesem Bericht wird der Be~iff des Aussetzens zu StraBenunf~dien yon allgemeiner his spezieller Anwendung mit Bezugnahme auf die Arbeit vieler Untersucher for Stral3ensicherheit entwickelt. Der Bericht kann als ein ziemlich umfassender l~'berblick Ober die Literatur for Aussetzung angesehen werden. Das Thema wird in folgender Reihenfolge dargestellt: Begriff der Aussetzung, Aussetzung bei ~ossen Gebieten, Gruppen und Zeiten, hervorgerufene Mal3nahmen gegen Aussetzung, Aussetzung als Gelegenheiten, spezielle Aussetzung nach Lage, for Personen oder nach Zeit.

the concept of exposure

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