Accident Severity Prediction Formula for Rail-Highway Crossings

Transcription

1 5 ident Severity Predition Formula for Rail-Highway Crossings JOHNS. HTZ STRCT The development of formulas to predit the severity of aidents at publi rail-highway rossings is desribed. The formulas make use of the previously developed DOT ident Predition Formula, the u.s. DOT-R National Rail-Highway Crossing nventory, and the FR aident files. When these new formulas are used in the DOT Resoure lloation Proedure, information will be available to assist in making better deisions about to install motorist-warning devies to further inrease rossing safety for a given level of funding. Established statistial tehniques were used to develop two formulas: one that estimates the number of fatal aidents per year at a rossing and one that estimates the number of injury aidents per year at a rossing. rt was found that the fators in the inventory that signifiantly influene fatal aident severity, given that an aident ourred, were maximum timetable train speed, the number of through trains per day, the number of swith trains per day, and urban or rural loation. For injury aident severity, given that an aident ourred, the signifiant fators were maximum timetable train speed, the number of traks, and urban or rural loation. The performane of these severity formulas is disussed and alulated results are presented. The DOT Rail-Highway Crossing Resoure lloation Proedure, developed at the U.S. Department of Transportation's Transportation Systems Center (TSC), employs an aident predition formula. n an attempt to improve the effetiveness and usefulness of the resoure alloation proedure, a study was undertaken to inorporate a quantitative measure of severity in the aident predition formula. That study (1) is doumented in this paper. Two severity formulas were developed using established statistial tehniques: one formula estimates the number of fatal aidents per year at a rossing and the other estimates the number of injury aidents per year at a rossing. The resulting formulas are to be inorporated in the DOT Rail-Highway Crossing Resoure lloation Proedure <1 1> CKGROUND The Highway Safety ts of 1973 and 1976 and the Surfae Transportation ssistane ts of 1978 and 1982 provide federal funding authorizations to states speifially for safety improvement projets at publi rail-highway rossings. Suh safety improvements frequently involve the installation of ative motorist-warning devies suh as flashing lights or gates. To promote the effetive use of federal funds for these safety projets, the u.s. Department of Transportation (DOT) has developed a proedure to assist states and railroads in planning rail-highway rossing safety programs. This proedure, the DOT Rail-Highway Crossing Resoure lloation Proedure (DOT proedure), determines rossing safety improvements that result in the greatest aident redution benefits based on onsideration of predited aidents at rossings, the osts and effetiveness of safety improvement opt ions, and budget limits. Two analyti methods have been developed as part of the DOT proedure. Their development followed ompletion of a joint U.S. DOT-ssoiation of merian Railroads (R) National Rail-Highway Crossing nventory (inventory), whih numbered and olleted inventory information for all publi and private rossings in the United States (4). The first analyti method inluded in the DOT proedure is the DOT aident predition formula, whih omputes the expeted number of aidents at rossings based on information available in the inventory and rossing aident data files (5). The seond analyti method is a resoure alloc"ation model designed to rank rossings that are andidates for improvement on a ost-effetive basis and to reommend the type of warning devie that is to be installed (6). The urrent effort is motivated by the r e ~n i t ion that not all rail-highway rossing aidents are equally severe. n 1981 there were a total of 8,546 rail-highway rossing aidents (7 ). Of t hese aidents 5, 761 aused no asualties, -2, 22 4 aused injur ies only, and 561 i nvolved fatalit i es. Thus, 67 perent of the a idents involved no measurable asualty severity, and only 6.6 perent involved fatalities. This unequal distribution of severity among rossing aident s ma ke s it important, but diffiult, to identify t hose rossings t hat are l ikely to have high-severity aidents. priority r ank ing of rossings by number o f p r ed i ted aidents (as done by urrent DOT proedure) ould be s ignifiantly different from s u h a ranking by pred i ted s everity o f ai dent. This differene might a f f et the use o f i mprovemen t f unds. CCDENT SEVERTY FORMUL The traditional approah to risk analysis (8) views safety risk as the produt of two independent fators: (a) the frequeny of aident ourrene, and (b) the severity or onsequenes of aident ourrene. The produt of these two fators for a given hazardous situation provides the total safety risk for that situation. For example, a rail-highway rossing with a predited aident frequeny of o. 5 aidents per year and a predited aident severity of.2 fatalities per aident poses a total safety risk of O. l fatalities per year. The division of safety risk into aident frequeny and severity

2 6 Transportation Researh Reord 956 ' omponents is partiularly appropriate for the urrent effort beause one of the omponents, the DOT aident predition formula, already exists. The proposed severity predition formula would be used with the aident predition formula to provide a predition of total safety risk as follows: R = x S (1) R s risk of a rossing measured in expeted asualties per year, predited aident frequeny from the urrent DOT aident predition formula, and predited aident asualties from the severity predition model. ~ ' LU > LU "' - z LU u 5i '.6 <C - <C LL,,C,C major benefit of this approah is that the urrent DOT aident predition formula will remain unhanged and an be used either with or without the severity formula. Proedures for use of the severity formula with the DOT aident predition formula and the DOT Rail-Highway Crossing Resoure lloation Proedure will be desribed in an updated version of the Rail-Highway Crossing Resoure lloation Proedures User's Guide (3), due for ompletion during fisal year MXMUM TMETLE TRN SPEED, MPH =FTLTES PER CCDENT =FTL CCDENTS PER CCDENT C =FTLTES PER OCCUPNT FGURE 1 Comparison of fatality severity measures PPROCH Under this effort two severity formulas were developed: one formula to predit fatality severity and another to predit injury severity. These formulas provide preditions on the basis of the rossing harateristis desribed in the inventory. The first task in developing the severity formulas involved the seletion of speifi measures of severity to be quantified by the formulas. The next task was to identify in the inventory rossing fators that showed a strong orrelation with measures of severity for possible inlusion in the severity formulas. The severity formulas were then developed using a regression proedure, referred to as the logisti disriminant approah, whih employs an iterative weighted regression tehnique that is a modifiation of a method desribed in Cox (9). The last task in development of the severity formulas was to evaluate their performane by omparing predited versus atual aident severity. ~ ::.5 LLl [;'; (/) - z LLl.35 u <( >- :: ~ z ,C,C,C,C - C,C MXMUM Ti1V1ETDLE TRN SPEED, MPll NJURES PER CCDENT NJURY CCDENTS PER CCDENT NJURES PER OCCUPNT FGURE 2 Comparison of injury severity measures..~ 8,C SEVERTY PREDCTON FORMUL DEVELOPMENT Seletion of Severity Measures The proposed use of the severity formulas ditates that severity be measured in terms of onsequenes, given that an aident ourred. The severity measures must therel"ore be expressed in terms 1" onsequenes per aident. The urrent effort onentrated on developing formulas for quantifying fatalities and injuries as measures of severity. For the purposes of this study, a fatal aident is an aident in whih at least one fatality ourred independent of injuries or property damage i an injury aident is an aident in whih there were no fatalities and at least one injury ourred independent of property damage. To assist in evaluating alternative measures of fatality and injury severity, histograms were developed as shown in Figures l and 2. These histograms relate average values of the measures, alulated from aident reords, to aidents grouped by intervals of maximum train speed. This permits a review of how the measures vary as a funtion of a fator (maximum ~irne~aoie train speeaj previously shown to be orrelated with aident severity ( 1). t should be noted that maximum timetable t;ain speed is a rossing harater is ti inluded in the inventory, and it is used here as a surrogate for atual train speed at the time of an aident. The histograms in Figure l show that the three l"atality measures onsidered vary with train speed in the same general manner. ll three inrease with train speed to about 6 mph beyond whih they remain relatively onstant. This is intuitive beause, heyona some high uolue of Reverityr fatol itip.s ~an no longer inrease. s originally surmised, values for fatalities per aident are higher than values for fatal aidents per aident whih, in turn, are higher than those for fatalities per oupant per tl;(;iu~nl. Tin~ oiadp~ ur Lilt: iii::;i:.uyr.tmo fur. Ll1t::! Llu~t: measures is generally the same, however, suggesting that any of the measures ould be used with similar results. Given the general ompatibility of the measures, fatal aidents per aident was hosen as the measure of fatality severity beause it avoids the omplexities of dealing with vehile oupants.

3 Hitz 7 This measure an be restated, in statistial terms, as the probability of a fatal aident, given an aident. The same reasoning led to the seletion of injury aidents per aident as the measure of injury severity. This measure an be restated as the probability of an injury aident, given an aident. t is of interest to note from Figure 2 that the shape of the injury severity histograms inreases and then dereases with inreasing train speed. This is also intuitive beause, beyond some severity threshold, asualties will inreasingly be fatalities rather than injuiies. Seletion of Severity Fators V U V.3 is the expeted number of aidents per year at the rossing from the DOT aident predition formula. The analyti harater of the fatal aident probability funtion, P(F), relative to observed data is shown in Figure 3. This graph is a frequeny plot of the observed ratio of fatal aidents to total aidents versus maximum timetable train speed. The funtion P(F) is represented by the dashed line that is a best fit to the observed data points onneted by the solid line. Of ourse, the severity formula is multivariate and, hene, the dashed line for P(F) would be a multidimensional "surfae." The analyti harater of P() relative to observed data is shown in Figure 4. This graph is a frequeny plot of the observed ratio of injury ai- ~ ~. 2 _.Cl -.: t--u -.:u '-'- < CLCULTED ~ OSERVED P(F ) MXMUM TMETLE SPEED Development of the severity formulas started with identifiation of fators that orrelate with the severity measures and are thus potential preditors of severity. ll rossing harateristi fators in the inventory were systematially reviewed to identify those orrelated with the severity measures. To aomplish this, histograms similar to Figures 1 and 2 were developed relating average values of the measures alulated for aidents grouped by intervals of the fator in question. Results of this analysis showed that train speed was the strongest preditor of fatal aident severity of all the fators in the inventory. This is onsistent with results obtained by Coleman and Stewart (1) in an earlier study of rossing aident data. Histograms were also onstruted relating the severity measures to two fators. The following fators were identified as potentially useful in prediting fatality and injury severity: -Maximum timetable train speed, -Urban or rural rossing, -Number of main traks, -Number of other traks, -Number of through trains, and -Number of swith trains. Summary of Formula Development The analyti objetive of this phase of the study was to develop formulas that would predit the probability of a fatal aident given an aident, P(F), and the probability of an injury aident given an aident, P(). From these two formulas the safety risk expressed in terms of expeted number of fatal aidents, Rf, and injury aidents, Ri, per year at a rossing an be determined from x P(F) (2) x P() (3) FGURE 3 Typial plot of observed fatal aident frequeny und alulated values of P(F ). V U V u>-- -.:z w >- Cl.4.3 ::Ju "" , u z< -. l CLCULTED OSERVED MXMUM TMETLE SPEED FGURE 4 Typial plot of observed injury aident frequeny and alulated values of P(). dents to total aidents versus the same variable, maximum timetable train speed. n this ase, the funtion P() does not inrease monotonially with severity. However, the partiular regression proedure used to develop the severity formulas involved fitting a monotoni funtion to the observed data. The required formula for prediting injury aident probability ould, therefore, not be obtained diretly from the regression analysis. This problem was overome by limiting the aident data to nonfatal aidents. formula was then developed, from the regression analyses, to predit the probability of an injury aident given that a nonfatal aident ourred, P(NF). The formula for P(NF) is, as required, a monotonially inreasing funtion of.severity. Having obtained the formula for P (!l NF), the desired formula for P ( ) was then obtained from the following relationship: P() = P(NF) x P(NF) (4) nonfatal a P(NF) is the probability of a ident, given an aident, that is, P (NF) = 1 - P(F) (5) P(F) is the fatal aident probability formula obtained earlier. Hene,

4 8 Transportation Researh Reord 956 P() = P(NF) x [l - P(F)] (6) n performing the regression analyses, the observed data for the dependent variable were assigned only two values. n the ase of the fatal aident formula these values were +l for a fatal aident and -1 for a nonfatal aident. For the injury aident formula the values assigned were +l for an injury aident and -1 for a noninjury aident. The data used for the analyses were for the years The regression analyses resulted in nonlinear formulas for the dependent variable f, from the fatal aident data, and i, from the injury aident data. The resulting regression formulas typially produed values between +l and -1 for the independent variables f and i. Extreme values of the independent variables f and i an, in theory, be from + to -oo. The leslred values for f and i, however, are between and 1 as required by the probability funtions P(F) and P(). The formulas for f and i therefore had to be transformed into probability funtions. To aomplish this the following transformation was made to f to obtain the desired fatal aident probability formula: P(F) a 1/(1 + e-2f) (7) For the injury aident formula, the probability of an injury aident given a nonfatal aident, P(NF), was obtained first: P(NF) 1/(1 + e-2i) (8) The probability of an injury aident given an aident, P(), was then obtained b~ substituting Equations 7 and 8 into Equation 6 as desribed previously. This disussion has provided an overview of the strategy involved in obtaining the formulas required for prediting fatal aident and injury aident probabilities. more detailed disussion of the regression analysis is presented else <.!>. Resulting Severity Predition Formulas The resulting formulas for prediting the probabilities of fatal aidents and injury aidents an be expressed in terms of several fators that are ombined by simple mathematial operations. Eah fator in the formulas represents a rossing harateristi desribed in the inventory. The probability of a fatal aident given an aident, P(Fl), is expressed as P(F) = 1/(1 +CF x MS x TT x TS x UR) (9) CF formula onstant = 6'l~, MS fator for maximum timetable train speed, TT= fator for through trains per day, TS fator for swith trains per day, and UR fator for urban or rural rossing. The equations for alulating rossing harateristi fators for the fatal aident probability formula are CF 695 MS ms TT (tt + l)-.125 TS (ts + 1) o.12s UR = e.188ur ms maximum timetable train speed {mph) ; ts number of swith trains per day; tt number of through trains per day; and ur 1 for urban rossing, O for rural rossing. The probability of an injury aident given an aident, P(), is expressed as P() = [l - P(F)]/(l +C x MS x TK x UR) (1) P (F) C MS probability of a fatal aident, given an aident, obtained from Equation 9, formula onstant = 4.28, fator for maximum timetable train speed, fator for number of traks, and TK UR= fator for urban or rural rossing. The equations for alulating rossing harateristi fators for the injury aident probability formula are C MS ms TK e.1176tk UR e.1844ur ms maximum timetable train speed (mph) 1 ur 1 for urban rossing, for rural rossing; and tk total number of traks at rossing. To simplify use of the formulas, the values of the rossing harateristi fators have been tabulated for typial values of rossing harateristis. These values are given in Tables 1 and 2 for the fatal aident and injury aident probability formulas, respetively. use of Severity Predition Formula sample appliation of the fatal and injury aident severity formula for a typial rossing is provided to demonstrate their use. Charateristis of the sample rossing are listed in Table 3. To determine the probability of a fatal aident given an aident at the sample rossing, Equation 9 is used. Values for the fators in the fatal aident severity formula (Equation 9) an be omputed from the equations given previously or looked up in Table 1. Table 1 gives the following fator values for the rossing harateristis speified: CF:: 695. MS.19 TT"'.782 TS "' 1.22 UR"' 1. Substituting the fator values into the fatal aident probability formula yields P (Fl/) l/! l + CF x MS x TT x TS x UR) 1/( x.19 x.782 x 1.22 x 1. ).75 To determine the probability of an injury ai-

5 Hitz 9 TLE 1 Fator Values for Fatal ident Probability Formula Maximum Formula Timetable No. of No. of Urban or Constant Train Speed Through Swith Rural (CF) (mph) MS Trains/Day TT Trains/Day TS Crossing 8 UR ODO 1. s S a.ass so so =rural, 1 = urban. TLE 2 Fator Values for njury ident Probability Formula Maximum Formula Timetable Constant Train Speed (C) (mph) MS Total Urban or Number Rural of Traks TK Crossing 8 UR s S S JOO =rural, 1 =urban. 2 3 s JO 15 2.ODO l. l.l 2S S S S TLE 3 Charateristis of Sample Crossing Charateristi Value Maximum timetable train speed (mph) 4 Through trains per day Swith trains per day S Total number of traks (main plus other) 2 Urban or rural loation Rural dent given an aident, at the same sample rossing, Equation 1 is used. values for the fators in Equation 1 an be obtained from the equations given previously or from Table 2. Table 2 gives the following fator values for the harateristis of the sample rossing: P {F) C MS TK.75 (from fatal aident severity formula) UR= 1. Substituting the fator values into the injury aident probability formula yields P{) [l - P{F))/{l +C x MS x TK x UR) (1 -.75)/( x.423 x x 1.).281 SEVERTY FORMUL PERFORMNCE To illustrate harateristis of the fatal and injury severity formulas, the two funtions P(F) and P() are plotted as a funtion of maximum timetable train speed and one other severity fator in Figures 5 and 6. The probability of a fatal aident given an aident P(F) (Figure 5) inreases as a nearly linear funtion of timetable train speed. Changes in the number of through trains do not have a major influene on fatal aident severity. The probability of an injury aident given an aident P() (Figure 6) inreases as a nonlinear funtion of timetable train speed. njury aident severity generally inreases rapidly with timetable train speed and then remains relatively onstant beyond 4 mph. The funtion atually dereases at high speeds under ertain onditions as previously predited from observation of atual aident data (see Figure 4). The number of traks at the rossing has a signifiant influene on the funtion (injury aident severity dereases with the number of traks). The performane of the severity formulas was evaluated using two methods: (a) omparing predited versus atual severity for sample sets of aidents and (b) omparing the ability of the formulas to rank aidents by severity with a random ranking. Results of the first evaluation are summarized in Table 4. Using 1978, 1979, and 198 data, the severity formulas were used to predit the number of

6 1 Transportation Researh Reord URN CROSS NG SWTCH TRNS = 1.15 < <!i:.1 "- = MX TRN SPEED, MPH FGURE 5 Probability of fatal aident, given an aident, verau11 maximum timetable train ~peetl. represent expeted long-term annual rates and should be used with aution when estimating severity at individual rossings for a short time. Results of the seond evaluation of the severity formulas are based on the premise that, for aidents properly ranked by predited severity, those at the top of the list (the most severe) should have a higher than average number of atual fatal and injury aidents. On the other hand, aidents at the top of a randomly ranked list should have only an average number of atual fatal and injury aidents. The ratio of atual aident severity for a set of aidents ranked by predited severity to atual aident severity for the same size set of aidents ranked by random seletion is a measure of the formula's ability to identify more seve r e aidents. This measure is referred to as the power fator for the p r ed i tion formula. The power fators for the fatal and injury formu l as f o r sets o f ai dents, r anked by pred i ted severity, are given in Table 5. The table indiates,.3 TLE 5 Ranking Performane of Severity Formulas <.2 ::!:... "-.1 URN CROSSNG SWTCH TRNS = 1 THRU TRNS = 1 No. of Fatal Severity njury Severity Ranked Formula Formula idents Power Fatorsa Power Fators , a tual severity For ranked group of aidents/atual severity for randomly seleted group of aidents. 2 4 MX TRN SPEED, MPH FGURE 6 Probability of injury aident, given an aident, versus maximum timetable train speed. TLE4 Predited Versus tual ident Severity No. of No. of No. of No. of No. of Predited tual Predited tual Ranked Fatal Fatal njury njury idents idents idents idents idents , 142, ,934 Si ,18.5 2,192 fatal and injury aidents for sets of aidents that ourred in The preditions were then ompared with atual aident reords for the same set s o f a idents. The sets of aidents onsidered were seleted from the top of a list of aidents ranked by predited severity. ording to Table 4 the severity predition formulas ompare well with ~bee!'. ed dat:_!'o!' e~a!!!p!e ; the fir~t: row RhnwR that, for the top 1 aidents in 1981, the formulas predited 18.2 fatal aidents versus 13 atual and injury aidents versus 42 atual. t should be noted that predited severity values for example, that for the top 1 ranked aidents the power fators for the fatal and injury formulas are 1.91 and 1.52, respetively. This means that the top 1 aidents ranked by the formulas have and times the number of fatal and injury aidents, respetively, as a randomly seleted group of 1 aidents. Similar omparisons are made for the top 5 and 1; aidents; The results all show that the fatal and injury severity formulas are quite effetive in prediting aident situations that tend to be. more severe than the average. CKNOWLEDGMENT The original work on the resoure alloation proedure and the present study were sponsored jointly by the FHW Offies of Researh, Development, and Tehnology and the FR Offie of Safety. The author expresses his appreiation to Janet Coleman, FHW, and rue George, FR, for their support and guidane and to Edwin Farr, Mary Cross, and.peter Menqert of TSC for their tehnial ontributions to this study. REFERENCES 1. E. Farr and J. Hitz. ident Severity Predition Formula for Rail-Highway Crossing. FRW, u.s. Department of Transportation, July (v"! l "hl P frnm ~h" Tr,.nsportation Systems Center, Kendall Square, Cambridge, Mass ) 2. R. Coulombre, J. Poage, E. Farr, and J. Hitz. Summary of the Department of Transportation Rail-Highway Crossing ident Predition For-

7 11 mula and Resoure lloation Model. Report DOT-TSC-FR FR, U.S. Department of Transportation, Sept J. Hitz and M. Cross. Rail-Highway Crossing Resoure lloation Proedure User's Guide. Report FHW-P FR, U. s. Department of Transportation, De J. Hitz, ed. Summary Statistis of the National Railroad-Highway Crossing nventory for Publi at Grade Crossings. Report FR-RPD FR, U.S. Department of Transportation, Sept P. Mengert. Rail-Highway Crossing Hazard Predition Researh Results. Report FR-RRS-8-2. U.S. Department of Transportation, Marh E. Farr. Rail-Highway Crossing Resoure lloation Model. Report FR-RRS U.S. Department of Transportation, pril Rail-Highway Crossing ident/nident and nventory ulletin No. 4. FR, U.S. Department of Transportation, Risk Conepts in Dangerous Goods Transportation Regulations. National Transportation Safety oard, U.S. Department of Transportation, D.R. Cox. nalysis of inary Data. Halstead Press/John W. Stey, New York, 197. J. Coleman and G.R. Stewart. nvestigation of ident Data for Railroad-Highway Grade Crossing. l!l Transportation Researh Reord 611, TR, National Researh Counil, Washington, D.C., 1976, pp Publiation of this paper sponsored by Committee on Railroad-Highway Grade Crossings. Stability and Other Considerations 1n Simulation nalysis of Signal Control FENG-OR LN STRCT Lak of understanding of the nature of simulation and the harateristis of a system to be simulated an result in misuse of simulation models and simulation results. To promote better appliations of simulation models to the evaluation of signal ontrols, three problems related to the generation and interpretation of simulation data are disussed in this paper. These problems inlude the stability of simulation results, the use of seed numbers for generating probabilisti events, and the aggregation of input data. Using simple examples of signal ontrol, several fallaies in the appliation of signal simulation models are illustrated. Suggestions for avoiding these fallaious appliations are presented. Simulation models are inreasingly used to aid in the design and evaluation of signal ontrol systems. Some of these models, suh as UTCS-1 (~) and NETSM (2), are intended for general appliation in the evaluation of traffi ontrol alternatives. These models require mirosopi simulation of traffi flow harateristis to approximate the real world. Experiene with existing mirosopi simulation models has produed a wealth of information on the potential and limitations of applying suh models (_}) Current onerns appear to fous on model enhanement, user needs and onstraints, resoure requirements for model appliation, and promotion and implementation of appliation by the traffi engineering ommunity. The problem of experimental design for simulation analysis has also drawn some attention. With inreased use of simulation models for evaluation purposes, the risk of misuse and misinterpretation of simulation results an be expeted to inrease. reason for this is that simulation models require substantial user interations. n evaluation model is essentially a tool for data olletion. Consequently, simulation results should be treated as a sample of observations. Estimates obtained from suh a sample should be subjeted to statistial tests for interpretation. t follows that experimental design should be an important part of simulation analysis. t issue is how, within the apability of a model, a user an apply the model effiiently to obtain statistially valid estimates. The experimental design for simulation analysis is a profound subjet. t requires a omprehensive understanding of the harater is tis of a system to be simulated and the nature of simulation. t the present time, suh an understanding is nonexistent. This is due in part to the large number of different systems a model has to aommodate. High osts and the reliability issue assoiated with the use of a model are also ontributing fators. Nevertheless, there are several aspets of simulation appliation