Evaluation of Accuracy of U.S. DOT Rail-Highway Grade Crossing Accident Prediction Models

Transcription

1 166 TRANSPORTATION RESEARCH RECORD 1495 Evaluation of Accuracy of U.S. DOT Rail-Highway Grad Crossing Accidnt Prdiction Modls M.I. MUTABAZI AND W.D. BERG Svral vrsions of th U.S. Dpartmnt of Transportation rail-highway grad crossing accidnt prdiction modls hav bn dvlopd and rcommndd for us in rsourc allocation procdurs. Th objctiv of this rsarch was to tst and valuat th ability of ths modls to accuratly prdict futur accidnt princ at individual grad crossings. Accidnt history and invntory data wr assmbld for 1, 798 grad crossings in Wisconsin for th priod from 1975 through Diffrncs btwn th actual and prdictd accidnt rats for 5- and 1-yar forcast priods wr valuatd using both th basic accidnt prdiction modls and th 5-yar accidnt history adjustmnt to th basic modl. It was found that th basic modl from th first and third vrsions providd th bst stimat of th long-run accidnt rat at individual grad crossings and wr, thrfor, rcommndd for us in rsourc allocation procdurs. Th U.S. Dpartmnt of Transportation (DOT) has dvlopd a rsourc allocation procdur to assist th railroad and highway industry in dvloping a cost-ffctiv program of improvmnts at rail-highway grad crossings. A critical componnt of th procdur is th accidnt prdiction modl that is usd in stimating th pctd numbr of accidnts at a crossing undr a givn st of physical and oprating charactristics. Svral vrsions of th modl hav bn dvlopd and rcommndd for application (l-3). A critiqu of two of th arlir vrsions indicatd significant inconsistncis in prdictd accidnt rats, with a rsulting potntial bias in th implid cost-ffctivnss of candidat improvmnts ( 4). It was shown that ths problms can, as a consqunc, lad to a rnisallocation of limitd rsourcs. Th dvloprs of th svral DOT accidnt prdiction modls had valuatd th rlativ ffctivnss of thir modls using a paramtr calld a powr factor. Th powr factor indicats th prcntag of all crossing accidnts that occur at a slctd prcntil of th most hazardous crossings as rankd by th accidnt prdiction modls. For ampl, if th powr factor for th fifth prcntil of rankd crossings is 4, thn on th avrag, ach 1 prcnt of th most hazardous 5 prcnt of all crossings is contributing 4 prcnt of th total accidnts for th ntir population of crossings. Th powr factor is usful whn comparing two or mor hazardranking modls (b thy absolut or rlativ accidnt prdiction modls) that ar not pctd to b applid in a bnfit-cost analysis framwork. For ampl, if thr ar rsourcs availabl for upgrading warning dvics at 5 prcnt of th crossings in a population, th act numbr of accidnts pctd to b rducd is M. I. Mutabazi, Dpartmnt of Civil Enginring, Kansas Stat Univrsity, Manhattan, Kans W. D. Brg, Dpartmnt of Civil and Environmntal Enginring, Univrsity of Wisconsin-Madison, Madison, Wisc immatrial bcaus what is important is to maimiz th pctd total numbr of accidnts rducd at crossings in th population. On only nd idntify that group of crossings pctd to princ th gratst numbr of accidnts, rgardlss of actual numbr. Howvr, whn th accidnt prdiction modls ar to b usd in a rsourc allocation or bnfit-cost analysis framwork, such as th rcommndd DOT procdur (3), thn an stimat of th actual magnitud of pctd accidnt princ at individual crossings is a prrquisit. This is tru whthr th pctd accidnt rduction is stimatd by using th DOT procdur by first prdicting th accidnt rat undr isting conditions and thn applying an ffctivnss ratio to th proposd upgrad or if th pctd accidnt rduction is stimatd by simply calculating th diffrnc in prdictd accidnt rats for th altrnativ warning dvics. Prfrnc for th lattr approach has bn prsntd and discussd in a prvious papr (4). Th objctiv of th rsarch rportd hrin was to tst and valuat th ability of th thr diffrnt vrsions of th DOT accidnt prdiction modl to accuratly prdict futur accidnt princ for a larg sampl of individual rail-highway grad crossings (5.) CHARACTERISTICS OF THE MODELS Th first of th thr accidnt prdiction modls to b valuatd was dvlopd during th lat 197s using 1975 accidnt and invntory data for all public grad crossings in th Unitd Stats (J.) Th modl consists of thr sts of quations, on for ach of thr catgoris of warning dvics: passiv (including cross bucks and STOP signs), flashing light signals, and gats. Indpndnt variabls usd in th quations ar indicatd in Tabl 1. Th scond st of accidnt prdiction modls was rlasd in 1982 and was intndd as an upgrad and improvmnt to th first st of modls (2.) A principal chang in th structur of th modls was th incorporation of a two-stag computational procdur. Th first stag consists of a basic accidnt prdiction formula similar to that found in th original modls, but with minor changs in th indpndnt variabls as indicatd in Tabl 1. Th scond stag is rfrrd to as th gnral accidnt prdiction formula, and computationality rprsnts a wighd avrag of th prdictd accidnt rat from th basic formula and th obsrvd accidnt rat for th immdiatly prcding 5-yar priod. Th third st of accidnt prdiction modls to b valuatd was rlasd in 1987 and is similar to th scond st of modls (3.) Som of th indpndnt variabls wr changd, as shown in Tabl 1, and th modls wr rcalibratd using 1981 through 1985 accidnt data and 1986 invntory data.

2 Mutabazi and Brg 167 TABLE 1 Indpndnt Variabls Usd in U.S. DOT Accidnt Prdiction Modls Variabl Passiv Flashing Lights Gats Trains pr day Numbr of day-through trains Numbr of main tracks \ Maimum timtabl spd Avrag daily traffic Numbr of lans Highway pavd? Highway typ Ara population Th inclusion of a 5-yar accidnt history in th scond and third modls was intndd as a mthod for accounting for th gnral ffct of important influncing factors not includd in th modls, such as availabl sight distanc. Evn if this approach is considrd rasonabl, thr was no rportd tst of th goodnss of th accidnt prdictions that rsult from th application of this wighting procdur. METHODOLOGY Th Offic of th Transportation Commission (OTC) for th stat of Wisconsin maintains rail-highway grad crossing accidnt history and warning dvic upgrad information in a card fil systm for vry crossing in th stat. In addition, th OTC has microfich copis of th DOT invntory data for th yars 1979, 1982, 1983, 1987, and This rprsntd a uniqu data bas that could b usd for tsting th prdictiv abilitis of th thr DOT accidnt prdiction modls. A total of 1,798 crossings found on two railroads oprating in Wisconsin wr slctd as an valuation data st. Thr wr 1, crossings quippd with crossbucks, 68 with flashing light signals, and 118 with gats. This sampl data bas was thn compard to th national invntory data bas to dtrmin whthr it was rasonably rprsntativ of grad crossing charactristics found nationwid. As illustratd in Figurs 1 through 3, th distribution of crossings by typ of warning dvic, avrag daily traffic volum, and avrag trains pr day ar similar. As a rsult, it was concludd that th study findings should b applicabl to thos of othr stats as wll as to Wisconsin. Th 1,798 sampl grad crossings wr initially analyzd on th basis of 198 conditions. This includd actual knowldg of accidnt princ during both th prior 5-yar priod from 1975 through 1979 and th post 1-yar priod from 198 through Each of th thr DOT modls was applid to th 198 conditions for ach of th 1, 798 grad crossings. Fiv prdictd rats wr calculatd for ach crossing using th following modl formulations (idntifid hraftr as Modls 1 through 5): n Cl c: 8 ~6 (.) (ij 4 'E ~2... Q) a Study data 198 National data X-Bucks Flashing Lights Gats FIGURE 1 Comparison of sampl vrsus national data: typ of warning dvic.

3 168 TRANSPORTATION RESEARCH RECORD First modl (J); 2. Scond modl without accidnt history: basic formula (2); 3. Scond modl with accidnt history: gnral formula (2); 4. Third modl without accidnt history: basic formula (3); and 5. Third modl with accidnt history: gnral formula (3). 6 II 198. Study data 198 National data Each prdictd accidnt rat was compard with th obsrvd rat for post-5- and 1-yar priods from 198 through 1984, and 198 through 1989, rspctivly. Th qustions of intrst wr: (a) Ar th modls significantly diffrnt from ach othr; and (b) Which modl(s) ar bttr prdictors of actual accidnt rats at individual grad crossings. DIFFERENCES BETWEEN MODELS A null hypothsis that all fiv prdictd accidnt rats wr th sam was tstd against th altrnativ that at last two wr diffrnt. A two-way analysis of varianc in th prdictd rats for th fiv modls was prformd for ach of th thr warning dvic classs. Crossings wr considrd as a blocking factor to liminat crossing-to-crossing variation. Bcaus th calculatd F-ratio cdd th critical ratio at th 5 prcnt significanc lvl for th modls factor for ach warning dvic catgory, it was concludd that at last two modls wr significantly diffrnt from ach othr at th 95 prcnt lvl of confidnc. As pctd, it was also found that th sampl crossings wr significantly diffrnt from ach othr within ach warning dvic class. Th sam analysis was rpatd using only Modls 1, 3, and 5. Th sam conclusions wr drawn as thos in th prvious analysis, thus indicating that at last two of th thr vrsions of th gnral DOT accidnt prdiction modls wr significantly diffrnt from ach othr at th 95 prcnt lvl of confidnc. Bcaus th F-tst did not indicat whthr thr was any pair of modls whos diffrnc was statistically insignificant, confidnc intrvals for th diffrnc btwn all pairs of modls wr constructd. Th uppr and lowr limits wr calculatd at th 95 prcnt lvl of confidnc. Whn th rang btwn th uppr and lowr limits containd zro, it was concludd that th two modls wr not significantly diffrnt from ach othr. Th rsults rvald that th prdictd accidnt rats from Modl 5 wr not significantly diffrnt from thos producd by Modls 1 and 4, 35 ~3 c ~ 25 ~ 2 cu.:::: 15. ~ 1 ~ 5. - II-198-Study. data. --II 198 National.data -. < >25 Trains pr day FIGURE 2 Comparison of sampl vrsus national data: avrag daily traffic K 1K-5K 5K-1K >1K Annual Avrag Daily Traffic FIGURE 3 Comparison of sampl vrsus national data: avrag trains pr day. although Modls 1 and 4 yildd prdictd rats that wr significantly diffrnt from ach othr. Dtrmination of a prfrrd modl was approachd by analyzing th absolut dviations from a comparison of obsrvd and prdictd accidnt rats for ach modl. Th prfrrd modl would b th modl having th minimum sum of dviations. Comparisons wr undrtakn for obsrvation priods of 5 and 1 yars, first assuming that prvailing physical and oprating conditions rmaind constant and thn accounting for any actual changs that occurrd during th obsrvation priod. Tabl 2 illustrats th rsults of this analysis. It is clar that Modls 2 and 3 ar infrior to Modls 1, 4, and 5 undr all conditions. Th lattr modls appar to b of approimatly qual rlativ ffctivnss with rspct to prdicting th accidnt rat at an individual grad crossing for a 5- to 1-yar obsrvation priod. In addition, th prdictiv ability of th modls improvs as th lngth of th obsrvation priod incrass. This implis that obsrvd accidnt rats basd on short tim priods (such as 5 yars) do not offr good stimats of th tru man accidnt potntial at a grad crossing. This should probably not b unpctd givn that th avrag accidnt rat for all grad crossings as a whol is about on accidnt vry 3 yars. ACCIDENT IDSTORY AS A HAZARD PREDICTOR For any givn grad crossing, thr is a tru man accidnt rat that is unknown. Any obsrvd rat ovr a givn tim priod is simply an stimator for that tru man rat. Howvr, th 5-yar accidnt history priod usd in th scond and third vrsions of th DOT modls is usually not long nough to assss a tru trnd for th actual accidnt rat at a spcific grad crossing. For ampl, considr a crossbuck-quippd grad crossing with a tru accidnt rat of.4 accidnts pr yar, or on accidnt vry 25 yars. Furthr assum that th basic DOT accidnt prdiction formula (without th accidnt history adjustmnt) is abl to accuratly prdict th tru accidnt rat at this crossing. If by chanc no accidnts had occurrd during th 5-yar accidnt history priod slctd for application of th gnral DOT modl, thn th wightd prdictd accidnt rat would b.28 accidnts pr yar, or on accidnt vry 36 yars. This would suggst that th crossing is 43 prcnt safr than it actually is. Th obsrvation of no acci-

4 Mutabazi and Brg 169 TABLE 2 Comparison of Obsrvd with Prdictd Accidnt Rats: Sum of Absolut Dviations Modl Changs in Prvailing Conditions Accountd For Not Accountd For 5-yr Priod 1-yr Priod 5-yr Priod 1-yr Priod dnts in th 5-yar history priod dos not ncssarily man that th prdictd rat of.4 accidnts pr yar was incorrct bcaus th assumd avrag of on accidnt vry 25 yars could occur in any yar with th 25-yar rturn priod. Had that on accidnt occurrd during th 5-yar obsrvation priod, thn th wightd prdictd accidnt rat using th gnral DOT modl would b.9 accidnts pr yar, or on accidnt vry 11 yars. This would suggst that th crossing is 125 prcnt mor hazardous than it actually is. Evn if th tru accidnt rat is assumd to b unknown, th prdictd rat from th gnral DOT modl in this ampl can vary from on accidnt vry 11 yars to on accidnt vry 36 yars, dpnding on whthr on vhicl-train accidnt had occurrd during th prvious 5 yars. Th 5-yar obsrvation priod is only 14 to 45 prcnt as long as th avrag rturn priod on th basis of th prdictd accidnt rat (assuming a 5-yar accidnt history of or 1 accidnt, rspctivly). As a rsult, a 5-yar obsrvation priod should not b pctd to provid a good indication of th gnral trnd or tru accidnt potntial at a rail-highway grad crossing. Ths obsrvations suggst that rgrssion-to-th-man phnomna may nd to b considrd. This statistical concpt charactrizs a situation in which, if a random dviation from th man occurs, it is pctd that th nt obsrvation will b closr to th population man. For ampl, if a 1 prcnt sampl of grad crossings having th highst 3-yar accidnt history wr slctd from a givn rgion, thn it would b pctd that during th nt 3 yars th accidnt rat at ths crossings would dclin, vn if no safty masurs wr implmntd. Us of th accidnt history adjustmnt to th basic accidnt prdiction formula in th scond and third vrsions of th DOT modls is tantamount to an approimation for rgrssion to th man. By virtu of th way in which th basic formula was statistically calibratd, it provids a dirct stimat of th tru man or long-run accidnt rat for a spcific st of crossing charactristics. Howvr, if th obsrvd accidnt rat during th prvious 5 yars is gratr or lss than th basic prdictd rat, thn th DOT procdur adjusts th obsrvd rat toward th basic prdictd accidnt rat. Thus, th rsulting adjustd rat prsumably approimats th trnd pctd during th nt short-run obsrvation priod, with th basic formula still providing th bst stimat of th long-run man accidnt rat. To tst this hypothsis, th 1, 798 sampl grad crossings wr first groupd according to th numbr of vhicl-train accidnts actually obsrvd during th 1975 through 1979 tim priod. Th obsrvd accidnt rats for th subsqunt 5- and 1-yar priods of 198 to 1984 and 198 to 1989 wr also dtrmind for ach crossing and thn avragd within ach group. Similarly, th prdictd accidnt rats for ach crossing from Modls 1, 4, and 5 wr avragd within ach group. Figur 4 illustrats th rsults of this analysis. Modls 1 and 4, which do not incorporat any accidnt history adjustmnt, suggst a similar pctd long-run accidnt potntial. Th pctd rats from ths modls wr lowr than th obsrvd rats during th prcding 5-yar priod whn that obsrvd rat was gratr than 1.8 ~ 5-yr Pr...,_ 5-yr Post -- 1-yr Post -& Modl #1 ~ Modl #4 _. Modl # >.8 Fiv-Yar Accidnt History (#/yar) FIGURE 4 Comparison of obsrvd and prdictd accidnt rats for crossings groupd by 5-yar accidnt history.

5 17 TRANSPORTATION RESEARCH RECORD 1495 about.5 accidnts pr yar, or on accidnt vry 2 yars. Similarly, th prdictd rats ar gratr than th obsrvd rats whn th obsrvd rat was lss than about.5 accidnts pr yar. Ths pattrns imply that th obsrvd accidnt rat will rgrss toward th prdictd rat during th forcast priod. This obsrvation is rinforcd by noting that th actual accidnt rats during th post-5 and 1-yar obsrvation priods ar rgrssing toward th prdictd rats stimatd by Modls 1 and 4 and away from th accidnt rats obsrvd during th immdiatly prcding 5-yar priod. CONCLUSIONS AND RECOMMENDATIONS On th abov findings, it was concludd that th basic accidnt prdiction modl (ithr 1 or 4) is th prfrrd modl for us in th DOT rsourc allocation procdur bcaus it provids th bst stimat of th tru long-run accidnt rat at a spcific rail-highway grad crossing. Although som acknowldgd hazard influncing variabls (such as availabl sight distanc) do not appar in th modls, th rgrssion cofficints indirctly rflct th avrag impact of ths factors. An assrtion might b mad that, givn ral-world constraints on dcision making and th currnt confidnc in th slction and programming of proposd grad crossing safty improvmnts, th nginring community should b using th bst availabl modls. Th authors bliv that this rsarch offrs a rasonabl basis for modifying th rcommndd DOT rsourc allocation procdur by dlting th accidnt history adjustmnt stp and using only th basic accidnt prdiction modl (1 or 4) to stimat th pctd accidnt rduction associatd with a candidat safty improvmnt. Furthrmor, th accidnt history at a grad crossing provids usful information in both th dtrmination of whthr a spcific crossing is unrasonably hazardous and in th slction of a candidat safty improvmnt. Bcaus accidnt history data ar gnr- ally availabl in th national data bas bginning with th yar 1975, all of this information should b considrd, not just that for th immdiatly prcding 5-yar priod. If th actual accidnt rat at a spcific grad crossing dramatically cds th prdictd rat, as stimatd by DOT Modl 1 or 4, thr is clar indication of a uniqu problm that cannot b accountd for on th basis of a modl structur that is limitd to a fw crossing charactristics. Th prior accidnts will also oftn show a pattrn of similarity that can point to a spcific dficincy of th crossing that is advrsly affcting drivr prformanc. This knowldg will b of hlp in dtrmining what is causing th problm and how to corrct it. In many cass, th appropriat countrmasur will b somthing othr than simply upgrading th typ of warning dvic. REFERENCES 1. Mngrt, P. Rail-Highway Crossing Hazard Prdiction Rsarch Rsults. Rport FRA-RRS-8-2. U.S. Dpartmnt of Transportation, March Hitz, J., and M. Cross. Rail-Highway Crossing Rsourc Allocation Procdur Usr's Guid. Rport FHWA-IP Transportation Systms Cntr, U.S. Dpartmnt of Transportation, Cambridg, Mass., Dc Farr, H. E. Summary of th DOT Rail-Highway Crossing Rsourc Allocation Procdur-Rvisd. Rport DOT/FRA/OS-87/5. U.S. Dpartmnt of Transportation, Jun Brg, W. D. Critiqu of Rail-Highway Grad Crossing Effctivnss Ratios and Rsourc Allocation Procdur. In Transportation Rsarch Rcord 169, TRB, National Rsarch Council, Washington, D.C., 1986, pp Mutabazi, M. I. Tsting Dpartmnt of Transportation Modls for Accidnt Prdiction at Railroad-Highway Grad Crossings. M.S. thsis, Dpartmnt of Civil and Environmntal Enginring, Univrsity of Wisconsin-Madison, Aug Publication of this papr sponsord by Committ on Railroad-Highway Grad Crossings.