- Email: [email protected]
Empirical estimates of seat belt effectiveness in two-car collisions
EMPIRICAL ESTIMATES OF SEAT BELT EFFECTIVENESS IN TWO-CAR COLLISIONS K. S. Wayne (Received
State University,
II March 1982:
KRISHNAN Detroit.
MI 45202.
in revised form
U.2.A.
Ii September
1932)
Abstract-The objective of this research is to quantify occupant protection afforded by restraint systems in two-car head-on collisions. An accepted measure of occupant protection is “Restraint SyBtem Effectiveness” (RSE).This quantity is defined as the percent reduction in the probability of an occupant Injury due to the use of a restraint system. RSE estimates are calculated in the present paper using a previously developed mathematical model of occupant injuries in two-car collisions and obtaining parameter estimates from two data sets. The two sets of data used for estimating RSE are: New York police accident data and data collected by various multidisciplinary accident investigation teams. Both these data sets have been reported in the literature. The RSE estimates obtained from the two data sets range from 29 lo 40%. These estimates are shown to increase as the mass of the occupant’s vehicle increases, but decrease as the mass of the other colliding vehicle increases. On the average, the use of a restraint system can offset the decrease in occupant protection that would result from a 407.5 reduction in car weight. Consequently, the use of restraint systems 10 reduce occupant risk is estimated lo be even more important as the number of small vehicles in the U.S. vehicle fleet increases. INTRODUCTION
Restraint systems in automobiles are designed to protect occupants in case of automobile accidents. Because of the variety of ways in which automobile crashes can occur, the extent to which occupants are protected by a restraint system depends upon the type of accident (e.g. rollover, two-car collisions, etc.), where occupants are sittin g, seating posture and many other factors. Furthermore, a restraint system’s ability to protect occupants can be severely limited if the restraints are not properly used (for example, if seat belts are not worn snugly, as recommended by manufacturers). The objective of this research is to quantify restraint system effectiveness in two-car collisions. Such quantification would enable evaluation of the effectiveness of restraint system use relative to car size. Several studies reported in the literature have provided estimates of occupant protection for different restraint systems (e.g. seat belts and air cushion restraint systems) for a variety of accident types (e.g. rollover and two-car head-on collisions) [IIHS, 1976; Huelke et al., 1977; Mohan et al., 1976; Wilson et a!., 19731. Results of these studies are briefly summarized in Table 1. An accepted measure of occupant protection common to all of these studies is the percent reduction in the probability of an occupant injury where this reduction is attributable to the use of a restraint system at the time of an accident. Such a quantity is referred to in the literature as “Restraint System Effectiveness” (RSE) [IIHS, 1976; Kahane, 1975; Rininger et al., 1976; Robertson, 19761. Specifically, let p,, = the probability of an injury to an unrestrained in case of an automobile accident, and
occupant
pb = the probability of an injury to the sanle occupant had been restrained at the time of the accident. Restraint
System Effectiveness
is then expressed
if he
as
RSE = lfio X (pu - pb)/p, .
(1)
Note that p,, and pb denote probabilities of an injury to the same occupant with and without the use of a restraint system respectively, at the time of an accident. Since, at the time of an accident, an occupant is either restrained or unrestrained, but not both, estimating RSE theoretically requires the capability of reconstructing a given accident situation in order to estimate the values of pu and
I IC?~,l.
1
PE!GSYL7ISI.I /
La
CROSS
T.~auL.ATImI La
OCCWSZj DRIVE3
j :x , i ,
DRIVER
~:c..r\,a.c
La La+SH
LB+SH Ka+SH CROSS La TABULATIOS LBCSH
SOUTH CESTFUL TE.US USA
CROSS LBfSH TABULATION LB+SH LBfSH
OAKLAXD AXD
REGRESSION ON FRONTAL5 0h-I.Y REGRESSION ON ALL DIRECTIONS
42 -2 Ir 11
a ,i:
12” i AIS 2 FROYI i AIS 3 SEAT OCCLlP‘vcTsi FRONT pTy,,i;ig a
L
0.26 0.14 '0.13 0.061 ~.0043 0.9017 T 0.26 il.15 0.13 ,!).I52 3.0063'I).,30 I I '3.12 ;0.,:52 0.12 /0.3:8
t
%c 53 73 zi 60 00 io 61 T769 77
(FATAL) WASHTENAW COIJXTIES, XICHIGrLU
LB LB+SH LB
FRONT
AIS
2
KwcSl FRONT
AIS
2
LBfSH
SEAT occuP‘k%Ts FRONT SEAT OCCUPkVS FRONT
XORTH
CROSS
LB
AZRICA (USA + CASXIA)
TABULATION, FRONTALS ONLY
LBfSH La
t
-Gi 54 21 42
3 AIS
25 47 5
AIS
i
6
62 77
i
5 58
q.,:;
-
_L
ACRS
=
AIR CUSHIOS - RESTRAIXT SYSTEM (AIR BAG) La = LAP aELn ONLY
La+SH AIS
= LAP BELTS = &JaREVIATED
AND SHOULDER HARNESSES INJ!J~~ SCALE (COWITTEE
ON XDICAL
ASPECTS
OF AUTOFOTIVE SAFER,
K.A,a,C
= POLICE
CODES
FOR
INJURY
CLASSIFICATION
(SHEMAX
ET
AL.
,
1971).
1976)
ph simultaneously. An attempt to develop such a capability was made previously by developing a mathematical model of occupant injuries in two-car collisions [Krishnan et al., 1983; Krishnan, 19811. This model has been used in the present research to derive estimates of RSE. Some of the RSE estimates reported in the literature were based on a similar modeling approach [Dutt et al., 1977; Reinfurt et (11..19751. These studies used a linear regression model to statistically control variations in data. This research differs from the above studies in that the mathematical model used here was developed from consideration of principles of collision mechanics. Because of the causal nature of the model. it depicts the occurrence of occupant injuries far more accurately than regression models [Krishnan et al., 1983; Krishnan, 19811. Alternatively, RSE can be estimated by selecting random samples of unrestrained and restrained occupants from available automobile accident records and estimating pU and pb by the fractions of injured occupants in the two samples; substituting these estimates in eqn (1) yields an estimate of RSE. Errors associated with the RSE estimate so obtained can be statistically controlled to some extent by adopting suitable statistical sampling designs in the selection of unrestrained and restrained occupants. Many of the RSE estimates reported in the literature are based on such statistical sampling designs [Hochberg et al., 1975; Huelke et al., 1977; Rininger ef al., 19761. Since models of occupant injuries explicitly identify some of the sources of variations in data, RSE estimates derived from such models are likely to be more accurate than those based merely on sampling designs. A list of RSE estimates from ottier published studies is provided in Table 1. Since these RSE estimates vary considerably (from -2 to 100%). it raises a question as to what, exactly. is the “true” effectiveness of a given restraint system. Of course, no two types of restraint systems are alike in all respects. There are also likely to be differences in their relative effectiveness for different types of accidents. For example. some studies have shown that an air cushion restraint system is more effective than seat belts in preventing fatalities in head-on collisions, but less effective in rollover
Empirical
estimates
of
seat belt effectiveness
in two-car
collisions
219
crashes [IIHS. 1976; Mohan et al., 19761. The range of RSE estimates shown in Table I suggest that the variability in these estimates might have been caused by the differences in the following factors: data collection design, statistical techniques used in estimating RSE and the level of injury severity used in classifying whether an occupant was injured or not. As such, values of RSE obtained from different studies are not directly comparable. Furthermore, since occupant protection provided by restraint system use is such an important element in understanding accidents, it is necessary to investigate reasons for these variations in RSE estimates. This is addressed here. As mentioned earlier, estimates of RSE developed in this research are based on a mathematical model of an occupant injury, called the Injury Threshold Model (ITM). ITM was developed from consideration of the physics of two-car collisions and incorporates the notion of a threshold of human tolerance to impact forces. A brief description of ITM and some highlights of results obtained previously are provided in the next section.
INJURY
THRESHOLD
MODEL
An injury model was developed to predict the probability of an injury to an occupant of a vehicle involved in a two-car collision. The model incorporates principles of collision mechanics and a concept of a threshold of human tolerance to impact forces. The model was based on the idea that if the impact forces experienced by an occupant in a two-car collision exceed the threshold of the tolerance, an injury occurs; otherwise, no injury occurs. From the physics of the collision, the forces experienced by an occupant can be determined in terms of the deceleration of the center of gravity of the vehicle and the motion of the occupant relative to the center of gravity. The threshold of human tolerance to impact forces is modeled from experimental evidence with laboratory animals and other biological experiments. These data suggest the existence of a threshold of tolerance which can be considered to be a random variable with a logistic distribution. Taking this approach, from these results it ispossible to predict the probability of an occupant injury in a two-car collision, p, in terms of the mass of the occupant’s vehicle, m,, the ratio of the masses of the colliding vehicles, m,/mz, relative speed at impact, ]c, - ~~1,and the use of a restraint system. The mathematical equation which yielded the probability of an occupant injury is?
where I?, is a dichotomous variable which takes on value 1 (or 0) if the occupant whose injury probability is being modeled is unrestrained (or restrained). The Injury Threshold Model was subjected to rigorous statistical tests using available field accident data. In these tests, the injury criterion used was “severe” or “fatal” injuries. In police accident data, these injuries are coded as “A” and “K” respectively. However, in the MDA1 data the severity of injuries is coded on the Abbreviated Injury Scale; on this scale, injury levels of 3 or more were used. Statistical tests using available field accident data showed that ITM performed well with respect to a number of criteria that characterize a good model. For a discussion of the criteria and the statistical tests, see Krishnan et al. [ 19831. Two sets of field accident data were used to calibrate ITM: New York State police accident data and the Multidisciplinary Accident Investigation data. The New York State police accident data consist of all of the police-reported accidents in that state occurring in 1971 and 1972. These data were compiled by the New York State Department of Motor Vehicles, and contained such variables as seat belt use, vehicle weight, model year, driver age and vehicle impact area. Over 300,000 accidents are contained in this data base. The second data base results from in-depth accident investigations that have been made on a subset of police-reported accidents by special teams of trained investigators. The latter are known as Multidisciplinary Accident Investigation (MDAI) teams. For each selected accident case, information on over 800 variables is recorded by MDA1 teams on special forms known as Collision fThe mathematical derivation details are not provided here.
of the model
is given in Krishnan
et al.
] 19831.
For the sake of brevity.
the mathematical
Performance Injury Report (CPIR). Detailed information on these variables is given in Marsh [19781. Several thousand accidents are investigated each year by MDA1 teams. Unfortunately, neither of the two data sets contained adequate information on the closing speed. While the closing speed information was totally absent in the New York State police accident data, the information was missing for most of the cases in the MDA1 data. Even for the few cases for which the information was available, the closing speed was estimated subjectivley by investigators using photographic evidences of cars involved in accidents. Our preliminary analysis using the closing speed information showed that the information was extremely unreliable. So we decided to exclude closing speed from our analysis. Table 2 shows the estimates of the ITM parameters obtained for two car accidents using New York state police accident data and the accident data collected by multidisciplinary accident investigation (MDAI) teams. Because of the limitations of the data, these estimates were obtained using only driver injury information. As mentioned previously, the injury criterion used was severe or fatal injuries. The parameters were estimated using the multiple- linear regression technique after making necessary transformation of variables. All parameters were significant at 95% level of significance. The multiple correlation coefficient, R’, was 0.67 indicating statistically good fit of the model to the data. Using split samples, it was demonstrated that ITM predicted overall number of injuries far better than any of the conventional regression models reported in the literature. The next section presents an algebraic expression for RSE derived from ITM and a comparison of the influence of a restraint system use with that of car size on occupant protection. ANALYSIS Dericntion of RSE As shown in eqn (l), RSE can be expressed in terms of the probabilities unrestrained and restrained occupant, p,, and pb RSE = 100 x (P,, - PIJP,, Using ITM, the values of p,, and pb can be determined In(llp,-1)--n+
of injury to an
(1)
from eqns (3) and (4)
b,Inm,+bz[ln(l+m,/m~)-InIc,-~~(l-b,
In(l/ph-1)=a+b,Inm,+bZ[ln(l+m,/m2)-In/c,-vz]].
(3) (4)
Hence, In (l/p,, - 1) = In (I/p,, - I) + b!
(3
or
lnl-pb -.-_ l--P,
h-b, Pb
3
(6)
From eqn (I), we get pb = p,,( l - RSE/lOO).
(7)
Empirical
estimates
of seat belt effectiveness
in two-car
131
collisions
Substituting this expression for pb in eqn (6), and solving for RSE gives RSE = 100x (1 - p,)/(k - pJ
(8)
where k=[l-exp(-b,)]-‘.
(9)
Since the estimates of b, shown in Table 2 are all positive. the value of k is greater than one for both New York and MDA1 data sets. Hence for pUranging from 0 to 1, RSE is a decreasing function of p,,. This phenomenon is partially supported by Fig. 1which shows a declining relationship between reported estimates of RSE and the corresponding values of p(,, given in Table 1.
In case of a collision between a large car and a small car, occupants of the large car genernllv suffer fewer and/or less severe injuries than those of the small car [Scott, 19761.It is also known that restrained occupants generally suffer fewer and/or less severe injuries than unrestrained occupants [General Motors Corporation, 19761.Therefore, an occupant of a car can enhance his protection against possible injuries in case of an automobile accident either by using a larger car or by using the available restraint system. Thus, if an occupant does not use a restraint system he can still ensure the same level of protection (in a statistical sense) as a restrained occupant by selecting a sufficiently larger sized vehicle for his travels. In this section we wish to determine the increase in car size required to offset the loss in protection that would be caused by not using a restraint system.
r, 100
-1
90
80
.
.
.
70
. :
60' l
. .
53'
.
RSE
.
(%I .
40 .
.
.
.
. .
30.
. 20-
lO_
O_
.I
I 0
0.05
0.10
Fig.
I 0.15
I. RSE estimates
I
I
I
0.20
0.25
0.30
reported
in the literature
I 0.35
vs pu.
I O.&O
-,
P
u
231
K. S. KRISHNAZ
Suppose that an occupant who is restrained is involved in an automobile accident. in which his car of mass m, collides with another car of mass mZ. The probability that the restrained occupant would suffer an injury, pb, can be determined from eqn (4). Suppose that the occupant who was previously assumed to be restrained at the time of the crash is indeed unrestrained and that the mass of his car is m, + Am,. instead of m,. Let pU denote the probability of an injury to the same occupant who is unrestrained. Then pI, can be determined by substituting m, + Am, for m, in eqn (3). Note that Am, is the additional mass required to enhance the level of occupant protection to that of a restrained system usage. ln(li~,,-1)=a+b,In(m,+Am,)+b~[ln{l+(m,tAm,)/m~}-In~~,-c~~l-b~ Equating
the right-hand
(3a)
sides of eqns (4) and (3a) gives
a+b,lnm,+b~[ln(l+m,/mz)-ln~u,-uz~]=a+b,In(m,+Am,) t bJln{l Equation
t (m,+Am,)/m2}-InIu,
(10) can be rewritten
- uz]]- bJ.
(10)
as
b,In(l+Am,/m,)+
b~In(l+Am,)/(m,+mz)=
bl.
(11)
The value of Am, can be determined from eqn (1 I) by trial and error. The existence of a solution to eqn (11) when bJ > 0 is guaranteed by the fact that the left-hand side of eqn (11) is a continuous function which increases from 0 (when Am, = 0) to infinity (when Am, is increased indefinitely).t RESULTS
Table 3 provides estimates of p,,, p,, and RSE obtained for several values of m, and my. As mentioned previously, the values oep, and pb indicate theoretical estimates of the probability of injury to unbelted and belted drivers respectively in a two-car collision. The injury criterion used was severe or fatal driver injury. These injuries correspond to “A” and “K” injuries in the police accident data, and to a level of 3 or more on the Abbreviated Injury Scale. From the table, we observe that for a given m,,the RSE estimate decreases as the other car weight, m?, increases. In other words, the RSE estimate would be the lowest when m, is the largest and vice versa. Since p,, increases with m,,the results are consistent with the trend observed in Fig. 1 where the RSE estimates listed in Table 1 are plotted as function of pU. A consistent finding reported in the safety literature is that for a given data set, the estimates of RSE is higher for accidents where more severe occupant injury levels occur. For example, from Table 1, Rininger et al. report the RSE estimate to be 57% for injuries with AIS 2 2,69% for injuries with AIS b 3 and 77% for injuries with AIS 2 6. Similar trends of RSE estimates increasing with increasing injury severity have been reported in other countries [Bohlin, 1967; Grime, 19791. This finding is consistent with the results of this research. If the occupant injury criterion (AIS) is limited to only severe injuries (e.g. AIS 2 3), the value of pU would be relatively small. From Fig. 1, small values of p,, correspond to large RSE estimates. Table 4 yields values of Am, derived from eqn (11) using New York police data and the MDA1 data. From the table, we note that Am, increases with m,,but decreases with ml. For example, using the New York Police data, when m, equals 2000 lb, Am, increases from 866 lb when m2 equals 2000 to 1069 lb when m, equals 4500 lb. This implies that in the event of a two-car collision, a restrained driver of 2000 lb car enjoys the same level of protection as (1) an unrestrained driver of a 2866 lb car colliding with a 2000 lb car and (2) an unrestrained driver of a 3069 lb car colliding with a 4500 lb car. From the viewpoint of occupant protection, then, the use of a restraint system can be considered as being equivalent to an additional car mass of 866 lb when the weight of the other is 2000 lb. As m, increases to 4500 lb, the additional mass equivalence increases to 1069 lb. The ratio, Ani,/m,, shown in Table 3 expresses this additional mass equivalence as a ratio to the original mass of the car. For all two-car collisions shown in the table, this ratio decreases as m, increases and/or m2 decreases. iThe
parameters
b,.b: and bj are required
to be non-negative
[Krishnan
et al.. 19821
.
Emplrd
estimates of seat belt effectiveness in two-car collisions
Table 3. Restraint system effectiveness estimates from IThi VEHICLE XGS
9
m2
.?lDAI
vEY YORK POLICE DATA
PU
'b
-
DATA RSE(%)
RSE(X)
i
!OOO
2000
0.0791
0.0486
38.5
0.3621
0.2325
32.0
2000
2500
0.0890
0.0549
38.3
0.3706
0.2554
31.0
2000
3000
0.0969
0.0600
38.1
0.3920
0.2731
30.3
2000
3500
0.1034
0.0642
37.9
0.4087
0.2871
29.7
2000
4000
0.1088
0.0676
37.8
0.4220
0.2985
29.2
2000
4500
0.1133
0.0706
37.6
0.4329
5.3579
28.8
2500
2000
0.0589
0.0358
39.0
0.3015
0.2010
33.3
2500
2500
0.0673
0.0412
38.8
0.3316
0.2243
32.3
2500
3000
0.0743
0.0456
38.7
0.3547
0.2426
31.6
2500
3500
0.0801
0.0493
38.5
0.3731
0.2575
30.9
2500
4000
0.0851
0.0524
38.4
0.3879
0.2697
30.4
2500
4500
0.0893
0.0551
38.3
0.4003
0.2800
30.0
3000
2000
0.0455
0.0276
39.4
0.2684
0.1762
34.3
3000
2500
0.0528
0.0321
39.2
0.2991
0.1991
33.4
3000
3000
0.0589
0.0359
39.0
0.3232
0.2177
32.6
3000
3500
0.0642
0.0392
38.9
0.3426
0.2329
32.0
3000
4000
0.0686
0.0420
38.8
0.3585
0.2457
31.4
3000
4500
0.0725
0.044li
38.7
0.3719
0.2565
31.0
3500
2000
0.0363
0.0219
39.6
0.2410
0.1561
35.2
3500
2500
0.0426
0.0257
39.5
0.2716
0.1785
34.2
3500
3000
0.0479
0.029L
39.3
0.2961
0.1969
33.5
3500
3500
O.OS26
0.0320
39.2
0.3161
0.2122
32.8
3500
4000
0.0567
0.0345
39.1
0.3328
0.2252
32.3
3500
4500
0.0602
0.0367
39.0
0.3469
0.2364
31.8
4000
2000
0.0296
0.0178
39.8
0.2179
0.1397
35.8
4000
2500
0.0351
0.0211
39.6
0.2680
0.1612
34.9
4000
3000
0.0398
0.0241
39.5
0.2726
0.1792
34.2
0.0266
39.4
0.2930
0.1945
33.6
4000
3500
0.0440
4000
4000
0.0477
0.0289
39.3
0.3101
0.2076
33.0
4000
4SOO
0.0509
0.0309
39.2
0.3247
0.2189
32.5
4500
2000
0.0246
0.0148
39.9
0.1982
0.1259
36.4
4500
2500
0.0294
0.0177
39.8
0.2277
0.1466
35.6
4500
3000
0.0336
0.0203
-39.7
0.2521
0.1641
34.8
4360
1500
o.om
0.0225
39.6
0.2725
0.1792
34.2
I 4500
4000
0.0407
0.0246
39.5
0.2899
0.1922
33.7
4500
4500
0.0437
0.0264
39.4
0.3068
0.2035
33.2
-
-
Table 4. Rejtraint
system used 3s an equi~alencr
to inirsascd
car height. Am,
L
=1 2000
lrn
g2 2500 2500
/
1
Cll+:lD
1
-I
I
866
2866
o.a33il
16::
z,
*:m _ 1
I
‘.rnL”2,
T367:
3.8360
,
3.9165
916
2916
0.4580
1333
3000
960
2960
0.4aoo
1987
3987
2000
3500
1000
3000
0.5000
2136
4:36
2000
4000
1036
3036
0.5140
22ao
4230
1.1400
2000
4500
1069
3069
0.5345
2LL9
4419
1.2095
0.9935 /
0.9935
2500
2000
1029
3529
0.4116
192L
4424
0.7696
2500
2500
1083
3583
0.4332
2090
4590
0.8360
2252
4752
0.9008
2500
3000
1133
3633
0.4532
2500
3500
1178
367.3
0.4712
2500
4000
1220
3720
0.4880
2500
4500
1259
3759
0.5036
3000
2000
1187
4187
0.3957 0.4150
3000
2500
1245
4245
3000
3000
1299
4299
0.4330
3000
3500
1349
4349
0.4497
3000
4000
1396
4396
0.4653
3000
4500
1439
4439
0.4797
3500
2000
1343
4843
0.3837
3500
2500
1405
4905
0.4014
3500
3000
1462
4962
0.4177
3500
3500
1516
5016
0.4331
3500
4000
1566
5066
0.4474
3500
4500
1613
5113
0.4609
2000
1497
5497
0.3742
4300
2503
156:
5362
5.39Jj
4000
3000
1622
5622
0.4055
4000
3500
1679
5679
0.4197
4000
4000
1732
5732
0.4330
4000
4500
1783
5703
0.4457
4500
2000
1651
6152
0.3669
4000
L 2408
4908
0.9632
2559
5059
1.0236
2706
5206
1.0824
2171
5171
0.7237
2342
5342
0.7807
2508
5jOa
0.8860
2670
56;l)
0.8900
2827
55:;
0.9423
2981
0.9937
2415
5915
0.6900
2590
6090
0.7400
2760
6260
0.7886
2926
6426
0.8360
3088
6588
0.8823
3247
67P7
0.9277
2658
6658
0.6645
2636
0030
0.7oro
4009
7009
0.7522
3179
7179
0.7947
3344
7344
0.8360
3507
7507
0.8767
2900
7400
0.6444
3080
7580
0.6844
1
1
I
4500
2500
1717
6217
1
0.3816
i
4500
3000
1780
62.30
0.3956
3256
7756
0.7236
7?,P
3.7619
so97
Q500
31,IJ
la39
6339
I,. mn7
>1.,R
Lb33
4500
1895
$396
C.4213
3597
4500
4500
1949
6449
0.4331
I
8262
3762 i
I
1.7297 0.8360
Empirical
estimates
of seat belt effectiveness
in two-car
collisions
135
For the New York data, the ratio 1m,/m, varies between 0.3669 and 0.5345: for the MDA1 data, it varies between 0.644 and 1.2095. Taking their average values we conclude that, from the occupant safety’s point of view, using a restraint system is equivalent to increasing car size by approximately 107~ for the New York data and 85% for the MDA1 data. Since MDA1 data contain many more cases of severe accidents than the New York data, the results indicate that. in terms of car size equivalence. the use of restraint systems affords a relatively high level of occupant protection in case of a severe accident. DISCUSSION
Restraint system effectiveness (RSE) is commonly defined as the percent reduction in the probability of an occupant injury when an occupant chooses to use an available restraint system (e.g. a seat belt). Although the RSE estimates reported in the literature vary considerably, there can be no doubt that the use of a restraint system affords substantial protection to occupants in case of automobile crashes. The results of this research indicate that by and large, RSE estimates would be large when pu is small, that is, when occurrence of an occupant injury in an automobile crash is relatively rare. This conclusion is supported by Fig. 1which shows a declining relationship between reported RSE estimates and the corresponding estimates of pl, given in Table 1. Thus RSE estimates can be misleading when they are not accompanied by estimates of p,,; the value of RSE alone is insufficient for comparing the effectiveness of restraint systems. Increasing numbers of smaller cars are being sold in the market in order to meet fuel economy requirements of consumers. Since it is well known that occupants of smaller cars face somewhat higher risks of injury in the event of an automobile accident, one way of offsetting these higher risks is to persuade the occupants of smaller cars to use available restraint systems at all times during their travel. This research shows that-the use of a restraint system would decrease the probability of severe or fatal injuries in the event of a two-car accident by at least 28.9% (from 0.43 for unbelted drivers to 0.31 to belted drivers). Inveterate non-users of available restraints could still offset higher risks associated with small cars, if they decided to travel in a car slightly larger than the one used by restrained occupants. Table 3 shows the increase in car size required to compensate the non-use of restraint systems. Since the MDA1 data were obtained from a non-statistical sample of police reported accident data, they are likely to be statistically biased. On the other hand, police accident data are comprised of all accidents reported to the police. Consequently, barring the few unreported accidents, police data are likely to be representative of automobile accidents occurring nationally both in their relative frequency and severity. Thus, we conclude that the use of a restraint system affords approximately the same level of protection in a two-car collision as would a 40% increase in car size. REFERENCES Bohlin N. J.. A statistical analysis of 28.000 accident cases with emphasis on occupant restraint value, Proc. I I fh Strapp Car Crash Conf.. Society of .4utomotive Engineers, New York, 299-316, 1967. Committeeon Medical Aspects of .4utom&ve Safety. Rating the severity of tissue damage, JAM.4. 213(Z), 277-280. 1971. Cromack J. R. and Mason R. L.. Restraint system use and misuse. Proc. 20th Conf. of AAAM. Atlanta. 367-381, 1976. Dutt 4. and Reinfurt D. W.. Accident involvement and crash injury rates by make:mddel and year of the car, a follow-up. HSRC. Chapel Hill, 1977. General Motors Corporation. Response to proposal to amend MVSS 208-occupant crash protection (OST DKT. No. U: N. 76-S). USG IJ10 Part 111. 1976. Grime G.. The protection afforded by seat belts. Transport and Road Research Laboratory. Supplement report -U9. ISSN0305-1315. Criwthorne. U.K.. 1979. Hochberg Y. and Reinfurt D. W.. An investigation of seat belt usage and effectiveness, Interim report DOT-HU-00897 (SYOSS). HSRC.Chapel Hill, 1975 Insurance Institute for Highway Safely. How air-bags and seat belts complement each other. Stators Report ll(7). 6-8, 1976. Huelke D. F.. Lawson T. E.. Scott R. and ,Uarsh J. C. IV. The effectiveness of belt systems in frontal and roll over crashes, Paper presented at Inf. Automofice Engineering Congress and Exposifion. SAE. 1977. Kahane C. J., Lee S. N. and Smith R. A.. A program to evaluate active restraint effectiveness. Proc. 4fh Inr. Congress on Arrtomorice Sa/ery, 321-348. 1975. Kahane C. 1.. Usage and effectiveness of seat shoulder belts in rural Pennsylvania accidents. Technical note N43-31-5. DOT-HS-801 398. Office of Statistics and Analysis. NHTSA, 1974. Krishnan K. S.. Carnahan J. V. and Beckmann M. J.. An injury threshold model for two-carcollisions. TI&1S, forthcoming issue. 1983. Krishnan K. S.. Evaluation of an injury threshold model using field accident data. Faculty Working Paper Series. Wayne State University. I98 I.
236 Marsh
K. S. KRISHVAX J. C.. Review
of multidisciplinary accident investigation (MDXI) report on automation and ultilization progam. HIT .4nn Arbor. 19X. Mohan D.. Zador P.. O’Neill B. and Ginsburg X, Air bags and lap shoulder belts-a comparison of their effectiveness in real world. frontal crashes. Document I transmitted by letter to DOT. IIhs. LVashington. D.C.. 1976. O’Neill B.. Joksch H. and Haddon W.. Relationship between car size, car &eight and crash injuries in car-to-car crashes. Proc. 3rd ht. Congress on r\utomorice Safety. San Francisco, 197-t. Reihfurt 0. W.. Silva C. Z. and Hochberg Y.. .A statistical analysis of seat belt effectiveness in 1973-75 model cars involved in tow-away crashes, DOT-HS-S-01255. HSRC. Chapel Hill. l9?5. Rininger A. R. and Boak R. W.. Lap/Shoulder belt effectiveness. Proc. 20th Coni. .~.-\.-M Atlanta, 262-279. 1976. Robertson L. S.. Estimates of motor vehicle seat belt effectiveness and use: implications for occupant crash protection, AJPH 66(9). 859-864. 1976. Scott R. E.. Flora J. D. and Marsh J. C. IV. ;\n evaluation of the 1971 and 19’5 restraint systems. Special report, UM-HSRI-7Gl3. HSRI, Ann Arbor. 1976. Sherman H. W.. Murphy M. J. and Huelke D. F.. A reappraisal of the use of police injury codes in accident data analysis. 1976.
Lob Reports 3(6). HSRI.
Wilson R. .4. and Savage C. M.. Restraint system effectiveness-a Sale0 seminor. GM Training Center. Warren, 1973.
study of fatal accidents.
Paper presented
at Automotive
State University,
II March 1982:
KRISHNAN Detroit.
MI 45202.
in revised form
U.2.A.
Ii September
1932)
Abstract-The objective of this research is to quantify occupant protection afforded by restraint systems in two-car head-on collisions. An accepted measure of occupant protection is “Restraint SyBtem Effectiveness” (RSE).This quantity is defined as the percent reduction in the probability of an occupant Injury due to the use of a restraint system. RSE estimates are calculated in the present paper using a previously developed mathematical model of occupant injuries in two-car collisions and obtaining parameter estimates from two data sets. The two sets of data used for estimating RSE are: New York police accident data and data collected by various multidisciplinary accident investigation teams. Both these data sets have been reported in the literature. The RSE estimates obtained from the two data sets range from 29 lo 40%. These estimates are shown to increase as the mass of the occupant’s vehicle increases, but decrease as the mass of the other colliding vehicle increases. On the average, the use of a restraint system can offset the decrease in occupant protection that would result from a 407.5 reduction in car weight. Consequently, the use of restraint systems 10 reduce occupant risk is estimated lo be even more important as the number of small vehicles in the U.S. vehicle fleet increases. INTRODUCTION
Restraint systems in automobiles are designed to protect occupants in case of automobile accidents. Because of the variety of ways in which automobile crashes can occur, the extent to which occupants are protected by a restraint system depends upon the type of accident (e.g. rollover, two-car collisions, etc.), where occupants are sittin g, seating posture and many other factors. Furthermore, a restraint system’s ability to protect occupants can be severely limited if the restraints are not properly used (for example, if seat belts are not worn snugly, as recommended by manufacturers). The objective of this research is to quantify restraint system effectiveness in two-car collisions. Such quantification would enable evaluation of the effectiveness of restraint system use relative to car size. Several studies reported in the literature have provided estimates of occupant protection for different restraint systems (e.g. seat belts and air cushion restraint systems) for a variety of accident types (e.g. rollover and two-car head-on collisions) [IIHS, 1976; Huelke et al., 1977; Mohan et al., 1976; Wilson et a!., 19731. Results of these studies are briefly summarized in Table 1. An accepted measure of occupant protection common to all of these studies is the percent reduction in the probability of an occupant injury where this reduction is attributable to the use of a restraint system at the time of an accident. Such a quantity is referred to in the literature as “Restraint System Effectiveness” (RSE) [IIHS, 1976; Kahane, 1975; Rininger et al., 1976; Robertson, 19761. Specifically, let p,, = the probability of an injury to an unrestrained in case of an automobile accident, and
occupant
pb = the probability of an injury to the sanle occupant had been restrained at the time of the accident. Restraint
System Effectiveness
is then expressed
if he
as
RSE = lfio X (pu - pb)/p, .
(1)
Note that p,, and pb denote probabilities of an injury to the same occupant with and without the use of a restraint system respectively, at the time of an accident. Since, at the time of an accident, an occupant is either restrained or unrestrained, but not both, estimating RSE theoretically requires the capability of reconstructing a given accident situation in order to estimate the values of pu and
I IC?~,l.
1
PE!GSYL7ISI.I /
La
CROSS
T.~auL.ATImI La
OCCWSZj DRIVE3
j :x , i ,
DRIVER
~:c..r\,a.c
La La+SH
LB+SH Ka+SH CROSS La TABULATIOS LBCSH
SOUTH CESTFUL TE.US USA
CROSS LBfSH TABULATION LB+SH LBfSH
OAKLAXD AXD
REGRESSION ON FRONTAL5 0h-I.Y REGRESSION ON ALL DIRECTIONS
42 -2 Ir 11
a ,i:
12” i AIS 2 FROYI i AIS 3 SEAT OCCLlP‘vcTsi FRONT pTy,,i;ig a
L
0.26 0.14 '0.13 0.061 ~.0043 0.9017 T 0.26 il.15 0.13 ,!).I52 3.0063'I).,30 I I '3.12 ;0.,:52 0.12 /0.3:8
t
%c 53 73 zi 60 00 io 61 T769 77
(FATAL) WASHTENAW COIJXTIES, XICHIGrLU
LB LB+SH LB
FRONT
AIS
2
KwcSl FRONT
AIS
2
LBfSH
SEAT occuP‘k%Ts FRONT SEAT OCCUPkVS FRONT
XORTH
CROSS
LB
AZRICA (USA + CASXIA)
TABULATION, FRONTALS ONLY
LBfSH La
t
-Gi 54 21 42
3 AIS
25 47 5
AIS
i
6
62 77
i
5 58
q.,:;
-
_L
ACRS
=
AIR CUSHIOS - RESTRAIXT SYSTEM (AIR BAG) La = LAP aELn ONLY
La+SH AIS
= LAP BELTS = &JaREVIATED
AND SHOULDER HARNESSES INJ!J~~ SCALE (COWITTEE
ON XDICAL
ASPECTS
OF AUTOFOTIVE SAFER,
K.A,a,C
= POLICE
CODES
FOR
INJURY
CLASSIFICATION
(SHEMAX
ET
AL.
,
1971).
1976)
ph simultaneously. An attempt to develop such a capability was made previously by developing a mathematical model of occupant injuries in two-car collisions [Krishnan et al., 1983; Krishnan, 19811. This model has been used in the present research to derive estimates of RSE. Some of the RSE estimates reported in the literature were based on a similar modeling approach [Dutt et al., 1977; Reinfurt et (11..19751. These studies used a linear regression model to statistically control variations in data. This research differs from the above studies in that the mathematical model used here was developed from consideration of principles of collision mechanics. Because of the causal nature of the model. it depicts the occurrence of occupant injuries far more accurately than regression models [Krishnan et al., 1983; Krishnan, 19811. Alternatively, RSE can be estimated by selecting random samples of unrestrained and restrained occupants from available automobile accident records and estimating pU and pb by the fractions of injured occupants in the two samples; substituting these estimates in eqn (1) yields an estimate of RSE. Errors associated with the RSE estimate so obtained can be statistically controlled to some extent by adopting suitable statistical sampling designs in the selection of unrestrained and restrained occupants. Many of the RSE estimates reported in the literature are based on such statistical sampling designs [Hochberg et al., 1975; Huelke et al., 1977; Rininger ef al., 19761. Since models of occupant injuries explicitly identify some of the sources of variations in data, RSE estimates derived from such models are likely to be more accurate than those based merely on sampling designs. A list of RSE estimates from ottier published studies is provided in Table 1. Since these RSE estimates vary considerably (from -2 to 100%). it raises a question as to what, exactly. is the “true” effectiveness of a given restraint system. Of course, no two types of restraint systems are alike in all respects. There are also likely to be differences in their relative effectiveness for different types of accidents. For example. some studies have shown that an air cushion restraint system is more effective than seat belts in preventing fatalities in head-on collisions, but less effective in rollover
Empirical
estimates
of
seat belt effectiveness
in two-car
collisions
219
crashes [IIHS. 1976; Mohan et al., 19761. The range of RSE estimates shown in Table I suggest that the variability in these estimates might have been caused by the differences in the following factors: data collection design, statistical techniques used in estimating RSE and the level of injury severity used in classifying whether an occupant was injured or not. As such, values of RSE obtained from different studies are not directly comparable. Furthermore, since occupant protection provided by restraint system use is such an important element in understanding accidents, it is necessary to investigate reasons for these variations in RSE estimates. This is addressed here. As mentioned earlier, estimates of RSE developed in this research are based on a mathematical model of an occupant injury, called the Injury Threshold Model (ITM). ITM was developed from consideration of the physics of two-car collisions and incorporates the notion of a threshold of human tolerance to impact forces. A brief description of ITM and some highlights of results obtained previously are provided in the next section.
INJURY
THRESHOLD
MODEL
An injury model was developed to predict the probability of an injury to an occupant of a vehicle involved in a two-car collision. The model incorporates principles of collision mechanics and a concept of a threshold of human tolerance to impact forces. The model was based on the idea that if the impact forces experienced by an occupant in a two-car collision exceed the threshold of the tolerance, an injury occurs; otherwise, no injury occurs. From the physics of the collision, the forces experienced by an occupant can be determined in terms of the deceleration of the center of gravity of the vehicle and the motion of the occupant relative to the center of gravity. The threshold of human tolerance to impact forces is modeled from experimental evidence with laboratory animals and other biological experiments. These data suggest the existence of a threshold of tolerance which can be considered to be a random variable with a logistic distribution. Taking this approach, from these results it ispossible to predict the probability of an occupant injury in a two-car collision, p, in terms of the mass of the occupant’s vehicle, m,, the ratio of the masses of the colliding vehicles, m,/mz, relative speed at impact, ]c, - ~~1,and the use of a restraint system. The mathematical equation which yielded the probability of an occupant injury is?
where I?, is a dichotomous variable which takes on value 1 (or 0) if the occupant whose injury probability is being modeled is unrestrained (or restrained). The Injury Threshold Model was subjected to rigorous statistical tests using available field accident data. In these tests, the injury criterion used was “severe” or “fatal” injuries. In police accident data, these injuries are coded as “A” and “K” respectively. However, in the MDA1 data the severity of injuries is coded on the Abbreviated Injury Scale; on this scale, injury levels of 3 or more were used. Statistical tests using available field accident data showed that ITM performed well with respect to a number of criteria that characterize a good model. For a discussion of the criteria and the statistical tests, see Krishnan et al. [ 19831. Two sets of field accident data were used to calibrate ITM: New York State police accident data and the Multidisciplinary Accident Investigation data. The New York State police accident data consist of all of the police-reported accidents in that state occurring in 1971 and 1972. These data were compiled by the New York State Department of Motor Vehicles, and contained such variables as seat belt use, vehicle weight, model year, driver age and vehicle impact area. Over 300,000 accidents are contained in this data base. The second data base results from in-depth accident investigations that have been made on a subset of police-reported accidents by special teams of trained investigators. The latter are known as Multidisciplinary Accident Investigation (MDAI) teams. For each selected accident case, information on over 800 variables is recorded by MDA1 teams on special forms known as Collision fThe mathematical derivation details are not provided here.
of the model
is given in Krishnan
et al.
] 19831.
For the sake of brevity.
the mathematical
Performance Injury Report (CPIR). Detailed information on these variables is given in Marsh [19781. Several thousand accidents are investigated each year by MDA1 teams. Unfortunately, neither of the two data sets contained adequate information on the closing speed. While the closing speed information was totally absent in the New York State police accident data, the information was missing for most of the cases in the MDA1 data. Even for the few cases for which the information was available, the closing speed was estimated subjectivley by investigators using photographic evidences of cars involved in accidents. Our preliminary analysis using the closing speed information showed that the information was extremely unreliable. So we decided to exclude closing speed from our analysis. Table 2 shows the estimates of the ITM parameters obtained for two car accidents using New York state police accident data and the accident data collected by multidisciplinary accident investigation (MDAI) teams. Because of the limitations of the data, these estimates were obtained using only driver injury information. As mentioned previously, the injury criterion used was severe or fatal injuries. The parameters were estimated using the multiple- linear regression technique after making necessary transformation of variables. All parameters were significant at 95% level of significance. The multiple correlation coefficient, R’, was 0.67 indicating statistically good fit of the model to the data. Using split samples, it was demonstrated that ITM predicted overall number of injuries far better than any of the conventional regression models reported in the literature. The next section presents an algebraic expression for RSE derived from ITM and a comparison of the influence of a restraint system use with that of car size on occupant protection. ANALYSIS Dericntion of RSE As shown in eqn (l), RSE can be expressed in terms of the probabilities unrestrained and restrained occupant, p,, and pb RSE = 100 x (P,, - PIJP,, Using ITM, the values of p,, and pb can be determined In(llp,-1)--n+
of injury to an
(1)
from eqns (3) and (4)
b,Inm,+bz[ln(l+m,/m~)-InIc,-~~(l-b,
In(l/ph-1)=a+b,Inm,+bZ[ln(l+m,/m2)-In/c,-vz]].
(3) (4)
Hence, In (l/p,, - 1) = In (I/p,, - I) + b!
(3
or
lnl-pb -.-_ l--P,
h-b, Pb
3
(6)
From eqn (I), we get pb = p,,( l - RSE/lOO).
(7)
Empirical
estimates
of seat belt effectiveness
in two-car
131
collisions
Substituting this expression for pb in eqn (6), and solving for RSE gives RSE = 100x (1 - p,)/(k - pJ
(8)
where k=[l-exp(-b,)]-‘.
(9)
Since the estimates of b, shown in Table 2 are all positive. the value of k is greater than one for both New York and MDA1 data sets. Hence for pUranging from 0 to 1, RSE is a decreasing function of p,,. This phenomenon is partially supported by Fig. 1which shows a declining relationship between reported estimates of RSE and the corresponding values of p(,, given in Table 1.
In case of a collision between a large car and a small car, occupants of the large car genernllv suffer fewer and/or less severe injuries than those of the small car [Scott, 19761.It is also known that restrained occupants generally suffer fewer and/or less severe injuries than unrestrained occupants [General Motors Corporation, 19761.Therefore, an occupant of a car can enhance his protection against possible injuries in case of an automobile accident either by using a larger car or by using the available restraint system. Thus, if an occupant does not use a restraint system he can still ensure the same level of protection (in a statistical sense) as a restrained occupant by selecting a sufficiently larger sized vehicle for his travels. In this section we wish to determine the increase in car size required to offset the loss in protection that would be caused by not using a restraint system.
r, 100
-1
90
80
.
.
.
70
. :
60' l
. .
53'
.
RSE
.
(%I .
40 .
.
.
.
. .
30.
. 20-
lO_
O_
.I
I 0
0.05
0.10
Fig.
I 0.15
I. RSE estimates
I
I
I
0.20
0.25
0.30
reported
in the literature
I 0.35
vs pu.
I O.&O
-,
P
u
231
K. S. KRISHNAZ
Suppose that an occupant who is restrained is involved in an automobile accident. in which his car of mass m, collides with another car of mass mZ. The probability that the restrained occupant would suffer an injury, pb, can be determined from eqn (4). Suppose that the occupant who was previously assumed to be restrained at the time of the crash is indeed unrestrained and that the mass of his car is m, + Am,. instead of m,. Let pU denote the probability of an injury to the same occupant who is unrestrained. Then pI, can be determined by substituting m, + Am, for m, in eqn (3). Note that Am, is the additional mass required to enhance the level of occupant protection to that of a restrained system usage. ln(li~,,-1)=a+b,In(m,+Am,)+b~[ln{l+(m,tAm,)/m~}-In~~,-c~~l-b~ Equating
the right-hand
(3a)
sides of eqns (4) and (3a) gives
a+b,lnm,+b~[ln(l+m,/mz)-ln~u,-uz~]=a+b,In(m,+Am,) t bJln{l Equation
t (m,+Am,)/m2}-InIu,
(10) can be rewritten
- uz]]- bJ.
(10)
as
b,In(l+Am,/m,)+
b~In(l+Am,)/(m,+mz)=
bl.
(11)
The value of Am, can be determined from eqn (1 I) by trial and error. The existence of a solution to eqn (11) when bJ > 0 is guaranteed by the fact that the left-hand side of eqn (11) is a continuous function which increases from 0 (when Am, = 0) to infinity (when Am, is increased indefinitely).t RESULTS
Table 3 provides estimates of p,,, p,, and RSE obtained for several values of m, and my. As mentioned previously, the values oep, and pb indicate theoretical estimates of the probability of injury to unbelted and belted drivers respectively in a two-car collision. The injury criterion used was severe or fatal driver injury. These injuries correspond to “A” and “K” injuries in the police accident data, and to a level of 3 or more on the Abbreviated Injury Scale. From the table, we observe that for a given m,,the RSE estimate decreases as the other car weight, m?, increases. In other words, the RSE estimate would be the lowest when m, is the largest and vice versa. Since p,, increases with m,,the results are consistent with the trend observed in Fig. 1 where the RSE estimates listed in Table 1 are plotted as function of pU. A consistent finding reported in the safety literature is that for a given data set, the estimates of RSE is higher for accidents where more severe occupant injury levels occur. For example, from Table 1, Rininger et al. report the RSE estimate to be 57% for injuries with AIS 2 2,69% for injuries with AIS b 3 and 77% for injuries with AIS 2 6. Similar trends of RSE estimates increasing with increasing injury severity have been reported in other countries [Bohlin, 1967; Grime, 19791. This finding is consistent with the results of this research. If the occupant injury criterion (AIS) is limited to only severe injuries (e.g. AIS 2 3), the value of pU would be relatively small. From Fig. 1, small values of p,, correspond to large RSE estimates. Table 4 yields values of Am, derived from eqn (11) using New York police data and the MDA1 data. From the table, we note that Am, increases with m,,but decreases with ml. For example, using the New York Police data, when m, equals 2000 lb, Am, increases from 866 lb when m2 equals 2000 to 1069 lb when m, equals 4500 lb. This implies that in the event of a two-car collision, a restrained driver of 2000 lb car enjoys the same level of protection as (1) an unrestrained driver of a 2866 lb car colliding with a 2000 lb car and (2) an unrestrained driver of a 3069 lb car colliding with a 4500 lb car. From the viewpoint of occupant protection, then, the use of a restraint system can be considered as being equivalent to an additional car mass of 866 lb when the weight of the other is 2000 lb. As m, increases to 4500 lb, the additional mass equivalence increases to 1069 lb. The ratio, Ani,/m,, shown in Table 3 expresses this additional mass equivalence as a ratio to the original mass of the car. For all two-car collisions shown in the table, this ratio decreases as m, increases and/or m2 decreases. iThe
parameters
b,.b: and bj are required
to be non-negative
[Krishnan
et al.. 19821
.
Emplrd
estimates of seat belt effectiveness in two-car collisions
Table 3. Restraint system effectiveness estimates from IThi VEHICLE XGS
9
m2
.?lDAI
vEY YORK POLICE DATA
PU
'b
-
DATA RSE(%)
RSE(X)
i
!OOO
2000
0.0791
0.0486
38.5
0.3621
0.2325
32.0
2000
2500
0.0890
0.0549
38.3
0.3706
0.2554
31.0
2000
3000
0.0969
0.0600
38.1
0.3920
0.2731
30.3
2000
3500
0.1034
0.0642
37.9
0.4087
0.2871
29.7
2000
4000
0.1088
0.0676
37.8
0.4220
0.2985
29.2
2000
4500
0.1133
0.0706
37.6
0.4329
5.3579
28.8
2500
2000
0.0589
0.0358
39.0
0.3015
0.2010
33.3
2500
2500
0.0673
0.0412
38.8
0.3316
0.2243
32.3
2500
3000
0.0743
0.0456
38.7
0.3547
0.2426
31.6
2500
3500
0.0801
0.0493
38.5
0.3731
0.2575
30.9
2500
4000
0.0851
0.0524
38.4
0.3879
0.2697
30.4
2500
4500
0.0893
0.0551
38.3
0.4003
0.2800
30.0
3000
2000
0.0455
0.0276
39.4
0.2684
0.1762
34.3
3000
2500
0.0528
0.0321
39.2
0.2991
0.1991
33.4
3000
3000
0.0589
0.0359
39.0
0.3232
0.2177
32.6
3000
3500
0.0642
0.0392
38.9
0.3426
0.2329
32.0
3000
4000
0.0686
0.0420
38.8
0.3585
0.2457
31.4
3000
4500
0.0725
0.044li
38.7
0.3719
0.2565
31.0
3500
2000
0.0363
0.0219
39.6
0.2410
0.1561
35.2
3500
2500
0.0426
0.0257
39.5
0.2716
0.1785
34.2
3500
3000
0.0479
0.029L
39.3
0.2961
0.1969
33.5
3500
3500
O.OS26
0.0320
39.2
0.3161
0.2122
32.8
3500
4000
0.0567
0.0345
39.1
0.3328
0.2252
32.3
3500
4500
0.0602
0.0367
39.0
0.3469
0.2364
31.8
4000
2000
0.0296
0.0178
39.8
0.2179
0.1397
35.8
4000
2500
0.0351
0.0211
39.6
0.2680
0.1612
34.9
4000
3000
0.0398
0.0241
39.5
0.2726
0.1792
34.2
0.0266
39.4
0.2930
0.1945
33.6
4000
3500
0.0440
4000
4000
0.0477
0.0289
39.3
0.3101
0.2076
33.0
4000
4SOO
0.0509
0.0309
39.2
0.3247
0.2189
32.5
4500
2000
0.0246
0.0148
39.9
0.1982
0.1259
36.4
4500
2500
0.0294
0.0177
39.8
0.2277
0.1466
35.6
4500
3000
0.0336
0.0203
-39.7
0.2521
0.1641
34.8
4360
1500
o.om
0.0225
39.6
0.2725
0.1792
34.2
I 4500
4000
0.0407
0.0246
39.5
0.2899
0.1922
33.7
4500
4500
0.0437
0.0264
39.4
0.3068
0.2035
33.2
-
-
Table 4. Rejtraint
system used 3s an equi~alencr
to inirsascd
car height. Am,
L
=1 2000
lrn
g2 2500 2500
/
1
Cll+:lD
1
-I
I
866
2866
o.a33il
16::
z,
*:m _ 1
I
‘.rnL”2,
T367:
3.8360
,
3.9165
916
2916
0.4580
1333
3000
960
2960
0.4aoo
1987
3987
2000
3500
1000
3000
0.5000
2136
4:36
2000
4000
1036
3036
0.5140
22ao
4230
1.1400
2000
4500
1069
3069
0.5345
2LL9
4419
1.2095
0.9935 /
0.9935
2500
2000
1029
3529
0.4116
192L
4424
0.7696
2500
2500
1083
3583
0.4332
2090
4590
0.8360
2252
4752
0.9008
2500
3000
1133
3633
0.4532
2500
3500
1178
367.3
0.4712
2500
4000
1220
3720
0.4880
2500
4500
1259
3759
0.5036
3000
2000
1187
4187
0.3957 0.4150
3000
2500
1245
4245
3000
3000
1299
4299
0.4330
3000
3500
1349
4349
0.4497
3000
4000
1396
4396
0.4653
3000
4500
1439
4439
0.4797
3500
2000
1343
4843
0.3837
3500
2500
1405
4905
0.4014
3500
3000
1462
4962
0.4177
3500
3500
1516
5016
0.4331
3500
4000
1566
5066
0.4474
3500
4500
1613
5113
0.4609
2000
1497
5497
0.3742
4300
2503
156:
5362
5.39Jj
4000
3000
1622
5622
0.4055
4000
3500
1679
5679
0.4197
4000
4000
1732
5732
0.4330
4000
4500
1783
5703
0.4457
4500
2000
1651
6152
0.3669
4000
L 2408
4908
0.9632
2559
5059
1.0236
2706
5206
1.0824
2171
5171
0.7237
2342
5342
0.7807
2508
5jOa
0.8860
2670
56;l)
0.8900
2827
55:;
0.9423
2981
0.9937
2415
5915
0.6900
2590
6090
0.7400
2760
6260
0.7886
2926
6426
0.8360
3088
6588
0.8823
3247
67P7
0.9277
2658
6658
0.6645
2636
0030
0.7oro
4009
7009
0.7522
3179
7179
0.7947
3344
7344
0.8360
3507
7507
0.8767
2900
7400
0.6444
3080
7580
0.6844
1
1
I
4500
2500
1717
6217
1
0.3816
i
4500
3000
1780
62.30
0.3956
3256
7756
0.7236
7?,P
3.7619
so97
Q500
31,IJ
la39
6339
I,. mn7
>1.,R
Lb33
4500
1895
$396
C.4213
3597
4500
4500
1949
6449
0.4331
I
8262
3762 i
I
1.7297 0.8360
Empirical
estimates
of seat belt effectiveness
in two-car
collisions
135
For the New York data, the ratio 1m,/m, varies between 0.3669 and 0.5345: for the MDA1 data, it varies between 0.644 and 1.2095. Taking their average values we conclude that, from the occupant safety’s point of view, using a restraint system is equivalent to increasing car size by approximately 107~ for the New York data and 85% for the MDA1 data. Since MDA1 data contain many more cases of severe accidents than the New York data, the results indicate that. in terms of car size equivalence. the use of restraint systems affords a relatively high level of occupant protection in case of a severe accident. DISCUSSION
Restraint system effectiveness (RSE) is commonly defined as the percent reduction in the probability of an occupant injury when an occupant chooses to use an available restraint system (e.g. a seat belt). Although the RSE estimates reported in the literature vary considerably, there can be no doubt that the use of a restraint system affords substantial protection to occupants in case of automobile crashes. The results of this research indicate that by and large, RSE estimates would be large when pu is small, that is, when occurrence of an occupant injury in an automobile crash is relatively rare. This conclusion is supported by Fig. 1which shows a declining relationship between reported RSE estimates and the corresponding estimates of pl, given in Table 1. Thus RSE estimates can be misleading when they are not accompanied by estimates of p,,; the value of RSE alone is insufficient for comparing the effectiveness of restraint systems. Increasing numbers of smaller cars are being sold in the market in order to meet fuel economy requirements of consumers. Since it is well known that occupants of smaller cars face somewhat higher risks of injury in the event of an automobile accident, one way of offsetting these higher risks is to persuade the occupants of smaller cars to use available restraint systems at all times during their travel. This research shows that-the use of a restraint system would decrease the probability of severe or fatal injuries in the event of a two-car accident by at least 28.9% (from 0.43 for unbelted drivers to 0.31 to belted drivers). Inveterate non-users of available restraints could still offset higher risks associated with small cars, if they decided to travel in a car slightly larger than the one used by restrained occupants. Table 3 shows the increase in car size required to compensate the non-use of restraint systems. Since the MDA1 data were obtained from a non-statistical sample of police reported accident data, they are likely to be statistically biased. On the other hand, police accident data are comprised of all accidents reported to the police. Consequently, barring the few unreported accidents, police data are likely to be representative of automobile accidents occurring nationally both in their relative frequency and severity. Thus, we conclude that the use of a restraint system affords approximately the same level of protection in a two-car collision as would a 40% increase in car size. REFERENCES Bohlin N. J.. A statistical analysis of 28.000 accident cases with emphasis on occupant restraint value, Proc. I I fh Strapp Car Crash Conf.. Society of .4utomotive Engineers, New York, 299-316, 1967. Committeeon Medical Aspects of .4utom&ve Safety. Rating the severity of tissue damage, JAM.4. 213(Z), 277-280. 1971. Cromack J. R. and Mason R. L.. Restraint system use and misuse. Proc. 20th Conf. of AAAM. Atlanta. 367-381, 1976. Dutt 4. and Reinfurt D. W.. Accident involvement and crash injury rates by make:mddel and year of the car, a follow-up. HSRC. Chapel Hill, 1977. General Motors Corporation. Response to proposal to amend MVSS 208-occupant crash protection (OST DKT. No. U: N. 76-S). USG IJ10 Part 111. 1976. Grime G.. The protection afforded by seat belts. Transport and Road Research Laboratory. Supplement report -U9. ISSN0305-1315. Criwthorne. U.K.. 1979. Hochberg Y. and Reinfurt D. W.. An investigation of seat belt usage and effectiveness, Interim report DOT-HU-00897 (SYOSS). HSRC.Chapel Hill, 1975 Insurance Institute for Highway Safely. How air-bags and seat belts complement each other. Stators Report ll(7). 6-8, 1976. Huelke D. F.. Lawson T. E.. Scott R. and ,Uarsh J. C. IV. The effectiveness of belt systems in frontal and roll over crashes, Paper presented at Inf. Automofice Engineering Congress and Exposifion. SAE. 1977. Kahane C. J., Lee S. N. and Smith R. A.. A program to evaluate active restraint effectiveness. Proc. 4fh Inr. Congress on Arrtomorice Sa/ery, 321-348. 1975. Kahane C. 1.. Usage and effectiveness of seat shoulder belts in rural Pennsylvania accidents. Technical note N43-31-5. DOT-HS-801 398. Office of Statistics and Analysis. NHTSA, 1974. Krishnan K. S.. Carnahan J. V. and Beckmann M. J.. An injury threshold model for two-carcollisions. TI&1S, forthcoming issue. 1983. Krishnan K. S.. Evaluation of an injury threshold model using field accident data. Faculty Working Paper Series. Wayne State University. I98 I.
236 Marsh
K. S. KRISHVAX J. C.. Review
of multidisciplinary accident investigation (MDXI) report on automation and ultilization progam. HIT .4nn Arbor. 19X. Mohan D.. Zador P.. O’Neill B. and Ginsburg X, Air bags and lap shoulder belts-a comparison of their effectiveness in real world. frontal crashes. Document I transmitted by letter to DOT. IIhs. LVashington. D.C.. 1976. O’Neill B.. Joksch H. and Haddon W.. Relationship between car size, car &eight and crash injuries in car-to-car crashes. Proc. 3rd ht. Congress on r\utomorice Safety. San Francisco, 197-t. Reihfurt 0. W.. Silva C. Z. and Hochberg Y.. .A statistical analysis of seat belt effectiveness in 1973-75 model cars involved in tow-away crashes, DOT-HS-S-01255. HSRC. Chapel Hill. l9?5. Rininger A. R. and Boak R. W.. Lap/Shoulder belt effectiveness. Proc. 20th Coni. .~.-\.-M Atlanta, 262-279. 1976. Robertson L. S.. Estimates of motor vehicle seat belt effectiveness and use: implications for occupant crash protection, AJPH 66(9). 859-864. 1976. Scott R. E.. Flora J. D. and Marsh J. C. IV. ;\n evaluation of the 1971 and 19’5 restraint systems. Special report, UM-HSRI-7Gl3. HSRI, Ann Arbor. 1976. Sherman H. W.. Murphy M. J. and Huelke D. F.. A reappraisal of the use of police injury codes in accident data analysis. 1976.
Lob Reports 3(6). HSRI.
Wilson R. .4. and Savage C. M.. Restraint system effectiveness-a Sale0 seminor. GM Training Center. Warren, 1973.
study of fatal accidents.
Paper presented
at Automotive