Fig. 6.5 and 6.6 give the results for system “Warning” with different thresholds for the earliest possible warning. The baseline consists of the 18 million situations as explained in Section 6.1. As the difference in the warning TTC was 0.2 s, each TTC threshold was simulated 100 million times in order to reduce fluctuations in the Monte-Carlo results to a magnitude well below the effect size. All ISS levels in this Section have been computed using Optionc (starting from ISS16+) for the injury probability models (see Subsection 5.4.1).
One would expect as hypothesis that the efficacy for low TTC thresholds converges to zero, as the driver needs a particular time to react, decide on an action, and act in response to a warning.
It can be observed that TTC thresholds between 1.0 s and 2.6 s lead to a stronger reduc-tion of accidents and injury levels as larger TTC thresholds. The simulareduc-tion study confirms
6.4 Efficacy of system “Warning”
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Distribution (av
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Avoided accidents ISS0-8 ISS9-15 ISS16-25 ISS25+
Figure 6.5: Distribution of pedestrian injury severity and avoided accidents due to system
“Warning”.
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ibution (injury severity) [%]
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Figure 6.6: Enlargement of high injury outcome categories of Fig. 6.5.
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Accidents ISS9+ ISS16+ Warnings False-positive warnings
Figure 6.7: Reduction of accidents and injury severities (left axis) as well as warnings (all and false-positive; right axis) given to the driver for system “Warning”.
the hypothesis stated above. Warnings towards a TTC threshold of 1.0 s or smaller evi-dently have only marginal effects.
For the optimization of a system of active or integral safety, not only the positive effects, as given in Fig. 6.5, are important, but also the overall quality of the system and its com-ponents including false positives has to be considered. The number needed to treat (NNT) regarding specific outcome metrics is an appropriate metric as discussed in Section 2.2 (p. 15).
Fig. 6.7 gives the reduction of accidents and injuries relative to the baseline (as ISS25+
is a constant factor relative to ISS16+ in Option c, the relative reduction is identical to ISS16+ and not given in the following graphics). In addition, the number of warnings as well as false-positive warnings issued for each TTC threshold is included. The trends for accidents and injuries have been described above. The number of warnings increases steadily with rising TTC thresholds, with increasing gradient. The earlier a warning is given before a possible accident, the more uncertainty remains in the situation with the pedestrian itself, as more time for avoidance actions by both participants is available. As a result, an increasing number of warnings is given in situations which would not have resulted in accidents and thus are regarded as false-positive warnings.
The number needed to treat (NNT) describes the efficacy of a warning regarding acci-dent avoidance or the avoidance of different injury severities (see Section 2.2). The direct
6.4 Efficacy of system “Warning”
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er avoided accident, true-positive warning
ative reduction (accidents) [%]
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Rel
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Accidents
Warnings per avoided accident Warnings per true-positive warning
Figure 6.8: Number needed to treat for avoidance of accidents for system “Warning”.
relation between warnings and avoided accidents (Fig. 6.8) or injured persons (Fig. 6.9) is quantified by NNT together with the relation of all warnings to true-positive warnings.
Regarding accident avoidance, about 17 warnings must be given in the best case to avoid one accident (this is around 2.2 s TTC).
In relation to avoided accidents, the number of warnings shows a stronger increase with increasing TTC thresholds. For decreasing TTC thresholds, the number of avoided accidents decreases more rapidly in relation to the number of warnings. Thus, the NNT shows a U-like shape depending on the TTC of the earliest possible warning. (As there are no avoided accidents for a TTC of 1.0 s, NNT cannot be computed there.) The NNTs for ISS9+ and 16+ injured persons show a similar U-like shape, but the absolute number of NNT is by far greater than that of avoided accidents. If one assumes that avoiding higher levels of injuries justifies higher efforts, also higher absolute values of NNT are acceptable.
The fewer warnings required per true-positive warning, the more effective the system is with respect to functional costs. This ratio increases with accelerated pace with increasing TTC thresholds.
Finding an optimal system configuration regarding the TTC threshold for a warning can thus follow several lines. The first one sets a goal for accident or injury avoidance and thus uses the reduction given in Figures 6.5 or 6.7. For example, if the desired objective is an accident avoidance of 20 %, a TTC of about 2.4 s would be appropriate. Consequently,
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Warnings per avoided ISS9+ Warnings per avoided ISS16+
Figure 6.9: Number needed to treat for different injury levels for system “Warning”.
using Fig. 6.8, this would result in an NNT for avoided accidents of 18 and 64 per ISS9+
injury (162 per ISS16+ injury). For every true-positive warning, four false-positive warn-ings would be given.
Considering these numbers, the developer can decide whether the system quality is suf-ficient or not. The NNT is especially important if one considers the possible consequences of false-positive system actions. More false activations can lead to lower acceptance or in the worst case to the creation of new critical situations in traffic (see Section 2.2). If the consequences of a false-positive warning are assessed using appropriate experiments, a functional “cost function” can be constructed, giving the number of new accidents cre-ated by false-positive warnings and inappropriate subsequent reactions of the driver. (An appropriate quantification and the definition of such a function would suggest itself for further research.)
Another approach can directly use NNT in order to find the optimal operating point for the system. In this case, a warning between 1.5 s and 2.2 s could be optimal, as all kinds of NNTs for accidents, ISS9+, and ISS16+ have their minimum in that interval.
Additionally taking the desired absolute effect of the system into account and considering the consequences of false-positive activations, an operating point can be defined. For example, if the NNTs for accidents and both injury outcomes should be around their minimum and it is desired to avoid about 15 % of accidents, a TTC of 1.9 s could be chosen.
6.4 Efficacy of system “Warning”
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Marginal co Warnings
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Marginal costs per avoided ISS9+ Marginal costs per avoided ISS16+
Marginal costs per avoided accident Warnings per avoided accident Warnings per avoided ISS9+ Warnings per avoided ISS16+
Figure 6.10: Absolute and marginal number needed to treat for avoidance of accidents and different injury levels for system “Warning”. The marginal NNT refers to one incremental increase in TTC.
Fig. 6.10 gives theabsoluteandmarginal functional costs depending on the TTC thresh-old (see Section 2.2). The discussion of the U-like shape of overall NNT already showed that an increase at low TTC threshold is beneficial. This is also reflected in the slope of the overall NNT curve as given by the marginal NNT. For example, a change in TTC from 1.0 s to 1.2 s for ISS9+ has negative marginal costs (meaning about 150 warning less per avoided ISS9+). A decision to choose a TTC threshold of 1.2 s instead of 1.0 s is thus both beneficial in terms of overall functional costs (about 100 warnings per avoided ISS9+
instead of about 250) and marginal costs. With increasing TTC thresholds, the marginal costs become positive. Each additionally avoided outcome thus is associated with a defined additional effort. If the goals for ISS16+ are maximum overall costs of 400 and maximum marginal costs of 50, the highest TTC acceptable would be 3.2 s (overall costs are about 300 and 3.0 s to 3.2 s results in about 50 additional warnings per avoided ISS16+).