Crash Potential Index (CPI)#

Description#

The CPI is a scenario-level metric and calculates the average probability that a vehicle can not avoid a collision by deceleration. It sums over the probabilities that a given vehicle’s \({a}_{\mathit{long,req}}\) exceeds its \(a_{\mathit{long},\mathit{min}}\) for each time point and normalizes the value over the length of the scenario [Cunto2007] [Cunto2008]. The target value \(a_{\mathit{long},\mathit{min}}\) is assumed to be normally distributed and dependent on factors such as road surface material and vehicle brakes. While originally defined in discrete time, the CPI for a scenario can be defined in continuous time as

\[\mathit{CPI}(A_1, A_2) = \frac{1}{t_e-t_0}\int_{t_0}^{t_e}P({a}_{\mathit{long,req}}(A_1, A_2, t) < a_{1,\mathit{long,min}}(t)) \mathrm{dt}\,.\]

Note that this concept of aggregation over time can be generalized to be applicable to other metrics, assuming that a valid probability distribution of the target value can be given. This potentially enables a more precise identification of criticality within a scenario.

Properties#

Run-time capability#

Target values#

Average CPI was found to be 0.00491% in simulation, suggesting higher values as target values, e.g. 0.0072% (upper limit of 95%-confidence interval) [Cunto2008]

Subject type#

Road vehicles (automated and human)

Scenario type#

Intersecting predicted paths for a significant time span in the scenario

Inputs#

\(a_{\mathit{long,req}}\), \(a_{\mathit{long,min}}\) probability distribution

Output scale#

\([0,1]\), probability, ratio scale

Reliability#

Depends on reliability of \(a_{\mathit{long,req}}\), but is potentially increased due to integration over time

Validity#

Comparable to BTN, potentially increased due to comparison with a normally distributed target value, but depends on validity of distribution [Guido2011], initially validated [Cunto2008]

Sensitivity#

Potentially high, but strongly depends on \(a_{\mathit{long,req}}\) and validity of \(a_{\mathit{long,min}}\) distribution for the given scenario

Specificity#