# Statistical Analysis of the Crosswalk Lighting Design Correctness
## 4 Massive Compliance Tests: Discussion  
Although the above results reveal standard compliance issues for simplified crosswalk lighting, the open question is the scale of the problem. In particular, how those changes interfere: whether they compensate for each other or magnify the effect of nonconformity. To obtain the fully reliable answer, massive tests should be carried out. The results of this investigation are presented in this section.  
Testing design compliance sensitivity against crosswalk lighting situation layout distortions is achieved in three steps:  
1. Setting a reference layout (e.g., a typical crosswalk) with a set of parameters such as length, width, etc., being subject to deviations and defining allowable variability ranges for particular parameters. Those ranges can be expressed as corrections (in %) of reference values. We reject all distortions which are not acceptable _a priori_, e.g., the crosswalk width equal to 50 m or a pole of the 1 m height.
2. Preparing software checking if a given layout is standard compliant (answer: _yes/no_).
3. Analyzing generated big data consisting of all acceptable layouts. It can be accomplished using an artificial intelligence method (namely, so called _graph grammars_), but these details are beyond the scope of this paper, and they will not be discussed here.  
To test the lighting design method robustness, we prepared 898,500,000 layouts based on the initial reference situation shown in Figure 1. Each particular layout was produced by modifying (up to 50% of an initial value, with the step 5%) _at least_ one of the following parameters:  
Figure 6: Scenario 3:(a) the reference pedestrian crossing; (b) crossing width increased by 0.5 m relative to (**a**).  
\begin{table}
\begin{tabular}{c c c c c} \hline  & \(E_{\text{\tiny{p,avg}}}\) [lx] & \(U_{\text{\tiny{p,o}}}\) & \(E_{h,\text{avg}}\) [lx] & \(U_{\text{\tiny{o,h}}}\) & \(E_{\text{\tiny{p,min}}}^{(6)}\) [lx] \\ \hline Scenario 1 & 24.56 \(\mathcal{K}\) & 0.38 & 60.64 & 0.45 & 5.88 \\ Scenario 2 & 25.96 & 0.36 & 58.71 & 0.38 \(\mathcal{X}\) & 6.67 \\ Scenario 3 & 24.46 \(\mathcal{K}\) & 0.43 & 56.97 & 0.47 & 6.30 \\ Reference values & 25.00 & 0.35 & 25.00 & 0.40 & 3.00 \\ \hline \end{tabular}
\end{table}
Table 3: Photometry for modified crosswalk layouts (the PC4 class was assumed). The symbol \(\mathcal{K}\) denotes violating standard constraints.  
* Road width,
* Crosswalk width,
* Lamp spacing,
* Pole setback,
* Row of lamps shifting with respect to the crosswalk,
* Crosswalk lamp position shift \((\delta x,\delta y)\); it was assumed that locations of those lamps are axially symmetric with respect to the crosswalk center.  
Note that neither fixture power nor photometric solid is subject to modifications. It is because once a fixture setup was selected (for the reference situation) we only verify whether it also complies with lighting standard requirements for a geometrically modified scene.  
To show how the standard conformity depends on distortion (\(\Delta\)) magnitude, we probed a ratio of non-compliant solutions for consecutive distortion values. For example, a distortion \(\Delta=35\%\) denotes that neither value change applied to the parameters listed above, and it exceeds 35% of a reference value.  
Figure 7 presents the obtained results for \(\Delta\) ranging from 5% to 50%, with the step 5%.  
As can be seen on the above chart, even the slight modifications of the basic layout yield a very high 40% rejection rate; \(\Delta=15\%\) impacts nearly the half of the designs.