# Performance Evaluation of a Lane Correction Module Stress Test: A Field Test of Tesla Model 3
## 5 Experimental Results  
For the analysis of random occurrences of fatal errors discovered during the initial field test, the Notion of a Random Variable statistical analysis model was best suited to capture the randomness of events. The model verifies that the test design capturing errors is quantitatively precise. A random variable X is a function that assigns a real number, \(X(\mu)\), to each outcome \(\mu\) in the sample space of a random experiment. Recall that a function is simply a rule for assigning a numerical value to each set element, as shown below in Figure 6. The measurement specification on the outcome of a random experiment defines a function on the sample space and hence a random variable [x]. Each test starting consecutively with classification number 6.0.1 and ending with 9.0.1 is considered a sample space denoted by \(S_{x}=6.0.1,7.0.1,8.0.1,\) and 9.0.1. In Figure 6, \(\chi(\mu)=\mu\) is the relationship between the number of lane corrections and the error. For example, to check that the data collection method was quantitatively repeatable, \(\chi(\mu)\) is denoted by the number of lane corrections, and \(\mu\) for the module error. Say we want to demonstrate that data were collected where they can be verified within a statistical framework. \[S=\chi(\mu)=\mu \tag{3}\]  
When randomness is observable, it can be measured against what is expected as a normal operation, in this case, a machine or function. Using a standard deviation equation will give more metadata behind the statistical nature of the numerical spread and the confidence interval. \begin{table}
\begin{tabular}{c c} \hline \hline
**Category Description** & **Accuracy Rate Range** \\ \hline Pass & (95–100)\% \\ \hline Moderate & (90–94)\% \\ \hline Fail & 89\% and below \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Accuracy rating percentage. Now we have established a statistical notion of the random variable, which is the error discovered during the test, we can assume \(\chi(\mu)=T_{i}c\) and \(\mu=T_{e}r\). It must be noted that errors in a set of lane corrections are denoted by \(-1\). For the calculations of the error rate and accuracy rate of the lane correction module, we use \(|x|\), which is the absolute value of any negative integer calculations. This is the formula that will be used to process results in field tests 6.0.1, 7.0.1, 8.0.1, and 9.0.1. This is illustrated in Figures 7-10. The total sample size of data collected from the experiment cumulatively is 359 lane correction events, with 43 of them ending in a fatal error event. Therefore, approximately 12% of events cumulatively are errors. As a result, approximately 88% of lane correction events are non-errors. In test \(S_{6.0.1}\) (see Figure 7), we can calculate the error rate overall by adding all total lane corrections, so \(T_{lc}=108\) and \(T_{cr}=10\), which gives us an error rate ratio of 10.8 and an error rate percentage of 9.26 in all. If we were to isolate one event within this testing instance, we would find that the error rate varies significantly, giving another view of the random nature of the error events. For example, if we take \(T_{lc}=3\) and \(T_{cr}=1\), we obtain an error rate percentage of 33.3, yet if we isolate from the test \(T_{lc}=29\) and \(T_{cr}=1\), we receive an error rate percentage of 3.45. Next, we want to establish the accuracy rate of the lane correction module in test 6.0.1; when we add all events within the test, we obtain a rating of 90 percent, according to Table 3. This is barely a moderate accuracy rating and 1 percentage point away from a failing grade. It can be assumed that more events would have yielded a failure as they are consistent across lane correction events. If we calculate the accuracy rate on each instance separately, we will find there are more failures per instance than a pass. Interestingly, the standard deviation of this data set is 12.1 and it has a confidence interval of 3.8, which can also represent a module failure. Some anomalies were noted that are worth mentioning.