# A Rule-Based System for Human Performance Evaluation: A Case Study
## 4 Case Study of PTI Inspectors' Performance Evaluation in Croatia
### Data Analysis for Defining Significant Parameters  
The data included all M1 vehicles that had been inspected during PTI in Croatia in 2016 at the observed PTI station where 11 PTI inspectors were employed. The sample included 24,035 vehicles, and it was preprocessed to remove all extreme values (outliers) from the sample related to irregularities in the PTI duration. The new sample size included 22,804 vehicles. An analysis of the results from 11 PTI inspectors was taken to show what influenced whether the car passed or failed the inspection. It provided an insight into which parameters are relevant and which may have a significant effect on decision-making regarding the technical condition of the vehicle. As it was mentioned before, the result of PTI can take two values, 1--pass or 0--fail. In other words, the result of PTI is a dichotomous variable. Therefore, binary logistic regression was conducted to analyze the relationship between the PTI result (dependent dichotomous variable), vehicle age in years, and PTI duration time in minutes (two independent continuous variables). It was important to define whether the association between independent variables and the dependent one is statistically significant. The question was posed as to whether the age of the vehicle and the duration of the PTI affect the ultimate result of the vehicle technical inspection. Thus, the aim was to determine the relevance of the parameters for PTII WQA ES design purposes. At the very beginning of the binary logistic regression conduction, all four assumptions were checked to ensure that none of them have been violated. The statistical analysis was carried out in a software package Statistica by Tibco company. Table 1 presents the results of binary logistic regression and the contribution of each independent variable to the model and its statistical significance. It is possible to conclude that changes in both independent variables are associated with changes in the probability that the event of failing on PTI occurs. Both variables are statistically significant at the significance level of 0.05, where the \(p\)-value of vehicle age is \(p=0.000000\) and of PTI duration is \(p=0.000080\). The positive estimate values of both variables indicate that the event of failing on PTI becomes more likely as the independent value increases, holding other independent variables constant. The estimate (i.e., regression coefficient or B) of variable vehicle age is 0.08476, which implies that for every one-year increase of vehicle age, the likelihood that the vehicle fails on PTI increases by approximately 1.09 times. The regression coefficient of variable PTI duration is 0.00601. Therefore, it means that for every one-minute increase of PTI duration time, it is approximately 1.01 times more likely for a vehicle to fail on PTI. In addition, an ANOVA test was conducted to determine the association between 11 PTI inspectors regarding PTI duration, as the value is prescribed by the legal regulations and monitored during the inspection of the PTI stations by competent authorities. Table 2 indicates the relationship between them and determines whether there are differences in the duration of the PTI when performed by the 11 inspectors in the observed PTI station. The results indicate the evident fact that the difference exists, i.e., the difference is significant (\(p=0.0000\), \(p<0.05\)). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Estimate** & **Odds Ratio** & **Standard Error** & **Wald Stat.** & **Lower CL 95\%** & **Upper CL 95\%** & \(p\)**-Value** \\ \hline Intercept & \(-2.55109\) & 0.077997 & 0.059292 & 1851.228 & \(-2.66731\) & \(-2.43488\) & 0.00000 \\ Vehicle age (years) & 0.08476 & 1.088456 & 0.002739 & 957.838 & 0.07939 & 0.09013 & 0.00000 \\ PTI duration (min) & 0.00601 & 1.006028 & 0.001523 & 15.555 & 0.00302 & 0.00899 & 0.000080 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The results of binary logistic regression.