## 3 Analysis of Examples
### Confidence Analysis Based on Blind-Number Theory  
Taking into account the uncertainty associated with randomness, fuzziness, grayness, and uncertainty in the evaluation of pavement performance, the blind number theory is employed to establish blind number expressions for pavement performance evaluation indexes. Additionally, a confidence model is developed to analyze the confidence of pavement performance. The integration of blind information into the evaluation system ensures that it remains unaffected by probability distribution functions. This approach not only provides a clear assessment grade for pavement performance but also assigns corresponding credibility to the assessment grade, thereby enhancing the scientific nature of the evaluation. The sample data and weight coefficients used in this study are based on the research conducted by [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON] [12]. By utilizing Equations (14)-(16), blind numbers and reliabilities for the pavement performance indexes are computed, as shown in Table 5.  
\[PQ\dot{I}=w_{PCI}\otimes PC\dot{I}\oplus w_{RQI}\otimes RQ\dot{I}\oplus w_{RDI} \otimes RD\dot{I}\oplus w_{SRI}\otimes SR\dot{I} \tag{14}\]  
\[R_{PQ\dot{I}}(90)=\frac{1}{90}\otimes PQ\dot{I} \tag{15}\]  
\[R_{PQ\dot{I}}(80)=\frac{1}{80}\otimes PQ\dot{I} \tag{16}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Serial Number**} & \multirow{2}{*}{**Distribution Function**} & \multicolumn{2}{c}{**Kolmogorov–Smirnov**} & \multicolumn{2}{c}{**[PERSON]–Darling**} & \multicolumn{2}{c}{**Chi-Squared**} \\ \cline{3-8}  & & **Statistic** & **Sort** & **Statistic** & **Sort** & **Statistic** & **Sort** \\ \hline \multirow{8}{*}{PCI} & Log-Logistic & 0.10416 & 5 & 2.5466 & 5 & 18.017 & 6 \\  & Log-Logistic (3P) & 0.05657 & 1 & 1.3167 & 1 & 8.0729 & 2 \\  & Logistic & 0.07701 & 2 & 1.6292 & 2 & 6.5873 & 1 \\  & Lognormal & 0.10857 & 6 & 3.0129 & 6 & 17.641 & 5 \\  & Lognormal (3P) & 0.10026 & 4 & 2.5372 & 4 & 13.059 & 4 \\  & Normal & 0.09952 & 3 & 2.3536 & 3 & 13.057 & 3 \\ \hline \multirow{8}{*}{RQI} & Log-Logistic & 0.08961 & 5 & 2.83 & 6 & 14.394 & 3 \\  & Log-Logistic (3P) & 0.06286 & 1 & 1.6038 & 1 & 10.768 & 1 \\  & Logistic & 0.09492 & 6 & 2.3974 & 2 & 11.416 & 2 \\  & Lognormal & 0.08381 & 4 & 2.8015 & 5 & 19.881 & 6 \\  & Lognormal (3P) & 0.07966 & 3 & 2.6147 & 4 & 18.457 & 5 \\  & Normal & 0.07928 & 2 & 2.4687 & 3 & 15.721 & 4 \\ \hline \multirow{8}{*}{RDI} & Log-Logistic & 0.169 & 6 & 9.2652 & 6 & 79.025 & 6 \\  & Log-Logistic (3P) & 0.10865 & 1 & 4.6751 & 1 & 41.345 & 1 \\  & Logistic & 0.16246 & 4 & 6.3528 & 2 & 60.395 & 2 \\  & Lognormal & 0.16794 & 5 & 8.9946 & 5 & 77.588 & 5 \\  & Lognormal (3P) & 0.15262 & 2 & 6.606 & 4 & 63.712 & 4 \\  & Normal & 0.15298 & 3 & 6.4046 & 3 & 62.267 & 3 \\ \hline \multirow{8}{*}{SRI} & Log-Logistic & 0.09108 & 6 & 2.1105 & 6 & 5.8546 & 1 \\  & Log-Logistic (3P) & 0.0554 & 1 & 1.2219 & 1 & 8.7292 & 5 \\ \cline{1-1}  & Logistic & 0.07973 & 2 & 1.8442 & 4 & 10.447 & 6 \\ \cline{1-1}  & Lognormal & 0.08903 & 5 & 2.031 & 5 & 7.0076 & 4 \\ \cline{1-1}  & Lognormal (3P) & 0.08081 & 3 & 1.7982 & 3 & 6.5312 & 3 \\ \cline{1-1}  & Normal & 0.08172 & 4 & 1.6595 & 2 & 6.3648 & 2 \\ \hline \end{tabular}
\end{table} 
Table 4: Comparison of fitting function statistical test results of pavement performance indexes. The results of these calculations are presented in Table 4. It is evident that the calculated PQI' results do not align with those obtained using the current standard. The PQI' interval determined by the current standard is [83.64, 92.94], whereas the PQI interval computed is [73.32, 91.01]. Three of the judgment values for the optimal pavement performance evaluation grade exceed 1, indicating that the confidence of judgment values greater than 1 in the sample group is 0.075. There are 36 judgment values for the good pavement performance evaluation grade that surpass 1, signifying a confidence of 0.9 or 90% for judgment values greater than 1 in the sample group. Moreover, confidence is considered as 1 for values exceeding 0.9.