# Operationalisation of Building Inspections and Repair: Systematisation-Based Approach
## 2 Materials and Methods  
### Building New Inter-Defects Three-Dimensional Correlation Matrices  
[PERSON] and [PERSON] [35] defined the methodology to create an inter-defects correlation matrix based on the defects-probable causes correlation matrix. In the context of expert knowledge-based inspection systems, the inter-defects correlation matrix shows the probability of the occurrence of a second defect when one defect is first detected. I.e., the inter-defects correlation matrix functions as an empirical tool to predict the conditioned probability of subsequent anomalies following the detection of an initial anomaly. Within the global inspection system for the non-structural building envelope [12], the harmonisation of the inter-defects correlation matrix followed the methodology determined by [PERSON] and [PERSON] [35], considering the harmonised defects-probable causes correlation matrix [13]. In that context, correlation matrices followed a three-dimensional model, with rows of defects, columns of probable causes, diagnosis methods or repair techniques (according to the type of matrix), and layers of building elements/materials. Three-dimensional inter-defect correlation matrices have rows of given defects, columns of second defects and layers of building elements/materials. To build new inter-defects correlation matrices based on the correlation of defects with diagnosis methods (Table 4) or repair techniques (Table 5), a similar methodology was considered. The material used for this purpose was published by [PERSON] [12], created based on expert knowledge, validated by inspection data from significant samples [13], and then further validated (qualitatively) in more restricted inspection samples [34]. The algorithm to determine the theoretical percentage correlation index is as follows (considering the diagnosis methods for demonstration purposes) [35; 36]: \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & & & **Diagnosis Methods** & \\ \hline
**Defects** & **D-C1** & **D-C2** & **D-C3** & **D-D1** & **D-D2** & **D-D3** \\ \hline
**A-A1** & 1 & 0 & 1 & 0 & 0 & 1 \\
**A-A2** & 2 & 0 & 1 & 0 & 0 & 0 \\
**A-A3** & 1 & 0 & 0 & 0 & 0 & 0 \\
**A-A4** & 0 & 0 & 0 & 0 & 0 & 0 \\
**A-A5** & 0 & 0 & 0 & 0 & 0 & 0 \\
**A-A6** & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \hline \end{tabular} Note: refer to Table 3 and Table 1 for the designation of each defect and diagnosis method, respectively.  
\end{table} 
Table 4: Excerpt of the door and window frames’ layer of the defects–diagnosis methods correlation matrix from the global inspection system developed by [PERSON] [12]. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & & \\ \hline
**Defects** & **R-A1** & **R-A2** & **R-A3** & **R-A4** & **R-A5** & **R-A6** & **R-A7** & **R-A8** & **R-A9** & **R-A10** & **R-A11** & **R-A12** & **R-A13** & **R-A14** \\ \hline
**A-A1** & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 \\
**A-A2** & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 0 & 0 & 0 & 0 & 0 & 0 \\
**A-A3** & 2 & 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 \\
**A-A4** & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & **1** & 0 & 2 \\
**A-A5** & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
**A-A6** & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \hline \end{tabular} Note: refer to Table 3 and Table 2 for the designation of each defect and repair technique, respectively.  
\end{table} 
Table 5: Excerpt of the door and window frames’ layer of the defects–repair techniques correlation matrix from the global inspection system developed by [PERSON] [12].