# Structural Analysis of Factors Influencing the Costs of Facade System Implementation
## 4 Results and Discussion
### Conduct and Results of Factor Analysis  
The expert research was performed with 10 Polish companies dealing with and specialising in the implementation of external facades. In 2019, 15 experts were invited (including works managers, production managers, and bid managers) to describe the relationships between the identified factors. According to the principle of factor interdependence, one of the factors (\(X\)) may have a very strong influence on the other factor (\(Y\)), while the \(Y\) factor itself does not have to influence the \(X\) factor or the influence may be very weak. The evaluation involved a five-stage scale, where 0 = no impact, 1 = weak impact, 2 = medium impact (significant but not decisive), 3 = large impact (decisive), and P = potential impact. On the basis of the results obtained, matrix A (direct influence) was constructed. \[A=\left( \begin{array}{cccccccccccccccc}0&2&0&0&0&0&P&0&2&0&2&0&0&0&0\\ 3&0&0&0&0&0&0&0&1&0&3&0&0&0&0\\ 0&0&0&0&0&0&0&2&0&3&0&0&0&0\\ 2&2&2&0&3&0&1&0&3&P&0&0&0&0&0\\ 1&1&1&0&0&0&0&0&3&0&0&0&0&0\\ 2&3&2&0&0&0&P&0&3&0&3&0&0&0&0\\ 1&0&0&0&0&0&0&2&P&0&0&0&0&0\\ 1&2&P&0&0&0&0&0&1&P&0&0&0&0&0\\ 1&2&2&0&0&0&0&0&0&2&0&0&0&1\\ 0&1&2&0&0&0&0&2&0&0&0&0&0&1\\ 0&0&0&0&0&0&0&2&0&0&0&0&0\\ 2&1&2&0&0&0&0&0&2&0&P&0&3&0&0\\ 3&2&2&0&0&0&0&3&P&3&0&0&0&P\\ P&P&P&0&0&0&0&0&P&0&0&P&0&0&2\\ 0&0&0&0&0&0&0&3&1&0&0&0&0&0\end{array} \right) \tag{1}\]  
Using the example of the first row of the A matrix, the following interpretation of the influence of factor A on other factors can be made:  
* Factor A affects on average factors B, I, and K, which is why the matrix was assigned a grade 2 according to a five-degree scale;
* Factor A does not affect factors C, D, E, F, H, J, L, M, N, and O--therefore, a degree of 0 is assigned in the matrix;
* Factor A potentially affects factor G; therefore, a grade P is assigned in the matrix. Table 2 presents the results of the structural analysis as the total strength of influences and direct relationships for the analysed factors. The calculated values of the influence strength and dependencies are the dominants of the influence force of the factors on each other. The following variables reveal the greatest strength of direct influence on other factors: height of the facility (D), complexity of the building body (F), and specialisation of subcontractors (M). On the other hand, the variable showing the greatest dependence on other factors and the subsequent impact \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & **Group of Factors/Factor** & **Symbol** & **Total Strength of Influence** & **Total Strength of Dependencies** \\ \hline \multicolumn{5}{c}{Material} \\
1 & Type of aluminium–glass faced & A & 6 & 16 \\
2 & Type of glass used & B & 7 & 16 \\
3 & Type of external cladding used for & C & 5 & 13 \\  & Facility characteristics & & & & \\
4 & Height of the facility & D & 13 & 0 \\
5 & Facade surface & E & 6 & 3 \\
6 & Complexity of the building body & F & 13 & 0 \\
7 & Number of window and door frames. & G & 3 & 1 \\  & Contractal conditions & & & \\
8 & Location of construction & H & 4 & 0 \\
9 & Implementation time–duration & I & 8 & 29 \\
10 & Implementation deadline (season) & J & 6 & 1 \\  & Aesthetics & & & & \\
11 & Quality of execution & K & 2 & 16 \\  & \multicolumn{5}{c}{Macroeconomic factors} \\
12 & Company size & L & 10 & 0 \\
13 & Specialisation of subcontractors & M & 13 & 3 \\
14 & Inflation & N & 2 & 0 \\
15 & Availability of subcontractors & O & 4 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Power of influence and dependence on identified factors. on the costs of facade systems is implementation time-duration (I), while the following revealed less dependence on other factors, but also at a high level: type of aluminium-glass facade (A), type of glass used (B), and quality of execution (K).