## 2 Methods
### Mathematical Model
To obtain a detailed mathematical model based on a particular functional relationship, allowing to calculate IQI values, the factor systems modelling technique was used:  
\[\text{CQI}=\sum_{i=1}^{n}\text{Wi}_{i}\text{pi}, \tag{13}\]  
where _Wi_ is the coefficient of importance (weight) of the \(i\)-th parameter. The resulting model not only fully characterizes the process of studying the IQI, but can be modernized to complicate or simplify the process. The analysis of dependence between the IQI and the studied group of factors can be presented in a graphical form. To this end, a three-dimensional graph of the surface of the obtained regression equation must be created, depending on different groups of factors. Considering that there are four factors, it was convenient to study the obtained surfaces by alternating a combination of two active factors when the other two are in a fixed position. In this case, it became a series of six dependencies in a graph which describes the alternating influence of two groups of factors on changes in IQI The nature of the change in CPR from the influence of two groups of factors z1, z2 is reflected in Figure 2, the nature of the change in CPR from the influence of two groups of factors z1, z3 is reflected in Figure 3. For example:  
\[\text{IQI}=\text{f}\left(\text{z}_{1},\text{ z}_{2}\right)=54.83+8.89\text{ z}_{1}+9.45\text{ z}_{2}+0.2\text{ z}_{1}^{2}+5.2\text{ z}_{2}^{2}-2.5z_{1}z_{2}. \tag{14}\]  
Figure 3: The nature of changes in IQI caused by the influence of two groups of factors \(\text{z}_{1}\), \(\text{z}_{3}\). Figure 2: The nature of changes in IQI caused by the influence of two groups of factors \(\text{z}_{1}\), \(\text{z}_{2}\). The combined effect of factors \(\mathrm{z_{1}}\) and \(\mathrm{z_{2}}\) has a moderate effect on the value of IQI, and ensures the linear nature of processes that are underway. \[\mathrm{IQI}=\mathrm{f}\;(\mathrm{z_{1}},\;\mathrm{z_{3}})=54.83+8.89\;\mathrm{z _{1}}+5.83\;\mathrm{z_{3}}+0.2\;\mathrm{z_{1}^{2}}+2.7\;\mathrm{z_{3}^{2}}. \tag{15}\]  
When studying the joint influence of factors \(\mathrm{z_{1}}\) and \(\mathrm{z_{3}}\) on the value of integrated index \(\mathrm{IQI}=\mathrm{f}\;(\mathrm{z_{1}},\;\mathrm{z_{3}})\), linear dependence on \(\mathrm{z_{1}}\) and \(\mathrm{z_{3}}\) prevails, although a more pronounced quadratic dependence on factor \(\mathrm{z_{3}}\) was observed. Similar graphs were obtained for other variables. The final stage of data collection and structuring was the measurement of values of potential states of parameters, determined using parameter weights. The method of variation series was applied to find the weights of parameters. The process of determining the values of potential states of parameters followed the process of determining the value of parameter weights. Groups of experts using the analysis of hierarchies method created a table of parameters which allows evaluating the current state and effectiveness of administrative and engineering solutions. After obtaining a dimensionless discrete value for its qualitative interpretation in the course of constructing a multi-storey residential building, the \"use of quantitative ranges of values of the generalized Harrington's desirability function\" must be adapted. Since the quantitative range of values, having such qualitative interpretations as \"good\" and \"very good\", \"bad\" and \"very bad\", has the same meaning for construction, they should be combined. The final table of the qualitative interpretation of the discrete evaluation of the quality of multi-storey residential buildings is presented as Table 10.  
Description of a method of integrated assessment of the quality of multi-storey residential buildings followed the development of integrated quality assessment and IQI calculation algorithms:  
1. Monitoring of administrative and engineering solutions, involved in the process of construction of multi-storey residential buildings, factoring in their compliance with the current standards;
2.