## 2 Methods
### Mathematical Model  
It was found that there are four effective factors (\(z_{1}\), \(z_{2}\), \(z_{3}\), \(z_{4}\)) which significantly affect the response function Y. As a consequence, the experiment was multifactorial. Given that the model is statistical and the processes under study are of probabilistic nature, it is evident that the response function Y obeys the correlation dependence on factors \(z_{i}\) influencing it. This then leads to the identification of a series of different values as the output parameter if the value of the factor is non-variable. In this regard, the purpose of this multi-factor experiment was to find a mathematical model that is a regression equation that adequately describes the experiment results. In the present study, in order to perform the experiment, it was necessary to identify the number of trials (as well as the conditions under which they should be performed), \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Dispersion of the Group** & \multicolumn{2}{c}{**Importance Characteristic of the Group**} \\ \hline Group z\({}_{1}\) & 0.1914 & 0.0239 \\ \hline Group z\({}_{2}\) & 0.2421 & 0.0303 \\ \hline Group z\({}_{3}\) & 0.2248 & 0.0281 \\ \hline Group z\({}_{4}\) & 0.1812 & 0.0227 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Calculated values of D\(z_{i}\) and Y(\(z_{i}\)). adequate to solve the problems with sufficient accuracy. The theory of scheduling can be used to solve this problem. In this way, the cost and time of experiments can be minimized and, if necessary, the mathematical model can be upgraded without losing the available information. Experiment scheduling helps to effectively solve a number of vital problems in the course of experiments by:  
* Minimizing the total number of experiments;
* Applying appropriate algorithms to simultaneously change variables that determine the process;
* Using a special mathematical apparatus that formalizes the experimenter's actions;
* Choosing the strategy that enables researchers to make sufficiently informed decisions;
* Drafting appropriate experiment schedules to avoid correlation between regression equation coefficients. The following minor problems must be identified and solved to use the experiment scheduling method:  
* Identify a combination of groups of factors and a number of these combinations to determine response functions;
* Determine the response function accuracy;
* Determine coefficients for a regression equation;
* Use the resulting response function to find the most efficient values of the y function. To build an effective mathematical model, ranges of factor changes must be found, because they determine the area of values of objective function Y. In this case, the search for a solution was limited to the factor space restricted by the coordinate axes of each factor. Hence, factors should be converted into dimensionless values (which are encoded):  
\[\text{zi}=\frac{(\text{zi}-\text{z}0)}{\text{dzi}}, \tag{5}\]  
where \(\text{z}_{\text{i}}\) is the encoded value of the factor,  
\(\text{z}_{\text{i}}\) is the value of the factor (_i_) in the natural scale. \[\text{dzi} =\frac{\text{z}\text{i}\text{z}\text{z}\text{z}\text{min}}{2}, \tag{6}\]  
\[\text{z}0=\frac{\text{z}\text{i}\text{z}\text{z}\text{z}\text{min}}{2}. \tag{7}\]  
Each of the encoded factors \(\text{z}_{\text{i}}\) can only take certain values equal to \(-1\); 0 or +1. In other words, the scheduling area is a hypercube (Figure 1) with the following parameters:  
\[-1\leq\text{z}_{\text{i}}\leq 1, \tag{8}\]  
Here \(i\) = 1, 2, 3, 4. At the same time, factors must meet certain criteria: they must have a significant impact on the final IQI value, have an unambiguous description, and vary qualitatively at all three levels: the lower level (encoded value = \(-1\)), the main level (encoded value = 0), and the upper level (encoded value = +1). Following experts' consultations with and contributions from construction specialists, eight main factors meeting the above criteria could be identified.