## 3 Results
### Development of the Three Sigma Rule  
When implementing construction projects, it is crucial for decision-makers to make informed decisions in response to anomalies or changes that may occur at various stages of the investment implementation. For example, a construction manager, depending on his role, when preparing to implement an investment, determines certain parameters that characterize the investment project. When planning a construction project, the investor determines the available investment budget and completion date. In turn, the contractor develops a material and financial schedule to estimate the cost of construction works and subsequently determines the required time for their completion. The best-fit curves and designated areas of cost curves, which were obtained as a result of the research, help decision-makers plan the course of the construction project and, at the same time, take into account the investment's budget and its duration. Additionally, using the proposed cost curve areas, it is possible to monitor the progress of the construction project and respond appropriately to emerging situations. Depending on the moment in time at which the inspected project is completed, it is possible to quickly estimate \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Construction Group/Sector**} & \multicolumn{3}{c}{**Third-Degree Polynomial**} \\  & **The Actual Cost of Works Performed** & **Coefficient of Determination** & **Inflection Point** \\ \hline Apartment houses (A) & y = \(-0.57\)x\({}^{3}\) + \(0.94\)x\({}^{2}\) + \(0.63\)x & R\({}^{2}\) = \(0.9535\) & x = \(0.5497\) \\ Office buildings (B) & y = \(-0.67\)x\({}^{3}\) + \(1.36\)x\({}^{2}\) + \(0.31\)x & R\({}^{2}\) = \(0.9172\) & x = \(0.6766\) \\ Hotel buildings (C) & y = \(-0.65\)x\({}^{3}\) + \(1.71\)x\({}^{2}\) + \(0.06\)x & R\({}^{2}\) = \(0.9279\) & x = \(0.8769\) \\ Commercial and service & y = \(-1.30\)x\({}^{3}\) + \(1.99\)x\({}^{2}\) + \(0.31\)x & R\({}^{2}\) = \(0.9438\) & x = \(0.5103\) \\ buildings (D) & y = \(-0.57\)x\({}^{3}\) + \(0.94\)x\({}^{2}\) + \(0.63\)x & R\({}^{2}\) = \(0.9536\) & x = \(0.5497\) \\ \hline All buildings & y = \(-0.78\)x\({}^{3}\) + \(1.49\)x\({}^{2}\) + \(0.29\)x & R\({}^{2}\) = \(0.9162\) & x = \(0.6368\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Best fit curves—some of the results. deviations from the planned values in terms of cost and time. The determined polynomial functions and graphs of real areas of cost curves (in the form of nomograms) constitute a reliable graphic representation that is useful for the simple application of research results in typologically similar construction sectors. In order to monitor and control the progress of a construction project, it was proposed, in accordance with the Three Sigma Rule, to divide the area of cost curves into three ranges that correspond with three scenarios. The area was divided according to this rule due to the fact that such a division is used (with great effectiveness) as a warning system about danger, abnormal behavior, or something unusual. For this purpose, a model with specific parameters/\"a warning system for irregularities\" was developed. Therefore, the cost curve area was divided into the following three areas:  
* The range within \(<\!-\sigma\), \(\sigma\!\!>\), identified as the acceptable range (green in Figure 6);
* The range within \(<\!-2\sigma\), \(\sigma\!\!>\)\(\cup\!<\!-\sigma\), \(2\sigma\!\!>\), identified as the tolerable range (orange in Figure 6);
* The range within \(<\!-3\sigma\), \(2\sigma\!\!>\)\(\cup\!<\!-2\sigma\), \(3\sigma\!\!>\), identified as the unacceptable range (red in Figure 6). Monitoring is conducted based on the material and financial schedule planned by the decision-maker, specifically verifying against the budgeted cost of work scheduled (BCWS) curve. When evaluating the status of a construction project, three scenarios may arise, each with corresponding recommendations:  
* Scenario 1: The analyzed value falls within the acceptable range (green area).