## 2 Materials and Methods
\begin{table}
\begin{tabular}{c c c c c c c} \hline \(\boldsymbol{\text{N}}\) & \(\boldsymbol{B}\), \(\boldsymbol{\text{ton}}\) & \(\boldsymbol{W}\), \(\boldsymbol{\text{MWh}}\) & \(\boldsymbol{\text{N}}\) & \(\boldsymbol{B}\), \(\boldsymbol{\text{ton}}\) & \(\boldsymbol{W}\), \(\boldsymbol{\text{MWh}}\) & \(\boldsymbol{\text{N}}\) & \(\boldsymbol{B}\), \(\boldsymbol{\text{ton}}\) & \(\boldsymbol{W}\), \(\boldsymbol{\text{MWh}}\) \\ \hline
1 & 70.3 & 7.9 & 6 & 98.4 & 0.8 & 11 & 81.9 & 11.2 \\ \hline
2 & 85.0 & 0.9 & 7 & 59.2 & 6.0 & 12 & 97.1 & 0.5 \\ \hline
3 & 100.0 & 3.7 & 8 & 86.8 & 7.2 & 13 & 68.2 & 4.6 \\ \hline
4 & 78.1 The analysis of Figure 1 shows that there is no clear functional dependence between the values of \(w_{i}\) and \(\mathrm{n}_{i}\). However, it is obvious that smaller values of \(w_{i}\) in most cases correspond to larger values of \(w_{i}\). This allows us to conclude that power consumption increases when the technological process functions with reduced productivity. Estimates of the mathematical expectation, dispersion, standard deviations, and correlation coefficient are calculated using the known equations:  
\[M^{*}(B)=\frac{\sum_{i=1}^{15}B_{i}}{n}=5.8\ \text{ton};\ M^{*}(W)=\frac{\sum_{i=1}^{15}W_{ i}}{n}=299.6\ \text{MWh};\]  
\[D^{*}(B)=\frac{\sum_{i=1}^{15}[B_{i}-M^{*}(B)]^{2}}{n-1}=13.7\ \text{ton}^{2};\]  
\[\sigma_{B}^{*}=\sqrt{D^{*}(B)}\approx 3.7\ \text{ton};\]  
\[D^{*}(W)=\frac{\sum_{i=1}^{15}[W_{i}-M^{*}(W)]^{2}}{n-1}=255.6\ \text{MWh}^{2};\]  
\[\sigma_{W}^{*}=\sqrt{D^{*}(W)}\approx 16\ \text{MWh};\]  
\[r_{B,W}^{*}=\frac{\sum_{i=1}^{15}\left[B_{i}-M^{*}(B)\right]\cdot\left[W_{i}- M^{*}(W)\right]}{(n-1)\sigma_{B}^{*}\sigma_{W}^{*}}=-0.54.\]  
The given examples substantiate the necessity of taking into account the peculiarities of technological processes at industrial enterprises of different industries when analyzing the modes of power consumption. Let us consider the process of producing output based on probabilistic analysis methods. It is obvious that deviations of process parameters and power consumption values may differ between two contracts producing the same volume of identical products. For two contracts that have the same deviations from planned values \(\Delta B\) and \(\Delta W\) at time \(t\), the differences may be significant if in one case the technological process is in the initial stage, and in the other case, the process is in the final stage. Figure 2 presents an example schedule to fulfill the production plan for output \(B\) with a power consumption level \(W\) for a single technological process. Figure 1: Graphical representation of paired values (\(w_{i}\); \(\mathrm{n}_{i}\)) from Table 2.  
In general, Figure 2 shows a non-stationary random process [64], assuming that the planned values \(B_{pl}(t)\), \(W_{pl}(t)\) at time \(t\) are represented by mathematical expectations for the volume of production output and the amount of electricity consumption, which can be calculated using Equation (1):  
\[m_{B}(t)=B_{pl~{}t}\
eq\text{const};~{}m_{W}(t)=W_{pl~{}t}\
eq\text{const}. \tag{1}\]  
The expected state of the technological process is characterized by the probability of completing the scope of work \(p(B_{t})\) and, accordingly, the probability of power consumption \(p(W_{t})\) at time \(t\). The automatic power consumption management system records the actual values \(B_{t}\) and \(W_{t}\) at time \(t\). The probability of producing the planned output level in accordance with the contract is determined by the probability of producing any shortfall during time \(t_{pl}-t\)[64]. The production of output in accordance with the plan may be disrupted or adjusted for various reasons--administrative, technological, and electrical. This may be related to the untimely supply of raw materials and components, failures of process or electrical equipment in the power supply system, and an active power shortage in the power grid.