## 3 Results
Then, the probability of the absence of an event \(t_{i}\) is equivalent to the probability that the random variable \(\xi_{i}\) will not exceed the threshold value \(W_{\text{crmax}}\), which can be calculated using Equation (13):  
\[p^{-}=P(\xi_{i}<W_{cr\text{ max}})=F_{\xi}(W_{cr\text{ max}})=1-p^{+}. \tag{13}\]  
Thus, the values of the sample function \(\xi_{1},\ \xi_{2},\ \ldots,\xi_{n}\) of the random sequence \(\{\xi_{n},\ n=\overline{1,\ n}\}\) reflect the probabilities of occurrence \(p^{+}\) and non-occurrence \(p^{-}=1-p^{+}\) of a specific event at moments \(t_{1},t_{2},\ldots,t_{n}\) when the critical level of power consumption \(W_{cr\text{ max}}\) is exceeded. This approach is consistent with the classical Bernoulli scheme [79; 80], where a random variable \(n^{+}(W_{cr\text{ max}})\) is characterized by a binomial distribution:  
\[p_{k}\big{(}n^{+}\big{)}=P\big{\{}n^{+}(W_{cr\text{ max}},\ n)=k\big{\}}=C_{n}^{k} \big{(}p^{+}\big{)}^{k}\big{(}p^{-}\big{)}^{n-k},\ k=0,\ 1,\ 2,\ \ldots\,\ n, \tag{14}\]  
where \(C_{n}^{k}=n!/k! (n-k)!\) is the number of combinations of \(n\) elements by \(k\). Distribution (14) is used to estimate the probability \(P\{n^{+}(W_{cr\text{ max}},\ n)=k\}\) that exactly \(k\) exceedances of the electricity consumption threshold level \(W_{cr\text{ max}}\) will occur in a sequence of \(n\) independent measurements for time moments \(t_{1},t_{2},\ldots,t_{n}\) and, accordingly, values of the random function \(\xi_{1},\ \xi_{2},\ \ldots,\xi_{n}\). The mathematical expectation and variance of the number of possible exceedances of the electricity consumption level \(W_{cr\text{ max}}\) are calculated using Equation (15) [79], known from probability theory:  
Figure 4:0  
Practical experience in analyzing the power consumption in technological processes shows that there can be several increasing stages of critical power consumption levels \(W_{cr\text{ max}}\). Each of these levels may be crossed by the sample function \(\xi_{1},\ \xi_{2},\ \ldots,\xi_{n}\) at random moments in time \(t_{i}\). The sequence of crossings is considered a separate realization \(t_{1},t_{2},\ldots,t_{n}\) of a random point process \(\left\{t_{i}(W_{j})\right\}\) of exceeding the power consumption level \(W_{j}\). The graph of power consumption for a technological process with two critical power consumption levels \(W_{2}>W_{1}\) corresponds to the boundaries \(\left\{\gamma<X<\alpha\right\}\) and \(\left\{\delta<X<\beta\right\}\) (Figure 5) and is shown in Figure 4:1  
Given that the quantities \(\xi_{i}\) are independent, the conditions of the Bernoulli scheme are satisfied. In this case, the number of exceedances \(n^{+}(W_{j},n)\) of the power consumption level \(W_{j}\) follows a binomial distribution, similar to Equation (14). The mathematical expectation and variance of the number of possible exceedances of the power consumption level \(W_{j}\) can be calculated using Equation (15). An analysis of Figure 7 suggests the conclusion that the random point process \(t_{i}(W_{2})\) at level \(W_{2}\) is the result of \"thinning out\" the flow \(t_{i}(W_{1})\) from level \(W_{1}\). Consequently, the probabilities of the mathematical expectation and the variance of the number of possible exceedances of level \(p^{+}(W_{j})\) will decrease. Their difference is information about the probability that the values of the random sequence \(\xi_{n}\) under study lie in the range of levels \(\xi\in(W_{1},W_{2})\), which can be calculated using Equation (16):  
Figure 4:2  
which is shown in Figure 5 by boundaries \(\left\{\gamma<X<\alpha\right\}\) and \(\left\{\delta<X<\beta\right\}\). Thus, process control comes down to changing the output plan deadlines, redistributing raw materials and components, and altering the amount of power and electricity consumption.