## 3 Mathematical Model of Maintenance Standard  
The objective of the model is to determine the number and type of maintenance interventions, including the number of hours required to perform maintenance on the machine or equipment, for a calendar year [15]. The flow chart of the program for standard assignment is shown in Figure 9. The model algorithm is based on:  
1. Calculation of the basic level of labor intensity is based on: * machine complexity: \(B_{1}=\textit{PU-PU}\); * technical level: \(B_{2}=A\ +\ B\cdot S\ +\ C\cdot S^{2}+\ D\cdot S^{3}+\ E\cdot S^{4}\); * weight: \(B_{3}=A\ +\ B\cdot MW\ +\ C\cdot MW^{2}+\ D\cdot MW^{3}+\ D\cdot MW^{4}+\ F\cdot MW^{5}+\ G \cdot MW^{6}\); * machine accuracy: \(B_{4}=\textit{PRN}\); * total points: \(SB\ =\ B_{1}+B_{2}+B_{3}+B_{4}\). The basic level of labor intensity is then \[ZPS\ =\ \frac{A^{\prime\prime}\ +\ B^{\prime\prime}\cdot SB}{C^{\prime\prime}\ +\ D^{\prime\prime}\cdot SB}.\] (11)
2. Calculation of final degree of labor intensity is \[K\ =\ ZPS\ +\ \textit{OPC}.\] (12)
3. In the standards, find the number, type, and extent of maintenance operations for each machine according to \(A(SD,\ ZU,\ K)\). Note: The standard contains information on the annual norm of labor intensity in hours, number of inspections per year, extent of one inspection in hours, number of repairs per year, and the extent of one repair in hours. 4. Breakdown of annual standard of labor intensity for: * electrical maintenance: \(CRNE\ =\ \frac{ELU}{100}\cdot CRN\), * machine maintenance: \(CRNS\ =\ CRN-CRNE\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Serial**} & \multicolumn{3}{c}{**Sum Deviations**} & \multicolumn{3}{c}{**Sum Deviations**} \\ \cline{2-7}  & **Least Squares** & **Coordinate** & **Polynomial** & **Least Squares** & **Coordinate** & **Polynomial** \\  & **Method** & **Method** & **Method** & **Method** & **Method** & **Method** \\ \hline
1 & \(-1.3\) & 5.7 & \(-1.0\) & 0.0 & 1.0 & 0.0 \\
2 & \(-7.0\) & \(-0.8\) & 0.0 & \(-1.0\) & 0.0 & 0.0 \\
3 & \(1.2\) & 7.9 & 1.0 & 1.0 & 1.0 & 1.0 \\
4 & \(-2.2\) & 4.8 & \(-1.2\) & 0.0 & 0.0 & 0.0 \\
5 & \(-0.4\) & 7.3 & \(-0.4\) & 0.0 & 0.0 & 0.0 \\
6 & \(1.9\) & 9.6 & 1.7 & 0.0 & 0.0 & 0.0 \\
7 & \(2.3\) & 9.6 & 2.5 & 0.0 & 0.0 & 0.0 \\
8 & \(-8.1\) & \(-3.4\) & 5.7 & 0.0 & 1.0 & 0.0 \\
9 & \(-18.6\) & \(-11.7\) & \(-7.9\) & 0.0 & 0.0 & \(-1.0\) \\
10 & \(-18.0\) & \(-14.3\) & 5.3 & 0.0 & 0.0 & 95 \\ Dispersion & \(80.2\) & 70.9 & 13.6 & 0.2 & 0.3 & 902.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Analysis of results achieved by different methods. * Maintenance staffing calculation
* total hours of annual standard: \(C\ =\ \sum\limits_{i=1}^{n}\ CRN_{i}\)
* total hours of machine maintenance: \(S\ =\ \sum\limits_{i=1}^{n}\ CRNS_{i}\)
* total hours of electric maintenance: \(E\ =\ \sum\limits_{i=1}^{n}\ CRNE_{i}\)
* staffing total: \(KPCS\ =\ \frac{1.2\cdot C}{ED}\)  
\end{tabular}  
Figure 9: Flow chart of the program for standard assignment. Source: authors. Note: The value 1.2 in the above mentioned relation means that 20% is added to the total annual \(C\) standard as a reserve. **4. Model of Operational Maintenance Plan**  
Calculations for machines and labor force efficient pool are:  
* annual effective pool of the machine: \(E_{S}\ =\ (260\ -\ d_{d})\Big{(}1\ -\ \frac{\eta_{1}+m}{100}\Big{)}\cdot f_{d}\). * annual pool of one worker: \(E_{D}=\ (260\ -\ d_{d})\Big{(}1\ -\ \frac{\eta_{1}+m}{100}\Big{)}\cdot f_{d}\). The algorithm of the annual maintenance plan contains:  
* Basic information or possible changes:  
* machine importance group,
* way of use (shifts),
* repair characteristics,
* date of last repair,
* machine utilization in %,
* percentage of machine maintenance and electrical maintenance. * Calculation of cycles (time between maintenance operations for machine importance groups I, II, and III). * Division of maintenance tasks into time series.