## 3 Analytical Methodology for the Evaluation of Machinery Safety
### Evaluation of Current Measures Status in Operations or Organizations  
The level of measures efficiency \(\Delta_{k}\) expresses the fulfillment of safety requirements by means of the realized measures on the \(k\)-th machine and is expressed by the relation:  
\[\Delta_{k}=\frac{\sum_{i=1}^{m}w_{k,i}}{S_{MAX}}\times 100\%,\quad k=1,2, \ldots,n,\quad i=1,2,3,\ldots,\ m, \tag{1}\]  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Coefficient\(w_{k,i}\)** & **Explanation** \\ \hline \(w_{k,i}=0\) & Measures for the fulfillment of the \(i\)-th requirement on the \(k\)-th machine are not introduced. \\ \(w_{k,i}=1\) & Measures for the fulfillment of the \(i\)-th requirement on the \(k\)-th machine are introduced but not followed. \\ \(w_{k,i}=2\) & Measures for the fulfillment of the \(i\)-th requirement on the \(k\)-th machine are introduced and fully followed. \\ \hline \hline \end{tabular}
\end{table}
Table 2: Coefficient of current measure status \(w_{k,i}\)  
Figure 2: Proposal of the analytical procedure for the complex efficiency evaluation of machinery safety measures in a production organization.  
where \(n\) represents the number of machines, \(m\) is the number of safety requirements, and \(w_{k,i}\) is the coefficient of current measures status of the \(i\)-th requirement on the \(k\)-th machine. The \(S_{MAX}\) variable represents the coefficient of maximum reached efficiency of all measures on a given machine and is determined by the relation:  
\[S_{MAX}=w_{max}m, \tag{2}\]  
where \(m\) is the number of safety requirements and \(w_{max}\) is the maximum value of measures evaluation, in our case \(w_{max}=2\).  
The total efficiency level of measures \(\Delta\) in the given operation is expressed by the relation  
\[\Delta=\frac{\sum_{k=1}^{n}\Delta_{k}}{n}\times 100\%,\ \ k=1,2,\ldots,n, \tag{3}\]  
where \(\Delta_{k}\) is the level of measures efficiency in the case of the \(k\)-th machine and \(n\) is the total number of machines located in the given operation. The total level of measures efficiency \(\Delta\) in the given operation takes on values from the interval \(0,100\).  
For a complex safety level of a given operation conditioned by the status of introduced measures on machinery, evaluation according to the following scale was suggested:  
* if \(0\%\ <\ \Delta\ <\ 29\%\), then the level of safety measures efficiency in a given operation is _low_;
* if \(30\%\ <\ \Delta\ <\ 49\%\) then the level of safety measures efficiency in a given operation is _negligible_;
* if \(50\%\ <\ \Delta\ <\ 69\%\), then the level of safety measures efficiency in a given operation is _middle_;
* if if \(70\%\ <\ \Delta\ <\ 89\%\) then the level of safety measures efficiency in a given operation is _high_;
* if \(90\%\ <\ \Delta\), then the level of safety measures efficiency in a given operation is _very high_. If a production organization has \(p\) operations, then the **complex level of safety measures efficiency**\(\overline{\Delta}\) would be possible to be expressed by the relation:  
\[\overline{\Delta}=\frac{\sum_{j\ =\ 1}^{p}\Delta_{j}}{p}\ \times\ 100\%,\ \ j\ =\ 1,2,\ldots,p, \tag{4}\]  
where \(p\) is the number of operations (in our case 3) and \(\Delta_{j}\) is the level of measures efficiency in the case of \(j\)-th operation, which holds the relation:  
\[\Delta_{j}\ =\ \frac{\sum_{k\ =\ 1}^{n}\Delta_{k,j}}{n}\ \times\ 100\%,\ \ \ k\ =\ 1,2,\ldots,n,\ j\ =\ 1,2,\ldots,p \tag{5}\]  
where \(\Delta_{k,j}\) is the level of measures efficiency in the case of the \(k\)-th machine in the \(j\)-th operation and \(n\) is the total number of machines within the given operation.