# Application of Logistic Regression for Production Machinery Efficiency Evaluation
## 3 Estimation of Markov Logistic Model Parameters
Based on the above table it is possible to assess the effectiveness of model prediction in relation to successes and failures, using tools among which one can distinguish such statistics as accuracy, sensitivity or specificity, ROC (receiver operating characteristic) curve or values of rank correlations. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Machine Number** & **H2** & **H5** & **H6** & **H12** & **H21** \\ \hline OR & 3.460 & 2.904 & 3.169 & 1.950 & 2.246 \\ \hline
**Machine Number** & **H22** & **H23** & **H24** & **H25** & **H4** \\ \hline OR & 1.642 & 1.690 & 2.393 & 3.212 & 1.372 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Odds ratios for individual predictors. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Number of** & **Cut-off Point** & **True Positive** & **True Negative** & **False Positive** & **False Negative** & **SE** & **1-SP** & **Youden’s** \\
**Observations** & & & & & & & & **Index** \\ \hline
5 & 0.51 & 2864 & 13,903 & 2210 & 5905 & 0.33 & 0.14 & 0.19 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Cut-off point of the logistic regression model concerned. The simplest measure is accuracy, calculated according to the following formula:  
\[Accuracy=ACC=\frac{TP+TN}{TP+TN+FP+FN}, \tag{17}\]  
where:  
_TP_--number of true positive results,  
_TN_--number of true negative results,  
_FP_--number of false positive results,  
_FN_--number of false negative results. For the model concerned,  
\[ACC=\frac{2864+13903}{2864+5905+2210+13903}=0.674=67.4\%. \tag{18}\]  
However, the sensitivity \(SE\) and specificity \(SP\) are most often considered in such analyses but treated as pairs, which, after being marked on the plane and after connecting the points with segments, form the so-called ROC curve. For the analyzed model this curve is presented in Figure 6.  
The most important parameter for assessing the ROC curve is AUC--area under the ROC curve. It takes values from 0 to 1. The interpretation of the result was based on the [PERSON] and [PERSON] classification (Table 10), according to which discrimination is sufficient [37]. The model can therefore be considered satisfactory, although it is recommended rather for qualitative analysis of processes and modification of production strategy on its basis. Production in the company in question is carried out in a continuous three-shift system. Regardless of the production plan, the plant is fully manned and all machines are in operation at all times. The acceptable level of efficiency assumed by the management should be 90%, which allows all scheduled and expected downtime to be taken into account. The study indicates that in most cases \begin{table}
\begin{tabular}{c c} \hline \hline
**AUC Value** & **Score** \\ \hline \(0.9<\text{AUC}<1.0\) & Excellent discrimination \\ \(0.8<\text{AUC}<0.9\) & Good discrimination \\ \(0.7<\text{AUC}<0.8\) & Sufficient discrimination \\ \(0.6<\text{AUC}<0.7\) & Weak discrimination \\ \(0.5<\text{AUC}<0.6\) & Insufficient discrimination \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Cut-off point of the logistic regression model concerned. Figure 6: ROC curve for the model concerned. this level is not reached. In almost 25,000 out of over 156,000 observations, this level was not reached. It turned out that the efficiency of the first shift was lower compared to the second and third ones, which suggests the need to diagnose the causes of circumstances or even to restructure the shift system. The use of individual machines also has a negative impact on efficiency. It turns out that many of them represent much lower efficiency than the one taken as a reference point, the efficiency of which was the highest (but also less than 100%). Of course, a lack of orders also leads to a significant reduction in productivity. Such a result, next to failures that occur, indicates the need for a detailed analysis of the machinery. It might be advisable to exclude several machines from the production process so that production is closely correlated with demand.