## 3 Results
### Detection of the Required Calibration Moment--Neural Networks
The goal of the further models was to capture the dependencies of indicator impact on the calibration designation as necessary (DIFF = 1) or unnecessary (DIFF = 0), specifically identifying quality control points that could potentially be omitted since they are not essential. To achieve this, three models were developed: the first utilized decision trees, and the other two employed neural network models. The developed decision tree model indicates that, based on the two most important indicators, AoN and MA, an effective classifier can be created to distinguish between necessary and unnecessary calibrations without introducing significant changes. However, it was also demonstrated that the model is not entirely accurate. While many leaves exhibit high accuracy at 87% and 95%, there is a node that serves as a partition with high variability, associated with an error rate of 43% (for high values of moving averages and AoN when the device approaches a state requiring calibration). Hence, the employment of alternative techniques was deemed a necessity. The next algorithm used in the classification of the control points was a neural network model, which yielded significantly better fitting compared to the decision trees. We utilized the Automatic Neural Network (ANN from Statistica 13.1 Statsoft Poland) algorithm for architecture searching and exploring the spaces of possible architectures, including varying the number of layers and neurons in the hidden layers, as well as MLP and RBF architectures, different activation functions, determining the optimal architecture to be MLP 9-13-2 (Statistica 13.1, Statsoft, Krakow, Poland). The MLP 9-13-2 configuration specifies the architecture of the network, indicating that it consists of 9 input neurons (determined by input variables), a hidden layer with 13 neurons, and 2 output neurons. Also, the notation BFGS 92 refers to the Broyden-Fletcher-Goldfarb-Shanno training algorithm with 92 cycles of iteration. This optimization algorithm is used to minimize the objective function during the training process. The BFGS algorithm is a quasi-Newton method that approximates the second derivative (Hessian matrix) of the objective function and updates the parameters  
Figure 9: Box-and-whisker plots (boxplots) for sqrt (MA) for groups DIFF 0 and DIFF 1 in the context of the periods before and after calibration. iteratively to find the minimum of the function. SOS (\"Sum of Squares\") and entropy error functions are functions used in the context of neural networks for error calculation during the training process. Since the network architecture was generated automatically and the best configurations were tested, we can observe that neither error metrics nor the types of activation functions had a significant impact on the network's results. As evident from these comparisons, activation functions perform similarly regardless of whether they are hyperbolic tangents (tanh), exponential functions, or softmax functions. Numerous models were created, and the best exemplary architectures with good results are presented in Table 4. The presented network architectures differ in accuracy on the validation set, with noticeable differences. Interestingly, the networks labeled ID 2 and ID 5 exhibited higher effectiveness despite weaker performance on the test set, suggesting overfitting in network ID 4. Our observations reveal that a smaller number of input neurons, representing only two variables--AoN and MA--resulted in a decrease in accuracy. Hence, it can be inferred that utilizing additional indicators allows for better prediction. A sensitivity analysis of the network enables the assessment of the impact of individual indicators on the network output. The results can be compared by carrying out an evaluation using CART. As depicted in Table 5, neural networks exhibit a preference for MA over AoN, although ln(MMe) also proves to be a significant factor.