## 4 Conclusions  
Fatigue characteristics of materials in the form of SN curves are only the basis for fatigue calculations. Equally important here are all elements of the fatigue life determination algorithm, in particular stress determination and consideration of factors influencing fatigue, such as scale factor, stress concentration effect, average stress, amplitude distribution and sequence, and environmental factors. At the forefront of factors influencing fatigue life is the correct determination of stresses, on the basis of which the analysis is carried out. In real elements subjected to operating loads, it is difficult to assess the actual state of the load. Therefore, this element is burdened with the greatest uncertainty. For fatigue calculations in real conditions, the most suitable method is the spectral method, which statistically reflects the load. This is a well-known method and is often referred to as vibration fatigue method. The influence of the notch on fatigue life is usually expressed by an increase in the stress value. In the spectral method, if the notches are not sharp, their influence is taken into account in the FEM calculation, also by increasing the stress near the notch. Of course, the scale factor for the volume of loaded material should not be neglected. This study demonstrated the effectiveness of finite element modelling (FEM) and power spectral density (PSD) simplifications in predicting fatigue life for two different mechanical systems under random vibration conditions. Based on the results and analysis, the following key conclusions can be drawn:  
* Both investigated cases, the compressor suspension system and the Motorcycle Transport Device, show that not only fatigue properties, but also clear understanding of the system loading are crucial for proper fatigue assessment. * Experimental testing is crucial for calibrating FEM models. Combining testing with simulations ensures that models reflect real-world conditions more precisely and improves the accuracy of fatigue life predictions and the reliability of engineering designs. * Results obtained by proposed equivalent effective acceleration method follows the stress trend observed in real measurements, indicating that the FEM model captured the general behaviour and stress distribution in the system. This makes the method suitable for finding critical regions and for preliminary vibration fatigue calculations for new structures. * The study showed that simplifying the PSD function using methods such as normalization, reduction of characteristic points, and applying an interpolated envelope had minimal impact on the accuracy of fatigue life predictions. The deviations in predicted fatigue life across different PSD simplifications were less than 5%, indicating that these simplifications significantly reduce computational time without compromising accuracy. * Both the Dirlik and Rayleigh models used in fatigue life estimation produced consistent results, confirming their applicability in random vibration analysis. The compressor suspension system and Motorcycle Transport Device both demonstrated predictable fatigue life outcomes when subjected to realistic operational loads. * The application of PSD simplifications in fatigue life predictions provides significant benefits for engineering design, particularly in industries where time and computational resources are limited. The findings suggest that engineers can confidently apply these simplifications to accelerate the design process while maintaining accuracy in performance evaluations. * While the PSD simplification methods used in this study were effective, future research should explore adaptive simplification techniques that can dynamically adjust based on the system's complexity. Additionally, incorporating non-linear behaviour in FEM models, especially for components like dampers, will provide a more comprehensive understanding of fatigue life in real-world conditions.