# Reliability Analysis of Military Vehicles Based on Censored Failures Data
## 4 Conclusions  
In this publication, research has been carried out concerning the reliability modelling of military vehicles. A methodology based on the use of non-parametric estimation and reliability function approximation has been proposed. The estimation of the reliability function values was carried out using the Kaplan-Meier estimator. As opposed to the Benard approximation, it enables the study to be carried out on censored data. The estimated values of the reliability function were used to develop mathematical and neural models. From the set of developed neural models, based on the analysis of the _MSE_ error values and the correlation coefficient \(R\) and taking into account the low complexity of the model form, the MLP 1-1-1 model was selected. Then, the analytical form of the neural model was created, which allowed its further analysis. After comparing the exponential, Weibull and MLP 1-1-1 models, the neural model proved to be the best match for the estimated reliability function values. This confirms the feasibility of using artificial neural networks for accurate function approximation. Based on the approximated reliability functions, the reliability characteristics have been developed, i.e., the failure probability density functions, the failure intensity functions and the expected values of the mileage between failures. The plot of the failure probability density function was similar for all 3 models for mileage values exceeding 1000.0 km. The failure intensity function for the exponential model, according to the theoretical assumptions, is constant. For the Weibull and neural models, the course of the function \(\lambda(t)\) showed a decreasing monotonicity, but with different values. The expected mileage between failures, calculated as the definite integral of the reliability function, took a finite value for the exponential and Weibull models, reaching 4255.32 km and 4686.22 km, respectively. For the neural model, the expected value approached infinity. The above fact indicates the inability of the neural network to extrapolate the reliability function. Thus, when using a neural model, it is necessary to impose constraints derived from the empirical data set. The practical aspect of determining the \(ET\) (expected mileage between failures) value can be to use it as an indicator for planning periodic vehicle maintenance. The purpose of periodic servicing is to restore the technical life and minimise the risk of failure and malfunction. The technical system, in which the analysed group of vehicles operates, assumes the realisation of preventive maintenance at  
Figure 13: Definite integral graph of reliability function depending on integration interval. \begin{table}
\begin{tabular}{c c} \hline \hline
**Model** & \(ET\) (km) \\ \hline Exponential & 4255.32 \\ Weibull & 4686.22 \\ Neural & - \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Expected mileage between failures. intervals of 1 calendar year or every 5000.0 km of the mileage. Comparing this value to the expected mileage between failures, it can be concluded that the periodic services are carried out too rarely, which causes frequent failures and negatively affects the reliability of military vehicles. So far, the applications of artificial neural networks for modelling the reliability of technical objects have been focused mainly on the precise predictions of reliability function values and the times of subsequent failure occurrences. This study goes beyond these areas of application, as the focus is on creating an accurate neural model that can be expressed in terms of analytical relationships. This approach allows further analysis of the model and determination of the remaining reliability characteristics. The presented reliability testing methodology allows for the analysis and assessment of the reliability of military vehicles based on the observation of a certain period of operation in natural conditions, without the need for costly experiments and time-consuming simulations.