# Reliability Analysis of Military Vehicles Based on Censored Failures Data
## 1 Introduction
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Case Study** & **Results** & **Paper** \\ \hline \multirow{2}{*}{Regressive models based on neural networks (MLP and RBF)} & Turbocharges in diesel engine (time to failure) Car engines (miles to failure) & Normalized Root Mean Square Error \(NRMSE=3.9\times 10^{-3}\) (RBF) for turbocharges \(NRMSE=1.22\times 10^{-2}\) (MLP Gaussian activation) for engines & [17] \\ \hline Model (GA-SVR) based on Support Vector Regression (SVR) and Genetic Algorithm (GA) & Turbocharges in diesel engine (data from [17]) & \(MAPE=0.0387\%\) & [18] \\ \hline \multirow{2}{*}{Neural model with one and two hidden layers} & \multirow{2}{*}{Vehicles (mileage to failure)} & Correlation Coefficient \(R=0.80\) & [27] \\  & & Error = 9\% & \\ \hline Model based on Support Vector Machines (SVM) (time series regression as an alternative to probability distribution models) & Turbocharges in diesel engine (data from [17]) & \(NRMSE=1.25\times 10^{-2}\) for engines & [19] \\ \hline PSO+SVM (Particle Swarm-optimized Support Vector Machine) & Turbocharges in diesel engine and car engines (data from [17]) & \(NRMSE=2.0303\times 10^{-4}\) for turbocharges \(NRMSE=7.1126\times 10^{-3}\) for car engines \(NRMSE=2.0305\times 10^{-4}\) for submarine engines & [28] \\  & Submarine diesel engines & engines & engines \\ \hline Hybrid model: neural networks and Genetic Algorithm (GA) (Number of lag data calculated using Shannon entropy) & Turbocharges in diesel engine and car engines (data from [17]) & \(NRMSE=2.52\times 10^{-4}\) for turbocharges \(NRMSE=1.195\times 10^{-2}\) for engines \(R^{2}\): 0.94-0.99 and \(NRMSE=8.36\times 10^{-3}\) for LHD machines & [20] \\ \hline Neural model based on time series data & Control, operating and military systems & \(R\): 0.82-0.99 & [29] \\ \hline Hybrid model based on metaheuristics and neural networks & Validation on simulated data & Values of Reliability Index and probability of failure are the same as those obtained with other methods & [30] \\ \hline Model SDWPSO-BPNN (hybrid of dynamic weight particle swarm optimisation-based sine map and back propagation neural network) & Turbocharges in diesel engine (data from [17]) and industrial robot systems & \(NRMSE=2.3\times 10^{-6}\) for industrial robot systems & [21] \\ \hline Cascade feedforward neural network & CNC machine tool spindles & \(MAPE\): 1.56-2.53\% & [22] \\ \hline ANN supported stochastic process & Simulated data and degradation dataset of spindle systems & Mean absolute relative error \(<0.13\) for all samples of real degradation data & [24] \\ \hline ANN supported Wiener process & Simulated data and degradation dataset of spindle systems & Mean absolute relative error \(<0.06\) for all samples of real degradation data & [25] \\ \hline Model based on convolutional neural networks & IEEE Reliability Test Systems and Saskatchewan Power Corporation & Root Mean Square Error \(RMSE=0.1038\) for IEEE RTS & [26] \\ \hline Three-layer feedforward artificial neural network & Reliability of machine tools & Reliability of machine components obtained values 0.8966–0.9840 & [23] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Neural modelling of reliability—literature review. other authors. The methodology involving the use of artificial neural networks with a low complexity structure to approximate reliability functions is also an innovation. This allows the neural model to be presented as a relationship that can form the basis for determining the other reliability characteristics. The authors of the publications summarised in Table 1 focused on maximising the precision of representation of the estimated values of the reliability function, creating very complex models for this purpose. The complex structures of neural networks complicate the analysis of the developed models, making more difficult the calculation of the failure intensity function, the failure probability density function and the expected time (mileage) to failure or between failures functions.