# Reliability Analysis of Military Vehicles Based on Censored Failures Data
## 1 Introduction  
Modelling and reliability analysis of technical objects should be an important element in the process of technical systems management. Any failure can result in a decrease in the efficiency of production and logistics processes carried out using technical means [1, 2]. Modelling of a technical object operation while taking failure prediction into account makes it possible to minimise losses resulting from such failures. In addition, advanced knowledge of reliability should support the planning process for periodic maintenance and spare parts supply. Therefore, in many fields of science and technology, as well as branches of the economy, attempts are made to create models reflecting the real operational processes of exploitation of technical objects and devices [3, 4, 5]. Effective operation of military transport systems requires a fleet of reliable vehicles. The occurrence of failures to the means of transport during the task almost always results in greater or lesser losses for the entire system. In order to meet the challenges posed to the armed forces and the requirements for the efficient implementation of transport processes, appropriate maintenance, diagnostic and repair systems must be organised. Reliability models are useful tools for forecasting and evaluating the maintenance and repair needs of military vehicles [6, 7, 8]. Therefore, the development of accurate reliability models is critical to maintaining the assumed readiness and effectiveness of military transport systems. Research fields dealing with reliability problems are frequently addressed in the scientific literature [9, 10, 11, 12]. In the article [13], a reliability assessment method was developed as a decision support in the selection of a vehicle fleet for a transport company. The developed indicator took into account reliability characteristics such as mileages to the first failure, mileages between failures and the intensity of failures. The authors of the publication [14] presented a method for determining the reliability function using theKaplan-Meier estimator and a modified Kolmogorov-Smirnov statistical test. The case study consisted of 5 years of data on the driver's door locks usage for a sample size of 45 rail vehicles. Whereas in the study [15], an analysis of aircraft reliability was carried out. Several reliability models were analysed using statistical tests. The log-normal model proved to be the closest fitting model for the empirical data collected. In the paper [16], a Cox regression model was developed to account for the relationship between operational and maintenance conditions affecting aircraft reliability. Modelling the reliability of technical objects using artificial neural networks remains the subject of many scientific publications. [PERSON] et al. [17] proposed regression models based on Multilayer Perceptron (MLP) and Radial Basis Function (RBF) networks, which they then implemented to describe and predict the reliability of turbochargers and engines. The standardised roots of mean square error for the analysed objects reached acceptably low values. The authors of the paper [18], on the other hand, developed a model using the Support Vector Regression method combined with genetic algorithms, whose accuracy was an order of magnitude better than the model based on RBF networks for data taken from the publication [17]. In contrast, the Support Vector Machines-based model, when applied to the time series of failure occurrences presented in the paper [19], achieved accuracy similar to MLP and RBF models. A significant improvement in prediction accuracy occurred for models presented in publications [20,21]. The first was developed as a hybrid of artificial neural networks and genetic algorithms, for which the magnitude of the time series delay was determined using the Shannon entropy. The smallest error, close to zero, for the datasets from the article [17] was obtained by the one presented in the paper [21].