# Reliability Analysis of Military Vehicles Based on Censored Failures Data
## 3 Results and Discussion
### Analysis of Reliability Models  
The reliability function models developed as a result of the study showed a high degree of match with the estimated values. Table 5 summarises the values of the linear correlation coefficient \(R\) and the \(MSE\) error to compare the neural model with the exponential and Weibull models commonly used in literature. For all three models, the \(R\) correlation coefficient reached a value exceeding 0.99. However, the best fitting model is the neural model. The \(MSE\) error made by the MLP 1-1-1 is more than 2 times smaller than for the exponential model and about 14% smaller than the Weibull model.  
Figure 10: MLP 1-1-1 regression plot.  
The use of exponential and linear activation functions in the neural model allows for the utilisation of the differentiability of the analytical form of the approximating reliability function to calculate the relationships describing the failure probability density \(f(t)\) and the failure intensity \(\lambda(t)\). For the exponential and Weibull models, these relationships were developed according to the equations available in the literature. Table 6 shows the function \(f(t)\), while Table 7 presents the failure intensity \(\lambda(t)\) for each reliability model.  
To compare the courses of the individual reliability characteristics, their graphical interpretations are shown in Figures 11 and 12. The probability density function has a very similar course for all three models. The Weibull model for the mileage in the \(0.0\div 1000.0\) km range is an exception, for which the function \(f(t)\) significantly deviates from the values achieved by the other models. For all models, the function \(f(t)\) is decreasing.  
The failure intensity function, which is the quotient of the failure probability density value and the reliability value, takes different courses for each of the three reliability models developed. For the exponential model, according to the theoretical assumptions, the function is constant and takes the value 0.000235 [1/km] for the studied sample of vehicles. For the Weibull model, the course of the function \(\lambda(t)\) for arguments 0.0 \(\div\) 1000.0 km is similar to that of the function \(f(t)\). This is due to the reliability function taking values close to one for these arguments. The further course of the intensity function for the Weibull model is flattened and reaches values smaller than in the exponential model. In the neural model, the function \(\lambda(t)\) is decreasing, with values smaller than in the exponential model for the whole domain resulting from the model constraints.  
Figure 13 presents a plot showing the value of the integral of the reliability function over the integration interval [0.0, \(t\)] for \(t\leq\) 100,000.0 km. The calculated definite integral in the interval from 0.0 to infinity corresponds to the expected value of the mileage between failures. For the exponential and Weibull model, the expected value of \(ET\) is finite and is 4255.32 km and 4686.22 km, respectively (Table 8). For the neural model, the expected value of the mileage between failures approaches infinity. The use of the model, therefore, requires the implementation of appropriate constraints due to the inability of the neural network to extrapolate the value of the reliability function beyond the known data range. The empirical data for which the value of the reliability function was estimated range between [0.0; 21,477.0 km]. In this range, the \(ET\) value for the neural model attains similar levels to the Weibull model.  
The value of the expected mileage between failures can be an indicator that determines the intervals between periodic inspections and maintenance of technical objects. Appropriate adjustment of the maintenance intervals according to the determined reliability characteristics can positively influence the readiness of the technical object and can increase the probability of a task being properly carried out without failure occurring.  
Figure 12: Failure intensity functions of reliability models.