## 3 Materials and Methods
### Reliability Indicators  
The degree of vehicle serviceability can be continuously improved by evaluating reliability indicators based on the knowledge of damage that occurred during vehicle operation. Figure 6: A sample traffic zone in a built-up area: **(a)** the general view, **(b)** the view from the position of the driver of the car with the damaged suspension system, **(c)** the view from the position of the driver of the car moving correctly, **(d)** the view through the eyes of one of the pedestrians. Information about the vehicle's technical condition as well as reliability provided to maintenance personnel may improve the quality of maintenance activities and travel safety. Reliability indicators for technical objects may be estimated by means of several probabilistic models. This article uses the Weibull distribution. That distribution is a generalisation of the exponential distribution and is distinguished by non-zero values taken for positive values of a random variable. Hence, that distribution is of particular importance in the reliability theory. In addition, the Weibull distribution allows the estimation of reliability indicators, regardless of the change in the pattern of the damage intensity function. Accordingly, the Weibull distribution may be used to describe, for example, the fatigue life of materials, mechanical structures and operating costs of the facility, e.g., maintenance costs [27], etc. The amount of damage as well as its occurrence over time is the basis for determining the object's reliability indicators. Therefore, the technical condition of the cars that are subject to investigations in this article was monitored from the moment they were placed into service until their mileage exceeded 100,000 km. The results of the observations were recorded in maintenance logs specially created for the purpose. Table 2 provides information on the time of occurrence of damage in the suspension system. The time of occurrence of a defect in the suspension system was taken as the moment when any symptoms of malfunctioning of both rubber and metal components were noticed during daily technical observation. Owing to such an operation strategy, thirty times were collected at which repair and maintenance intervention was required, based on which reliability indicators may be estimated. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Item** & **The Car with the Damaged Suspension System** & **The Car Moving Correctly** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 2: Time of occurrence of damage in the car suspension system [km]. During the ongoing monitoring of the suspension system, no component damage was found that could be responsible for bringing the system to an undesirable state, i.e., exceeding the limit states that would cause permanent system unserviceability. The following reliability indicators were determined on the basis of the recorded suspension system failure times: the reliability function, damage intensity function, the cumulative distribution function of the operation time to the first damage, and probability distribution density function of correct operation time to the first damage. The reliability function is described by Formula (1):  
\[R(t)=e^{(-\frac{t}{\beta})^{\alpha}} \tag{1}\]  
In the reliability theory, the failure intensity function is very important; it is defined as the ratio of the probability of component damage in a time interval to the length of that interval. That function is determined by Formula (2):  
\[\lambda(t)=\frac{\alpha}{\beta}\bigg{(}\frac{t}{\beta}\bigg{)}^{\alpha-1} \tag{2}\]  
The operation time cumulative distribution function (the unreliability function) is the conditional probability of object damage until time \(t\), provided that the device was fit for service at the start-up.