# Application of a Selected Pseudorandom Number Generator for the Reliability of Farm Tractors
## 1 Introduction
Random number generators (in our case--pseudorandom number generators) have been known for several decades and are constantly being developed [27; 28; 29; 30]. If the algorithm is known, successive elements of the sequence can be predicted, so there is no randomness. The generated sequence of numbers has a discrete rather than continuous distribution. The first extensive use of the Monte Carlo (MC) method by [PERSON] in 1944 allowed for understanding of the fundamentals of the chain reaction, the basis for construction of the atomic bomb. The MC simulation method is intuitive and universal. It is used for solving both random and nonrandom tasks, such as complex integrals, differential equations, nonlinear equations and optimization (minimization), as well as simulation of dynamical systems in physics [31; 32; 33; 34; 35]. It can be used for issues where analytical methods fail, e.g., to assess the reliability of systems with a complex arrangement of elements or the analysis of systems with dependent operating times and device failures [37]. The accuracy of the result obtained with the MC method depends primarily on the number of randomizations (checks) and the quality of the pseudorandom number generator. It usually increases with the number of trials, although this is not always the case. The pseudorandom number generator has a finite quantity of random numbers in a cycle. For example, this method is used for integration when the time taken to obtain the result is more important than its accuracy. The classic Monte Carlo method has the following advantages: intuitive nature, ease of implementation, insensitivity to the shape of the failure area and the ability to make a simulation in an original space [31; 32; 34; 36; 38; 39]. The MC method is inextricably linked to the development of numerical methods and computer programs using random simulation techniques to mimic the statistical population. In conventional statistical analysis software packages, the computer constructs the community according to the user's recipe. Then, a random sample from the community for each MC repetition is simulated, analyzed and stored. After multiple repetitions, the stored results will imitate the distribution of the statistical sample. LHS is a statistical method of making a sample of probable sets of parameter values with a multivariate probability distribution. The LHS method has been used since 1980, after publication of the study by [PERSON] et al. [40] and the development of computer codes in the following years. The difference between the LHS method and standard randomization consists in the fact that it takes previously generated samples into account. Moreover, it is necessary to assume in advance how many sampling points are needed. In the standard MC method, samples are generated without taking the previously randomized ones into account, and the number of samples is unknown. In the LHS method, the places where the samples were taken from are remembered in the matrix notation (row and column). The optimal hypercube is generated in the orthogonal method, in which the probabilistic space is divided into equally probable subspaces. All orthogonal sampling points are selected simultaneously. Each subspace is sampled from the same density. In this way, orthogonal sampling ensures that the set of random numbers is a very good representation of actual random sample variability, whereas traditional (extensive) sampling is simply a set of random numbers without any guarantee of representativeness. Usually, the latter method is enough to achieve sufficient accuracy for frequent problems, on condition that the assumptions of the generation of the optimal hypercube are met. In the classic MC method, several hundred times more randomizations would normally be needed in order to achieve the same accuracy. The purpose of this study was to compare empirical defect/reliability data on Zetor tractors collected over the course of a year with data generated by Monte Carlo techniques or Latin hypercube sampling.