# Application of a Selected Pseudorandom Number Generator for the Reliability of Farm Tractors
## 2 Materials and Methods  
The service history of 74 agricultural tractors (4 Zetor models, 45-90 kW power) serviced at an authorized service center in 2012 was used as an empirical base (the actual data). The faults were not divided either by Zetor tractor model or by individual vehicle componetry. It was assumed that each defect eliminated the tractor from use and was equally important. It did not matter which defect occurred. The 200 records (as in Table 1) of tractor use-to-failure periods (time-to-failure), expressed as engine operating hours (EOH), were used to simulate 1000 consecutive use-to-failure periods with the commercial Statistica package (v13.3, StatSoft, Cracow, Poland). \begin{table}
\begin{tabular}{c c c c c c c} \hline
**No.** & **Model** & **VIN \({}^{*}\)** & **EOH \({}^{**}\)** & **Symptoms of Failure** & **Broken Part** & **Cause of Failure** \\ \hline
1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline
1. & Forterra 95 & 1337 & 330 & air escapes & quick coupler & damaged sealing flange \\
2. & Forterra 115 & 6708 & 323 & wrong sensor indication & air pressure & short circuit \\
3. & Forterra 125 & 2534 & 221 & worm out mounts & wheel disc & inaccurate processing \\
4. & Forterra 105 & 1286 & 130 & no light & headlight & short circuit \\
5. & Forterra 125 & 2408 & 220 & worm out mounts & wheels & wheel disc \\  & & & & & & \\  & & & & & & \\
196. & Proxima 85 & 2657 & 610 & shock absorption failure & cabin & gas spring \\
197. & Proxima 85 & 3028 & 487 & shock absorption failure & cabin & gas spring \\
198. & Proxima 85 & 3028 & 487 & engine hour meter failure & panel & short circuit \\
199. & Proxima Plus 85 & 1690 & 4 & voltage drop & battery & faulty battery cell \\
200. & Forterra 125 & 2743 & 304 & shock absorption failure & gas spring & damaged surface of sealing \\  & & & & & & \\ \end{tabular} \({}^{*}\) VIN chassis number; \({}^{**}\) engine operating hours.  
\end{table} 
Table 1: Data from 200 exemplary failures for different models of Zetor tractors [41], Pozané University of Life Sciences. In the first step, the empirical data were analyzed through a Weibull distribution because it is optimal for the failure times of tractors recorded since the beginning of their operation [7; 42]. The offset threshold was assumed to be zero, which meant that only values greater than zero could occur. A 95% confidence interval was assumed. The results were ranked using the Kolmogorov-Smirnoff algorithm. Simulated numerical data were generated with the 'Distributions and Simulation' module in the 'Statistics' tab of the Statistica software. This module enables 'experiments' by simulating multivariate data with a defined distribution while maintaining covariance between variables. In our study, two-parameter Weibull distribution was used (as for empirical data). In the second step, Monte Carlo (MC) and Latin hypercube sampling (LHS) methods were selected. For both methods, data generation is based on the best-fit distributions, whereas the correlations between variables are ignored. Latin hypercube sampling involves dividing the range of each theoretical distribution into N parts so that the probability of selecting each part is the same. N is the sample size. The values of each variable are randomized so that each interval for each variable occurs only once. For example, if there are two variables, X and Y, and the sample size is 3, the first sampling may produce X from interval no. 1 and Y from interval no. 2. In the second sampling, interval no. 1 for X and interval no. 2 for Y are disregarded. This ensures coverage of the full range of variability of all variables. There are four stages of sampling:  
1. The theoretical distributions are divided into N intervals of equal probability. 2. The value of the cumulative distribution function is randomized from each interval. 3. The cumulative distribution function is inverted to obtain the value of the variable for the randomized value of the cumulative distribution function. 4.