# Application of a Selected Pseudorandom Number Generator for the Reliability of Farm Tractors
## 4 Discussion  
Data deficiency is a problem in reliability research. Without a database of specific damage times (time-to-fail), it is not possible to calculate reliability functions and create user-relevant reliability rankings. The use of pseudorandom number generators has made it possible to enlarge the database. The assumed confidence interval results in the fact that is very likely (degree of probability--95%) that the plots and, in consequence, the reliability functions \(R(t)\) based on  
Figure 2: Scatter plots of the reliability function \(R(t)\) for Zetor farm tractors based on data generated by the MC (**a**), LHS (**b**), IC (**c**) and LHS + IC (**d**) methods. the empirical use-to-failure periods (times-to-fail) are almost identical to those generated randomly. Both the shape parameters \(\alpha\) and scale parameters \(\lambda\) for the two-parameter Weibull distribution \(R(t)=\exp(-\lambda\cdot t^{\alpha})\) are similar. The shape parameter \(\alpha\) is always greater than 1 (1.49, 1.53, 1.55, 1.54 and again 1.55). This means that the data well describe the third stage of machine wear on the Lorentz wear curve. The curve illustrates the inoperability of machinery as a result of the accumulation of irreversible changes, continuous ageing of materials, wear and tear, deformation of the structure or a gradual change in the value of device parameters beyond acceptable limits. For shape parameters \(\alpha>1\), the initial decrease in reliability \(R(t)\) is small, but later it increases considerably (as in the exponential distribution). It is a classic course of the reliability function for technological devices, including agricultural machinery and farm tractors. The values of scale factor \(\lambda\), and thus the expected value of failure occurrence (454, 450, 452, 455 and again 452 EOH), enable calculation of the failure intensity ratio. With the arithmetic mean of 453 EOH, as much as 63.2% (characteristic operability) of Zetor tractors will have failed to operate by that time, with an intensity of 0.0022 EOH\({}^{-1}\). In the graphs (Figures 1 and 2), it will always be the value of \(R(t)=36.8\%\) (exactly \(e^{-1}\)) on the ordinate axes. It is difficult to clearly indicate which of the random number generators is better for this task. In order to estimate which generator can be considered the best in the sense of the most accurate match, a 100% linear cumulative plot was constructed (Figure 3), which includes the deviation of the 200 time-to-fail data generated by the four methods from values obtained empirically at the Zetor brand service station. As shown in Figure 3, the actual state is best represented by the times-to-fail generated by the Monte Carlo (MC) method. The spread around the zero value is smallest among all the used methods. The sum of deviations is also the smallest as it amounts only to 510 EOH, compared to 1707 EOH (for the combined LHS and IC method) and 1821 EOH (for the LHS method only) in absolute terms. The least favorable results come from the IC method (as much as 2980 EOH difference). The efficiency of agricultural production largely depends on the performance of agricultural machinery in various operating conditions [5]. There are more than 100 different types of technological devices related to plant and animal production in a modern farm (or rather an agricultural enterprise). This is a wide spectrum of machinery ranging from simple devices (or rather tools), such as cultivators, to complex ones with several thousand (e.g., about 4000 individual parts in a farm tractor) or even more than a dozen thousand parts (e.g., about 18,000 parts in a combine harvester, and even 25,000 parts in a self-propelled  
Figure 3: A comparison of the failure times of Zetor farm tractors generated by means of pseudorandom number generators—100% linear cumulative plot. forage harvester). As far as the improvement of durability and reliability is concerned, such systems (usually serial structures) can be broken very easily.