Application of a Selected Pseudorandom Number Generator for the Reliability of Farm Tractors
Abstract
:1. Introduction
2. Materials and Methods
- The theoretical distributions are divided into N intervals of equal probability.
- The value of the cumulative distribution function is randomized from each interval.
- The cumulative distribution function is inverted to obtain the value of the variable for the randomized value of the cumulative distribution function.
- The values of individual variables are randomly combined to obtain a multivariate random variable. In this procedure, the relationships between variables are ignored.
3. Results
4. Discussion
5. Conclusions
- Empirical (sampling) data which allow for historical events give reliable results of the assessment of the reliability of technological devices such as farm tractors. However, it is difficult to obtain such data from reliable sources such as manufacturers and service technicians of agricultural equipment. Therefore, it is helpful to identify alternative ways of obtaining these data, e.g., available statistical methods such as random/pseudorandom number generators.
- Simulation methods are a separate group of methods of analysis of the reliability of technological devices, which is important for practice. The unquestionable advantages of simulation methods are ease of implementation, the possibility of obtaining results with any accuracy, and insensitivity to nondifferentiability of the limit function or the existence of multiple design points.
- The verification and validation of failure times of the working units obtained from four dedicated random number generators in the Statistica program showed that they could be successfully used in agricultural practice to estimate the failure probability value. It is impossible to indicate the best adaptive method due to the small dataset of only 200 elements, i.e., the failure times of Zetor tractors which were repaired at an authorized service station in Poland.
- Each of the random number generators tested in our study can be regarded as dedicated because it enables the estimation of failure times of technological devices in various units of durability, i.e., CTU (conventional time units). For farm tractors, it is an hour of engine operation, which depends on the engine load, i.e., an engine-operating hour. For agricultural machinery, these may also be a clock hour (e.g., for seed drills, combine harvesters or potato harvesting machines), hectare (e.g., for ploughs and sprayers) or year (e.g., for slurry tankers). Other conventional time units are kilometers travelled (e.g., for transport sets) and tones or kilograms of capacity (e.g., for forage harvesters and collecting presses). The durability of relays and contactors in mechatronic systems can be measured with the number of their correct operations. However, as such data are not publicly available, there are no rankings of machinery and vehicle reliability relevant to farmers.
- There are only two states describing the condition of a technological device in the classical theory of reliability. Proven random number generators are also based only on this assumption. All identified failures (their recorded times) are treated as equally important, which does not reflect reality. Therefore, further improvement of the quality of random number generators is necessary.
- The future is likely to be quantum generators of pseudorandom numbers. Such generators are already finding applications in encryption devices to enhance the security of distributed systems.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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No. | Model | VIN * | EOH ** | Symptoms of Failure | Broken Part | Cause of Failure |
---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 |
1. | Forterra 95 | 1337 | 330 | air escapes | quick coupler | damaged sealing flange |
2. | Forterra 115 | 6708 | 323 | wrong sensor indication | air pressure sensor | short circuit |
3. | Forterra 125 | 2534 | 221 | worn out mounts | wheel disc | inaccurate processing |
4. | Forterra 105 | 1286 | 130 | no light | headlight | short circuit |
5. | Forterra 125 | 2408 | 220 | worn 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 flange |
No. | Empirical DataEOH | New Random Data (EOH) Generated with Method | |||
---|---|---|---|---|---|
MC | LHS | IC | LHS + IC | ||
1 | 2 | 3 | 4 | 5 | 6 |
1. | 2 | 15 | 13 | 16 | 13 |
2. | 3 | 15 | 15 | 17 | 15 |
3. | 3 | 15 | 17 | 20 | 17 |
4. | 4 | 15 | 19 | 22 | 19 |
5. | 4 | 15 | 20 | 24 | 19 |
… | … | … | … | … | … |
196. | 1041 | 164 | 164 | 166 | 164 |
197. | 1474 | 165 | 165 | 166 | 165 |
198. | 1474 | 167 | 165 | 167 | 166 |
199. | 1474 | 168 | 166 | 169 | 166 |
200. | 1498 | 168 | 167 | 169 | 166 |
… | … | … | … | … | … |
996. | - | 1197 | 1281 | 1305 | 1284 |
997. | - | 1209 | 1304 | 1318 | 1309 |
998. | - | 1291 | 1319 | 1337 | 1313 |
999. | - | 1317 | 1349 | 1361 | 1356 |
1000. | - | 1357 | 1383 | 1389 | 1381 |
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Durczak, K.; Rybacki, P.; Sujak, A. Application of a Selected Pseudorandom Number Generator for the Reliability of Farm Tractors. Appl. Sci. 2022, 12, 12452. https://doi.org/10.3390/app122312452
Durczak K, Rybacki P, Sujak A. Application of a Selected Pseudorandom Number Generator for the Reliability of Farm Tractors. Applied Sciences. 2022; 12(23):12452. https://doi.org/10.3390/app122312452
Chicago/Turabian StyleDurczak, Karol, Piotr Rybacki, and Agnieszka Sujak. 2022. "Application of a Selected Pseudorandom Number Generator for the Reliability of Farm Tractors" Applied Sciences 12, no. 23: 12452. https://doi.org/10.3390/app122312452
APA StyleDurczak, K., Rybacki, P., & Sujak, A. (2022). Application of a Selected Pseudorandom Number Generator for the Reliability of Farm Tractors. Applied Sciences, 12(23), 12452. https://doi.org/10.3390/app122312452