Comparative Assessment of the Reliability of Non-Recoverable Subsystems of Mining Electronic Equipment Using Various Computational Methods; Mathematics; Vol. 14, iss. 4
| Parent link: | Mathematics.— .— Basel: MDPI AG Vol. 14, iss. 4.— 2026.— Article number 723, 48 p. |
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| Weitere Verfasser: | , , , , , , |
| Zusammenfassung: | Title screen The assessment of reliability in non-repairable subsystems of mining electronic equipment represents a computationally challenging problem, particularly for complex and highly connected structures. This study presents a systematic comparative analysis of several deterministic approaches for reliability estimation, focusing on their computational efficiency, accuracy, and applicability. The investigated methods include classical boundary techniques (minimal paths and cuts), analytical decomposition based on the Bayes theorem, the logic–probabilistic method (LPM) employing triangle–star transformations, and the algorithmic Structure Convolution Method (SCM), which is based on matrix reduction of the system’s connectivity graph. The reliability problem is formally represented using graph theory, where each element is modeled as a binary variable with independent failures, which is a standard and practically justified assumption for power electronic subsystems operating without common-cause coupling. Numerical experiments were carried out on canonical benchmark topologies—bridge, tree, grid, and random connected graphs—representing different levels of structural complexity. The results demonstrate that the SCM achieves exact reliability values with up to six orders of magnitude acceleration compared to the LPM for systems containing more than 20 elements, while maintaining polynomial computational complexity. Qualitatively, the compared approaches differ in the nature of the output and practical applicability: boundary methods provide fast interval estimates suitable for preliminary screening, whereas decomposition may exhibit a systematic bias for highly connected (non-series–parallel) topologies. In contrast, the SCM consistently preserves exactness while remaining computationally tractable for medium and large sparse-to-moderately dense graphs, making it preferable for repeated recalculations in design and optimization workflows. The methods were implemented in Python 3.7 using NumPy and NetworkX, ensuring transparency and reproducibility. The findings confirm that the SCM is an efficient, scalable, and mathematically rigorous tool for reliability assessment and structural optimization of large-scale non-repairable systems. The presented methodology provides practical guidelines for selecting appropriate reliability evaluation techniques based on system complexity and computational resource constraints Текстовый файл |
| Sprache: | Englisch |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://doi.org/10.3390/math14040723 |
| Format: | Elektronisch Buchkapitel |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=685389 |
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| 200 | 1 | |a Comparative Assessment of the Reliability of Non-Recoverable Subsystems of Mining Electronic Equipment Using Various Computational Methods |f N. V. Martyushev, B. V. Malozyomov, A. Y. Demin [et al.] | |
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| 330 | |a The assessment of reliability in non-repairable subsystems of mining electronic equipment represents a computationally challenging problem, particularly for complex and highly connected structures. This study presents a systematic comparative analysis of several deterministic approaches for reliability estimation, focusing on their computational efficiency, accuracy, and applicability. The investigated methods include classical boundary techniques (minimal paths and cuts), analytical decomposition based on the Bayes theorem, the logic–probabilistic method (LPM) employing triangle–star transformations, and the algorithmic Structure Convolution Method (SCM), which is based on matrix reduction of the system’s connectivity graph. The reliability problem is formally represented using graph theory, where each element is modeled as a binary variable with independent failures, which is a standard and practically justified assumption for power electronic subsystems operating without common-cause coupling. Numerical experiments were carried out on canonical benchmark topologies—bridge, tree, grid, and random connected graphs—representing different levels of structural complexity. The results demonstrate that the SCM achieves exact reliability values with up to six orders of magnitude acceleration compared to the LPM for systems containing more than 20 elements, while maintaining polynomial computational complexity. Qualitatively, the compared approaches differ in the nature of the output and practical applicability: boundary methods provide fast interval estimates suitable for preliminary screening, whereas decomposition may exhibit a systematic bias for highly connected (non-series–parallel) topologies. In contrast, the SCM consistently preserves exactness while remaining computationally tractable for medium and large sparse-to-moderately dense graphs, making it preferable for repeated recalculations in design and optimization workflows. The methods were implemented in Python 3.7 using NumPy and NetworkX, ensuring transparency and reproducibility. The findings confirm that the SCM is an efficient, scalable, and mathematically rigorous tool for reliability assessment and structural optimization of large-scale non-repairable systems. The presented methodology provides practical guidelines for selecting appropriate reliability evaluation techniques based on system complexity and computational resource constraints | ||
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| 463 | 1 | |t Vol. 14, iss. 4 |v Article number 723, 48 p. |d 2026 | |
| 610 | 1 | |a reliability of systems | |
| 610 | 1 | |a non-recoverable systems | |
| 610 | 1 | |a minimal paths and sections | |
| 610 | 1 | |a logical–probabilistic method | |
| 610 | 1 | |a system structure convolution method | |
| 610 | 1 | |a mining electronics | |
| 610 | 1 | |a computational methods | |
| 610 | 1 | |a электронный ресурс | |
| 610 | 1 | |a труды учёных ТПУ | |
| 701 | 1 | |a Martyushev |b N. V. |c specialist in the field of material science |c Associate Professor of Tomsk Polytechnic University, Candidate of technical sciences |f 1981- |g Nikita Vladimirovich |9 16754 | |
| 701 | 1 | |a Malozemov |b B. V. |g Boris Vitaljevich | |
| 701 | 1 | |a Demin |b A. Yu. |c specialist in the field of Informatics and computer engineering |c Associate Professor of Tomsk Polytechnic University, candidate of technical sciences |f 1973- |g Anton Yurievich |9 17327 | |
| 701 | 1 | |a Pogrebnoy |b A. V. |c specialist in the field of Informatics and computer engineering |c Associate Professor of Tomsk Polytechnic University, candidate of technical sciences |f 1973- |g Aleksandr Vladimirovich |9 17310 | |
| 701 | 1 | |a Kurdyumov |b G. E. |g Georgy Evgenjevich | |
| 701 | 1 | |a Kondratjev |b V. V. |g Viktor Viktorovich | |
| 701 | 1 | |a Karlina |b A. I. |g Antonina Igorevna | |
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