The Domain of Residual Lifetime Attraction for the Classical Distributions of the Reliability Theory
The asymptotic behavior of the residual lifetime of the system and its characteristics are studied for the main distributions of reliability theory. Sufficiently precise and simple conditions for the domain of attraction of the exponential distribution are proposed, which are applicable for a wide c...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/21/2831 |
| _version_ | 1797512058709737472 |
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| author | Vladimir Rusev Alexander Skorikov |
| author_facet | Vladimir Rusev Alexander Skorikov |
| author_sort | Vladimir Rusev |
| collection | DOAJ |
| description | The asymptotic behavior of the residual lifetime of the system and its characteristics are studied for the main distributions of reliability theory. Sufficiently precise and simple conditions for the domain of attraction of the exponential distribution are proposed, which are applicable for a wide class of distributions. This approach allows us to take into account important information about modeling the failure-free operation of equipment that has worked reliably for a long time. An analysis of the domain of attraction for popular distributions with “heavy tails” is given. |
| first_indexed | 2024-03-10T05:56:32Z |
| format | Article |
| id | doaj.art-22a472dd821842e5807f8c546647b5be |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T05:56:32Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-22a472dd821842e5807f8c546647b5be2023-11-22T21:19:32ZengMDPI AGMathematics2227-73902021-11-01921283110.3390/math9212831The Domain of Residual Lifetime Attraction for the Classical Distributions of the Reliability TheoryVladimir Rusev0Alexander Skorikov1Department of Higher Mathematics, National University of Oil and Gas (Gubkin University), 19991 Moscow, RussiaDepartment of Higher Mathematics, National University of Oil and Gas (Gubkin University), 19991 Moscow, RussiaThe asymptotic behavior of the residual lifetime of the system and its characteristics are studied for the main distributions of reliability theory. Sufficiently precise and simple conditions for the domain of attraction of the exponential distribution are proposed, which are applicable for a wide class of distributions. This approach allows us to take into account important information about modeling the failure-free operation of equipment that has worked reliably for a long time. An analysis of the domain of attraction for popular distributions with “heavy tails” is given.https://www.mdpi.com/2227-7390/9/21/2831Weibull–Gnedenko distributionresidual lifetimedomain of attractionGG distributionlog-normal distributionBurr distribution |
| spellingShingle | Vladimir Rusev Alexander Skorikov The Domain of Residual Lifetime Attraction for the Classical Distributions of the Reliability Theory Mathematics Weibull–Gnedenko distribution residual lifetime domain of attraction GG distribution log-normal distribution Burr distribution |
| title | The Domain of Residual Lifetime Attraction for the Classical Distributions of the Reliability Theory |
| title_full | The Domain of Residual Lifetime Attraction for the Classical Distributions of the Reliability Theory |
| title_fullStr | The Domain of Residual Lifetime Attraction for the Classical Distributions of the Reliability Theory |
| title_full_unstemmed | The Domain of Residual Lifetime Attraction for the Classical Distributions of the Reliability Theory |
| title_short | The Domain of Residual Lifetime Attraction for the Classical Distributions of the Reliability Theory |
| title_sort | domain of residual lifetime attraction for the classical distributions of the reliability theory |
| topic | Weibull–Gnedenko distribution residual lifetime domain of attraction GG distribution log-normal distribution Burr distribution |
| url | https://www.mdpi.com/2227-7390/9/21/2831 |
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