Об одном классе резервируемых устройств; Вестник Томского государственного университета. Математика и механика; № 4 (30)
| Parent link: | Вестник Томского государственного университета. Математика и механика/ Национальный исследовательский Томский государственный университет (ТГУ).— , 2007- № 4 (30).— 2014.— [С. 14-23] |
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| Riassunto: | Заглавие с экрана Рассмотрены 3 модели резервированных устройств и исследованы их общие свойства с использованием сигма-оператора. In this paper, we consider three models of redundancy: (1) By use of the mean time between system failures on a finite interval; (2) By use of the mean time between system failures on a infinite interval; (3) By use of the system reliability on a finite interval. For all three models, the redundancy criterion has the following form: k -m T(k,r) =? C[p k ''q''T(r - i). (1) i=0 Using the sigma-operator turns out to be an effective way for proving many properties of optimal strategies. Let T(r) > 0 and T(r) increase. The following properties are proved: T(r + 2) < T(r +1) ( ) T(r +1) T(r) '' Under more restrictive conditions, this inequality was obtained in the thesis of L.V. Ushakova. (4) The function ln T(r) is convex; (5) T(k +1,r) - T(k,r) increases with an increase in r. To find the optimal strategy, a simplified algorithm is obtained using the properties. This algorithm is based on a modification of the Bellman dynamic programming method mentioned in V.V. Travkina''s work. The essence of the algorithm is as follows. (1) If there are m elements, then we have k 0 (m) = m. For each model, T(m) is calculated. (2) All further calculations for the three models are similar. Режим доступа: по договору с организацией-держателем ресурса |
| Lingua: | russo |
| Pubblicazione: |
2014
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| Serie: | Математика |
| Soggetti: | |
| Accesso online: | http://journals.tsu.ru/mathematics/&journal_page=archive&id=1079&article_id=11426 http://elibrary.ru/item.asp?id=22020950 |
| Natura: | Elettronico Capitolo di libro |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=653493 |
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| 200 | 1 | |a Об одном классе резервируемых устройств |d On a class of reserved devices |f В. Н. Губин, Г. Г. Пестов | |
| 203 | |a Текст |c электронный | ||
| 225 | 1 | |a Математика | |
| 300 | |a Заглавие с экрана | ||
| 320 | |a [Библиогр.: с. 23 (9 назв.)] | ||
| 330 | |a Рассмотрены 3 модели резервированных устройств и исследованы их общие свойства с использованием сигма-оператора. | ||
| 330 | |a In this paper, we consider three models of redundancy: (1) By use of the mean time between system failures on a finite interval; (2) By use of the mean time between system failures on a infinite interval; (3) By use of the system reliability on a finite interval. For all three models, the redundancy criterion has the following form: k -m T(k,r) =? C[p k ''q''T(r - i). (1) i=0 Using the sigma-operator turns out to be an effective way for proving many properties of optimal strategies. Let T(r) > 0 and T(r) increase. The following properties are proved: T(r + 2) < T(r +1) ( ) T(r +1) T(r) '' Under more restrictive conditions, this inequality was obtained in the thesis of L.V. Ushakova. (4) The function ln T(r) is convex; (5) T(k +1,r) - T(k,r) increases with an increase in r. To find the optimal strategy, a simplified algorithm is obtained using the properties. This algorithm is based on a modification of the Bellman dynamic programming method mentioned in V.V. Travkina''s work. The essence of the algorithm is as follows. (1) If there are m elements, then we have k 0 (m) = m. For each model, T(m) is calculated. (2) All further calculations for the three models are similar. | ||
| 333 | |a Режим доступа: по договору с организацией-держателем ресурса | ||
| 461 | |t Вестник Томского государственного университета. Математика и механика |f Национальный исследовательский Томский государственный университет (ТГУ) |d 2007- | ||
| 463 | |t № 4 (30) |v [С. 14-23] |d 2014 | ||
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| 610 | 1 | |a система | |
| 610 | 1 | |a надежность | |
| 610 | 1 | |a стратегии | |
| 610 | 1 | |a модели | |
| 610 | 1 | |a оптимизация | |
| 700 | 1 | |a Губин |b В. Н. |c математик |c младший научный сотрудник Томского политехнического университета, кандидат физико-математических наук |f 1988- |g Владимир Николаевич |3 (RuTPU)RU\TPU\pers\38042 | |
| 701 | 1 | |a Пестов |b Г. Г. |g Герман Гаврилович | |
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