Об одном классе резервируемых устройств
| 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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| Summary: | 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 |
| Language: | Russian |
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2014
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| Series: | Математика |
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| Online Access: | http://journals.tsu.ru/mathematics/&journal_page=archive&id=1079&article_id=11426 http://elibrary.ru/item.asp?id=22020950 |
| Format: | Electronic Book Chapter |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=653493 |