Stability analysis of a new kind n-unit series repairable system
In this paper, we deal with a new model of an n-unit series repairable system, in which a concept of a repairman with multiple-delayed vacation is introduced and the impact on the system reliability due to a replaceable facility is also considered. This paper is devoted to studying the unique existe...
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| Veröffentlicht in: | Applied mathematical modelling 2011, Vol.35 (1), p.202-217 |
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| container_title | Applied mathematical modelling |
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| creator | Guo, Lina Xu, Houbao Gao, Chao Zhu, Guangtian |
| description | In this paper, we deal with a new model of an
n-unit series repairable system, in which a concept of a repairman with multiple-delayed vacation is introduced and the impact on the system reliability due to a replaceable facility is also considered. This paper is devoted to studying the unique existence and stability of the system solution.
C
0-semigroup theory is used to prove the existence of a unique nonnegative time-dependent solution of the system. Then by analyzing the spectra distribution of the system operator, we prove that the dynamic solution of the system asymptotically converges to the nonnegative steady-state solution which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Furthermore, we discuss the exponential stability of the system in a special case. Some reliability indices of the system are also studied and the optimal vacation time is analyzed at the end of the paper. |
| doi_str_mv | 10.1016/j.apm.2010.05.018 |
| format | Article |
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n-unit series repairable system, in which a concept of a repairman with multiple-delayed vacation is introduced and the impact on the system reliability due to a replaceable facility is also considered. This paper is devoted to studying the unique existence and stability of the system solution.
C
0-semigroup theory is used to prove the existence of a unique nonnegative time-dependent solution of the system. Then by analyzing the spectra distribution of the system operator, we prove that the dynamic solution of the system asymptotically converges to the nonnegative steady-state solution which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Furthermore, we discuss the exponential stability of the system in a special case. Some reliability indices of the system are also studied and the optimal vacation time is analyzed at the end of the paper.</description><identifier>ISSN: 0307-904X</identifier><identifier>DOI: 10.1016/j.apm.2010.05.018</identifier><identifier>CODEN: AMMODL</identifier><language>eng</language><publisher>Kidlington: Elsevier Inc</publisher><subject>Applied sciences ; Asymptotic properties ; Asymptotic stability ; Availability ; C0-semigroup theory ; Dynamic tests ; Dynamical systems ; Dynamics ; Exact sciences and technology ; Mathematical models ; Operational research and scientific management ; Operational research. Management science ; Operators ; Queuing theory. Traffic theory ; Reliability indices ; Reliability theory. Replacement problems ; Spectra ; Stability ; Steady-state solution</subject><ispartof>Applied mathematical modelling, 2011, Vol.35 (1), p.202-217</ispartof><rights>2010 Elsevier Inc.</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c402t-72c00a1cc5df5d4b4639ec07421b73da21b926575aaac71b78bfaeb89f11a0c73</citedby><cites>FETCH-LOGICAL-c402t-72c00a1cc5df5d4b4639ec07421b73da21b926575aaac71b78bfaeb89f11a0c73</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.apm.2010.05.018$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>315,781,785,3551,4025,27928,27929,27930,46000</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=23751207$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Guo, Lina</creatorcontrib><creatorcontrib>Xu, Houbao</creatorcontrib><creatorcontrib>Gao, Chao</creatorcontrib><creatorcontrib>Zhu, Guangtian</creatorcontrib><title>Stability analysis of a new kind n-unit series repairable system</title><title>Applied mathematical modelling</title><description>In this paper, we deal with a new model of an
n-unit series repairable system, in which a concept of a repairman with multiple-delayed vacation is introduced and the impact on the system reliability due to a replaceable facility is also considered. This paper is devoted to studying the unique existence and stability of the system solution.
C
0-semigroup theory is used to prove the existence of a unique nonnegative time-dependent solution of the system. Then by analyzing the spectra distribution of the system operator, we prove that the dynamic solution of the system asymptotically converges to the nonnegative steady-state solution which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Furthermore, we discuss the exponential stability of the system in a special case. Some reliability indices of the system are also studied and the optimal vacation time is analyzed at the end of the paper.</description><subject>Applied sciences</subject><subject>Asymptotic properties</subject><subject>Asymptotic stability</subject><subject>Availability</subject><subject>C0-semigroup theory</subject><subject>Dynamic tests</subject><subject>Dynamical systems</subject><subject>Dynamics</subject><subject>Exact sciences and technology</subject><subject>Mathematical models</subject><subject>Operational research and scientific management</subject><subject>Operational research. Management science</subject><subject>Operators</subject><subject>Queuing theory. Traffic theory</subject><subject>Reliability indices</subject><subject>Reliability theory. 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Management science</topic><topic>Operators</topic><topic>Queuing theory. Traffic theory</topic><topic>Reliability indices</topic><topic>Reliability theory. Replacement problems</topic><topic>Spectra</topic><topic>Stability</topic><topic>Steady-state solution</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Guo, Lina</creatorcontrib><creatorcontrib>Xu, Houbao</creatorcontrib><creatorcontrib>Gao, Chao</creatorcontrib><creatorcontrib>Zhu, Guangtian</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Applied mathematical modelling</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Guo, Lina</au><au>Xu, Houbao</au><au>Gao, Chao</au><au>Zhu, Guangtian</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stability analysis of a new kind n-unit series repairable system</atitle><jtitle>Applied mathematical modelling</jtitle><date>2011</date><risdate>2011</risdate><volume>35</volume><issue>1</issue><spage>202</spage><epage>217</epage><pages>202-217</pages><issn>0307-904X</issn><coden>AMMODL</coden><abstract>In this paper, we deal with a new model of an
n-unit series repairable system, in which a concept of a repairman with multiple-delayed vacation is introduced and the impact on the system reliability due to a replaceable facility is also considered. This paper is devoted to studying the unique existence and stability of the system solution.
C
0-semigroup theory is used to prove the existence of a unique nonnegative time-dependent solution of the system. Then by analyzing the spectra distribution of the system operator, we prove that the dynamic solution of the system asymptotically converges to the nonnegative steady-state solution which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Furthermore, we discuss the exponential stability of the system in a special case. Some reliability indices of the system are also studied and the optimal vacation time is analyzed at the end of the paper.</abstract><cop>Kidlington</cop><pub>Elsevier Inc</pub><doi>10.1016/j.apm.2010.05.018</doi><tpages>16</tpages><oa>free_for_read</oa></addata></record> |
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| source | Access via ScienceDirect (Elsevier); EZB-FREE-00999 freely available EZB journals |
| subjects | Applied sciences Asymptotic properties Asymptotic stability Availability C0-semigroup theory Dynamic tests Dynamical systems Dynamics Exact sciences and technology Mathematical models Operational research and scientific management Operational research. Management science Operators Queuing theory. Traffic theory Reliability indices Reliability theory. Replacement problems Spectra Stability Steady-state solution |
| title | Stability analysis of a new kind n-unit series repairable system |
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