Dynamic and Steady-State Solutions for a General Availability Model
Exact dynamic and steady-state solutions are given for the state equations of a fairly general availability model with known, constant, failure and repair rates for each component of the system. The states of all components are mutually statistically independent. Rules for writing the transition mat...
Gespeichert in:
| Veröffentlicht in: | IEEE transactions on reliability 1985-12, Vol.R-34 (5), p.539-544 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 544 |
|---|---|
| container_issue | 5 |
| container_start_page | 539 |
| container_title | IEEE transactions on reliability |
| container_volume | R-34 |
| creator | Johnson, L. Ensign |
| description | Exact dynamic and steady-state solutions are given for the state equations of a fairly general availability model with known, constant, failure and repair rates for each component of the system. The states of all components are mutually statistically independent. Rules for writing the transition matrix and its eigenvalues and eigenvectors are given, and explicit formulas for the solutions are given in terms of the latter. Three special cases are derived from this model. A dynamic solution is given for a reliability model with no repair. Steady-state solutions are found for a model in which all components have the same failure and repair rates and for a model in which repair is required before a second failure can occur. For all models, approximate upper bounds are developed for the time required for the systems to arrive at the steady state; the longest time constant in the solution is given in terms of the failure and repair rates. |
| doi_str_mv | 10.1109/TR.1985.5222258 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_RIE</sourceid><recordid>TN_cdi_ieee_primary_5222258</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ieee_id>5222258</ieee_id><sourcerecordid>24583951</sourcerecordid><originalsourceid>FETCH-LOGICAL-c350t-b1e4e2224dadc04713d3784083304f67564c3203713b4ac1da5292086a515aa53</originalsourceid><addsrcrecordid>eNqNkEFLAzEQhYMoWKtnD15yEG_bZjbJbvZYaq1CRWjrOUyzWYikuzXZCvvv3dLas3MZhvfN4_EIuQc2AmDFeL0cQaHkSKb9SHVBBiClSiBP4ZIMGAOVFDItrslNjF_9KUShBmT63NW4dYZiXdJVa7HsklWLraWrxu9b19SRVk2gSOe2tgE9nfyg87hx3rUdfW9K62_JVYU-2rvTHpLPl9l6-posPuZv08kiMVyyNtmAFbbPJkosDRM58JLnSjDFORNVlstMGJ4y3gsbgQZK7OOmTGUoQSJKPiRPR99daL73NrZ666Kx3mNtm33UqZCKFxL-A2Z5lh7A8RE0oYkx2Ervgtti6DQwfWhVr5f60Ko-tdp_PJ6sMRr0VcDauHh-UzIHKESPPRwxZ609q38mv0lofUI</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>24567621</pqid></control><display><type>article</type><title>Dynamic and Steady-State Solutions for a General Availability Model</title><source>IEEE Electronic Library (IEL)</source><creator>Johnson, L. Ensign</creator><creatorcontrib>Johnson, L. Ensign</creatorcontrib><description>Exact dynamic and steady-state solutions are given for the state equations of a fairly general availability model with known, constant, failure and repair rates for each component of the system. The states of all components are mutually statistically independent. Rules for writing the transition matrix and its eigenvalues and eigenvectors are given, and explicit formulas for the solutions are given in terms of the latter. Three special cases are derived from this model. A dynamic solution is given for a reliability model with no repair. Steady-state solutions are found for a model in which all components have the same failure and repair rates and for a model in which repair is required before a second failure can occur. For all models, approximate upper bounds are developed for the time required for the systems to arrive at the steady state; the longest time constant in the solution is given in terms of the failure and repair rates.</description><identifier>ISSN: 0018-9529</identifier><identifier>EISSN: 1558-1721</identifier><identifier>DOI: 10.1109/TR.1985.5222258</identifier><identifier>CODEN: IERQAD</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Applied sciences ; Availability ; Differential equations ; Eigenvalue ; Eigenvalues and eigenfunctions ; Eigenvector ; Exact sciences and technology ; Failure analysis ; Inspection ; Linear systems ; Markov model ; Operational research and scientific management ; Operational research. Management science ; Reliability theory. Replacement problems ; State variable ; Steady-state ; Upper bound ; Vectors ; Writing</subject><ispartof>IEEE transactions on reliability, 1985-12, Vol.R-34 (5), p.539-544</ispartof><rights>1986 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c350t-b1e4e2224dadc04713d3784083304f67564c3203713b4ac1da5292086a515aa53</citedby><cites>FETCH-LOGICAL-c350t-b1e4e2224dadc04713d3784083304f67564c3203713b4ac1da5292086a515aa53</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/5222258$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27901,27902,54733</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/5222258$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=8571194$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Johnson, L. Ensign</creatorcontrib><title>Dynamic and Steady-State Solutions for a General Availability Model</title><title>IEEE transactions on reliability</title><addtitle>TR</addtitle><description>Exact dynamic and steady-state solutions are given for the state equations of a fairly general availability model with known, constant, failure and repair rates for each component of the system. The states of all components are mutually statistically independent. Rules for writing the transition matrix and its eigenvalues and eigenvectors are given, and explicit formulas for the solutions are given in terms of the latter. Three special cases are derived from this model. A dynamic solution is given for a reliability model with no repair. Steady-state solutions are found for a model in which all components have the same failure and repair rates and for a model in which repair is required before a second failure can occur. For all models, approximate upper bounds are developed for the time required for the systems to arrive at the steady state; the longest time constant in the solution is given in terms of the failure and repair rates.</description><subject>Applied sciences</subject><subject>Availability</subject><subject>Differential equations</subject><subject>Eigenvalue</subject><subject>Eigenvalues and eigenfunctions</subject><subject>Eigenvector</subject><subject>Exact sciences and technology</subject><subject>Failure analysis</subject><subject>Inspection</subject><subject>Linear systems</subject><subject>Markov model</subject><subject>Operational research and scientific management</subject><subject>Operational research. Management science</subject><subject>Reliability theory. Replacement problems</subject><subject>State variable</subject><subject>Steady-state</subject><subject>Upper bound</subject><subject>Vectors</subject><subject>Writing</subject><issn>0018-9529</issn><issn>1558-1721</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1985</creationdate><recordtype>article</recordtype><recordid>eNqNkEFLAzEQhYMoWKtnD15yEG_bZjbJbvZYaq1CRWjrOUyzWYikuzXZCvvv3dLas3MZhvfN4_EIuQc2AmDFeL0cQaHkSKb9SHVBBiClSiBP4ZIMGAOVFDItrslNjF_9KUShBmT63NW4dYZiXdJVa7HsklWLraWrxu9b19SRVk2gSOe2tgE9nfyg87hx3rUdfW9K62_JVYU-2rvTHpLPl9l6-posPuZv08kiMVyyNtmAFbbPJkosDRM58JLnSjDFORNVlstMGJ4y3gsbgQZK7OOmTGUoQSJKPiRPR99daL73NrZ666Kx3mNtm33UqZCKFxL-A2Z5lh7A8RE0oYkx2Ervgtti6DQwfWhVr5f60Ko-tdp_PJ6sMRr0VcDauHh-UzIHKESPPRwxZ609q38mv0lofUI</recordid><startdate>19851201</startdate><enddate>19851201</enddate><creator>Johnson, L. Ensign</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>H8D</scope></search><sort><creationdate>19851201</creationdate><title>Dynamic and Steady-State Solutions for a General Availability Model</title><author>Johnson, L. Ensign</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c350t-b1e4e2224dadc04713d3784083304f67564c3203713b4ac1da5292086a515aa53</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1985</creationdate><topic>Applied sciences</topic><topic>Availability</topic><topic>Differential equations</topic><topic>Eigenvalue</topic><topic>Eigenvalues and eigenfunctions</topic><topic>Eigenvector</topic><topic>Exact sciences and technology</topic><topic>Failure analysis</topic><topic>Inspection</topic><topic>Linear systems</topic><topic>Markov model</topic><topic>Operational research and scientific management</topic><topic>Operational research. Management science</topic><topic>Reliability theory. Replacement problems</topic><topic>State variable</topic><topic>Steady-state</topic><topic>Upper bound</topic><topic>Vectors</topic><topic>Writing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Johnson, L. Ensign</creatorcontrib><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><collection>Aerospace Database</collection><jtitle>IEEE transactions on reliability</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Johnson, L. Ensign</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Dynamic and Steady-State Solutions for a General Availability Model</atitle><jtitle>IEEE transactions on reliability</jtitle><stitle>TR</stitle><date>1985-12-01</date><risdate>1985</risdate><volume>R-34</volume><issue>5</issue><spage>539</spage><epage>544</epage><pages>539-544</pages><issn>0018-9529</issn><eissn>1558-1721</eissn><coden>IERQAD</coden><abstract>Exact dynamic and steady-state solutions are given for the state equations of a fairly general availability model with known, constant, failure and repair rates for each component of the system. The states of all components are mutually statistically independent. Rules for writing the transition matrix and its eigenvalues and eigenvectors are given, and explicit formulas for the solutions are given in terms of the latter. Three special cases are derived from this model. A dynamic solution is given for a reliability model with no repair. Steady-state solutions are found for a model in which all components have the same failure and repair rates and for a model in which repair is required before a second failure can occur. For all models, approximate upper bounds are developed for the time required for the systems to arrive at the steady state; the longest time constant in the solution is given in terms of the failure and repair rates.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TR.1985.5222258</doi><tpages>6</tpages></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | ISSN: 0018-9529 |
| ispartof | IEEE transactions on reliability, 1985-12, Vol.R-34 (5), p.539-544 |
| issn | 0018-9529 1558-1721 |
| language | eng |
| recordid | cdi_ieee_primary_5222258 |
| source | IEEE Electronic Library (IEL) |
| subjects | Applied sciences Availability Differential equations Eigenvalue Eigenvalues and eigenfunctions Eigenvector Exact sciences and technology Failure analysis Inspection Linear systems Markov model Operational research and scientific management Operational research. Management science Reliability theory. Replacement problems State variable Steady-state Upper bound Vectors Writing |
| title | Dynamic and Steady-State Solutions for a General Availability Model |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-12T20%3A45%3A31IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_RIE&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Dynamic%20and%20Steady-State%20Solutions%20for%20a%20General%20Availability%20Model&rft.jtitle=IEEE%20transactions%20on%20reliability&rft.au=Johnson,%20L.%20Ensign&rft.date=1985-12-01&rft.volume=R-34&rft.issue=5&rft.spage=539&rft.epage=544&rft.pages=539-544&rft.issn=0018-9529&rft.eissn=1558-1721&rft.coden=IERQAD&rft_id=info:doi/10.1109/TR.1985.5222258&rft_dat=%3Cproquest_RIE%3E24583951%3C/proquest_RIE%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=24567621&rft_id=info:pmid/&rft_ieee_id=5222258&rfr_iscdi=true |