Birnbaum importance-based simulated annealing algorithm for solving the component assignment problem of linear connected-(r, s)-out-of-(m, n):F lattice systems
The component assignment problem (CAP) is one of the most important problems in reliability engineering. This paper proposes a Birnbaum importance-based simulated annealing (SA) algorithm for the CAP of linear connected-( r , s )-out-of-( m , n ):F lattice systems. Here, the CAP is assigning the c...
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| Vydané v: | International journal of system assurance engineering and management Ročník 15; číslo 4; s. 1407 - 1414 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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New Delhi
Springer India
01.04.2024
Springer Nature B.V |
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| ISSN: | 0975-6809, 0976-4348 |
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| Abstract | The component assignment problem (CAP) is one of the most important problems in reliability engineering. This paper proposes a Birnbaum importance-based simulated annealing (SA) algorithm for the CAP of linear connected-(
r
,
s
)-out-of-(
m
,
n
):F lattice systems. Here, the CAP is assigning the components to maximize system reliability, and Birnbaum importance is a measure of the importance of a component assigned at a certain position in the CAP. If the number of components is small, this problem can be solved within an acceptable time by enumerating all solution candidates. However, it is difficult to solve the problem by using this approach with large numbers of components, because the required computational time increases rapidly with the number of components. Based on these factors, we propose an algorithm to solve the CAP of large-sized linear connected-(
r
,
s
)-out-of-(
m
,
n
):F lattice systems within an acceptable time. We performed numerical experiments to evaluate the effectiveness of combining Birnbaum importance and SA because the proposed algorithm could aid in designing reliable systems. |
|---|---|
| AbstractList | The component assignment problem (CAP) is one of the most important problems in reliability engineering. This paper proposes a Birnbaum importance-based simulated annealing (SA) algorithm for the CAP of linear connected-(r, s)-out-of-(m, n):F lattice systems. Here, the CAP is assigning the components to maximize system reliability, and Birnbaum importance is a measure of the importance of a component assigned at a certain position in the CAP. If the number of components is small, this problem can be solved within an acceptable time by enumerating all solution candidates. However, it is difficult to solve the problem by using this approach with large numbers of components, because the required computational time increases rapidly with the number of components. Based on these factors, we propose an algorithm to solve the CAP of large-sized linear connected-(r, s)-out-of-(m, n):F lattice systems within an acceptable time. We performed numerical experiments to evaluate the effectiveness of combining Birnbaum importance and SA because the proposed algorithm could aid in designing reliable systems. The component assignment problem (CAP) is one of the most important problems in reliability engineering. This paper proposes a Birnbaum importance-based simulated annealing (SA) algorithm for the CAP of linear connected-( r , s )-out-of-( m , n ):F lattice systems. Here, the CAP is assigning the components to maximize system reliability, and Birnbaum importance is a measure of the importance of a component assigned at a certain position in the CAP. If the number of components is small, this problem can be solved within an acceptable time by enumerating all solution candidates. However, it is difficult to solve the problem by using this approach with large numbers of components, because the required computational time increases rapidly with the number of components. Based on these factors, we propose an algorithm to solve the CAP of large-sized linear connected-( r , s )-out-of-( m , n ):F lattice systems within an acceptable time. We performed numerical experiments to evaluate the effectiveness of combining Birnbaum importance and SA because the proposed algorithm could aid in designing reliable systems. |
| Author | Nakamura, Taishin Homma, Isshin Yamamoto, Hisashi |
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| Cites_doi | 10.21236/AD0670563 10.1007/s10479-012-1223-1 10.1002/1520-6750(199408)41:5<683::AID-NAV3220410510>3.0.CO;2-Y 10.1109/TR.2019.2925142 10.1109/24.159819 10.1088/1757-899X/1043/3/032019 10.1587/transfun.E92.A.1578 10.1080/0740817X.2010.532856 10.1109/24.387391 10.1126/science.220.4598.671 10.1109/3477.484436 10.1016/j.ress.2021.108051 10.1007/s12204-019-2125-z |
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| Copyright | The Author(s) under exclusive licence to The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. The Author(s) under exclusive licence to The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2022. |
| Copyright_xml | – notice: The Author(s) under exclusive licence to The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. – notice: The Author(s) under exclusive licence to The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2022. |
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| Keywords | Birnbaum importance out-of- F lattice system Simulated annealing Linear connected- Component assignment problem |
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| References | YaoQZhuXKuoWA Birnbaum-importance based genetic local search algorithm for component assignment problemsAnnal Op Res20122121185200314815610.1007/s10479-012-1223-1 NakamuraTYamamotoHAlgorithm for solving optimal arrangement problem in connected-(r,s)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(r, s)$$\end{document}-out-of-(m,n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(m, n)$$\end{document}: F lattice systemIEEE Trans Reliab201969249750910.1109/TR.2019.2925142 Birnbaum ZW (1968) On the importance of different components in a multicomponent system. Washington Univ Seattle Lab Stat Res HollandJHAdaptation in natural and artificial systems1975USAUniversity of Michigan Press KoutrasMVPapadopoulosGKPapastavridisSGNote: pairwise rearrangements in reliability structuresNaval Res Logistics1994415683687128351210.1002/1520-6750(199408)41:5<683::AID-NAV3220410510>3.0.CO;2-Y KirkpatrickSGelattCDVecchiMPOptimization by simulated annealingScience1983220459867168070248510.1126/science.220.4598.671 DorigoMManiezzoVColorniAAnt system: optimization by a colony of cooperating agentsIEEE Trans Syst, Man, Cybern, Part B: Cybern1996261294110.1109/3477.484436 LinFHKuoWReliability importance and invariant optimal allocationJ Heuristics1991392244253 HommaIYamamotoHNakamuraTNecessary condition based simulated annealing algorithm for the component assignment problem of linear connected-(r,s)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(r, s)$$\end{document}-out-of-(m,n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(m, n)$$\end{document}: F systemsProc Reliab Maintenance Eng Summit202120218089 WangWCaiZZhaoJSiSoptimization of linear consecutive-k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-out-of-n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document}: F systems with birnbaum importance based ant colony optimization algorithmJ Shanghai Jiao Tong University (Science)202025225326010.1007/s12204-019-2125-z YaoQZhuXKuoWHeuristics for component assignment problems based on the Birnbaum importanceIIE Trans201143963364610.1080/0740817X.2010.532856 ShingyochiKApplication of simulated annealing method to optimal arrangement problems in a consecutive-k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-out-of-n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document}: F system (in Japanese)Reliab Eng Assoc Japan20133513743 GuanZShiYQiuSA Birnbaum Importance and regression analysis based heuristic algorithm for multi-type component assignment problemIOP Conf Ser: Mater Sci Eng2021104331810.1088/1757-899X/1043/3/032019 ShingyochiKYamamotoHEfficient genetic algorithm for optimal arrangement in a linear consecutive-k-out-of-n: F systemIEICE Trans Fundam Electron, Commun Computer Sci20099271578159410.1587/transfun.E92.A.1578 QiuSMingXSallakMLuJA Birnbaum importance-based two-stage approach for two-type component assignment problemsReliab Eng Syst Safety202221811110.1016/j.ress.2021.108051 ZuoMKuoWDesign and performance analysis of consecutive-k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-out-of-n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document} structureIIE Trans19903722032301045963 BoehmeTKKossowAPreussWA Generalization of consecutive-k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-out-of-n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document}: F systemsIEEE Trans Reliab199241345145710.1109/24.159819 CaiZSiSSunSLiCOptimization of linear consecutive-k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-out-of-n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document} system with a Birnbaum importance-based genetic algorithmIEEE Trans Reliab2016413451457 YamamotoHMiyakawaMReliability of a linear connected-(r,s)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(r, s)$$\end{document}-out-of-(m,n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(m, n)$$\end{document}: F lattice systemIEEE Trans Reliab199544233333610.1109/24.387391 M Zuo (1848_CR19) 1990; 37 TK Boehme (1848_CR2) 1992; 41 MV Koutras (1848_CR9) 1994; 41 K Shingyochi (1848_CR14) 2009; 92 FH Lin (1848_CR10) 1991; 39 K Shingyochi (1848_CR13) 2013; 35 Z Cai (1848_CR3) 2016; 41 Q Yao (1848_CR17) 2011; 43 W Wang (1848_CR15) 2020; 25 Q Yao (1848_CR18) 2012; 212 Z Guan (1848_CR5) 2021; 1043 H Yamamoto (1848_CR16) 1995; 44 M Dorigo (1848_CR4) 1996; 26 T Nakamura (1848_CR11) 2019; 69 1848_CR1 I Homma (1848_CR7) 2021; 2021 S Qiu (1848_CR12) 2022; 218 JH Holland (1848_CR6) 1975 S Kirkpatrick (1848_CR8) 1983; 220 |
| References_xml | – reference: Birnbaum ZW (1968) On the importance of different components in a multicomponent system. Washington Univ Seattle Lab Stat Res – reference: DorigoMManiezzoVColorniAAnt system: optimization by a colony of cooperating agentsIEEE Trans Syst, Man, Cybern, Part B: Cybern1996261294110.1109/3477.484436 – reference: HollandJHAdaptation in natural and artificial systems1975USAUniversity of Michigan Press – reference: ShingyochiKApplication of simulated annealing method to optimal arrangement problems in a consecutive-k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-out-of-n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document}: F system (in Japanese)Reliab Eng Assoc Japan20133513743 – reference: GuanZShiYQiuSA Birnbaum Importance and regression analysis based heuristic algorithm for multi-type component assignment problemIOP Conf Ser: Mater Sci Eng2021104331810.1088/1757-899X/1043/3/032019 – reference: KirkpatrickSGelattCDVecchiMPOptimization by simulated annealingScience1983220459867168070248510.1126/science.220.4598.671 – reference: WangWCaiZZhaoJSiSoptimization of linear consecutive-k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-out-of-n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document}: F systems with birnbaum importance based ant colony optimization algorithmJ Shanghai Jiao Tong University (Science)202025225326010.1007/s12204-019-2125-z – reference: ZuoMKuoWDesign and performance analysis of consecutive-k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-out-of-n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document} structureIIE Trans19903722032301045963 – reference: KoutrasMVPapadopoulosGKPapastavridisSGNote: pairwise rearrangements in reliability structuresNaval Res Logistics1994415683687128351210.1002/1520-6750(199408)41:5<683::AID-NAV3220410510>3.0.CO;2-Y – reference: ShingyochiKYamamotoHEfficient genetic algorithm for optimal arrangement in a linear consecutive-k-out-of-n: F systemIEICE Trans Fundam Electron, Commun Computer Sci20099271578159410.1587/transfun.E92.A.1578 – reference: YaoQZhuXKuoWHeuristics for component assignment problems based on the Birnbaum importanceIIE Trans201143963364610.1080/0740817X.2010.532856 – reference: LinFHKuoWReliability importance and invariant optimal allocationJ Heuristics1991392244253 – reference: YamamotoHMiyakawaMReliability of a linear connected-(r,s)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(r, s)$$\end{document}-out-of-(m,n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(m, n)$$\end{document}: F lattice systemIEEE Trans Reliab199544233333610.1109/24.387391 – reference: QiuSMingXSallakMLuJA Birnbaum importance-based two-stage approach for two-type component assignment problemsReliab Eng Syst Safety202221811110.1016/j.ress.2021.108051 – reference: HommaIYamamotoHNakamuraTNecessary condition based simulated annealing algorithm for the component assignment problem of linear connected-(r,s)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(r, s)$$\end{document}-out-of-(m,n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(m, n)$$\end{document}: F systemsProc Reliab Maintenance Eng Summit202120218089 – reference: BoehmeTKKossowAPreussWA Generalization of consecutive-k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-out-of-n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document}: F systemsIEEE Trans Reliab199241345145710.1109/24.159819 – reference: NakamuraTYamamotoHAlgorithm for solving optimal arrangement problem in connected-(r,s)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(r, s)$$\end{document}-out-of-(m,n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(m, n)$$\end{document}: F lattice systemIEEE Trans Reliab201969249750910.1109/TR.2019.2925142 – reference: YaoQZhuXKuoWA Birnbaum-importance based genetic local search algorithm for component assignment problemsAnnal Op Res20122121185200314815610.1007/s10479-012-1223-1 – reference: CaiZSiSSunSLiCOptimization of linear consecutive-k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-out-of-n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document} system with a Birnbaum importance-based genetic algorithmIEEE Trans Reliab2016413451457 – ident: 1848_CR1 doi: 10.21236/AD0670563 – volume: 212 start-page: 185 issue: 1 year: 2012 ident: 1848_CR18 publication-title: Annal Op Res doi: 10.1007/s10479-012-1223-1 – volume: 41 start-page: 683 issue: 5 year: 1994 ident: 1848_CR9 publication-title: Naval Res Logistics doi: 10.1002/1520-6750(199408)41:5<683::AID-NAV3220410510>3.0.CO;2-Y – volume: 69 start-page: 497 issue: 2 year: 2019 ident: 1848_CR11 publication-title: IEEE Trans Reliab doi: 10.1109/TR.2019.2925142 – volume: 41 start-page: 451 issue: 3 year: 1992 ident: 1848_CR2 publication-title: IEEE Trans Reliab doi: 10.1109/24.159819 – volume: 1043 start-page: 1 issue: 3 year: 2021 ident: 1848_CR5 publication-title: IOP Conf Ser: Mater Sci Eng doi: 10.1088/1757-899X/1043/3/032019 – volume: 92 start-page: 1578 issue: 7 year: 2009 ident: 1848_CR14 publication-title: IEICE Trans Fundam Electron, Commun 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| Snippet | The component assignment problem (CAP) is one of the most important problems in reliability engineering. This paper proposes a Birnbaum importance-based... |
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| SubjectTerms | Algorithms Assignment problem Cameras Computing time Engineering Engineering Economics Experiments Failure Genetic algorithms Logistics Marketing Organization Original Article Quality Control Reliability Reliability engineering Safety and Risk Simulated annealing Surveillance System reliability |
| Title | Birnbaum importance-based simulated annealing algorithm for solving the component assignment problem of linear connected-(r, s)-out-of-(m, n):F lattice systems |
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