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Doğrusal genelleştirilmiş ağırlıklı n-den k çıkışlı F sistemin güvenilirlik analizi

Year 2021, Volume 14, Issue 1, 1 - 12, 30.06.2021

Abstract

Belirli sayıdaki bileşenlerin paralel bağlanmasıyla oluşan yapı modül olarak adlandırılır. N tane modülün dairesel veya doğrusal sıralanmasıyla genelleştirilmiş n-den k çıkışlı sistem elde edilir. Bu çalışmada, doğrusal genelleştirilmiş ağırlıklı n-den k çıkışlı F sistem tanımlanmıştır. Bu sistemin güvenilirliği ve sistem imzası elde edilmiştir. Ağırlıklı sistemlerde her bir bileşenin sisteme katkısı farklı olduğundan bu katkı bileşen ağırlığı olarak ifade edilir. Sistemdeki her bir bileşenin kendine ait ağırlığı ve çalışma olasılığı vardır. Modülü oluşturan bileşenlerin toplam ağırlığına modül ağırlığı denir. Ardışık arızalı modüllerin toplam ağırlığı en az k olduğunda veya sistemdeki arızalı bileşenlerin toplam ağırlığı en az τ olduğunda doğrusal genelleştirilmiş ağırlıklı n-den k çıkışlı F sistem arızalanır.

References

  • J. M. Kontoleon, 1980, Reliability determination of a r-successive-out-of-n:F system, IEEE Transactions on Reliability, 29(5), 437.
  • D. T. Chiang, S. C. Niu, 1981, Reliability of consecutive-k-out-of-n : F system, IEEE Transactions on Reliability, 30(1), 87–89.
  • C. Derman, G. J. Lieberman, S. M. Ross, 1982, On the consecutive-k-of-n : F system, IEEE Transactions on Reliability, 31(1), 57–63.
  • M. Lambiris, S. Papastavridis, 1985, Exact reliability formulas for line & circular consecutive-k-out-of-n:F systems, IEEE Transactions on Reliability, 34(2), 124–126.
  • M. T. Chao, J. C. Fu, M. V. Koutras, 1995, Survey of reliability studies of consecutive-k-out-of-n:F & related systems, IEEE Transactions on Reliability, 44(1), 120–127.
  • J. Guan, Y. Wu, 2006, Repairable consecutive-k-out-of-n:F system with fuzzy states, Fuzzy Sets and Systems, 157(1), 121–142.
  • X. Zhu, M. Boushaba, M. Reghioua, 2015, Joint reliability importance in a consecutive-k-out-of-n: F system and an m-consecutive-k-out-of-n:F system for Markov-dependent components, IEEE Transactions on Reliability, 64(2), 784–798.
  • J. Guo, Y. Shen, Z. Lu, H. Che, Z. Liu, S. Zeng, 2020, Reliability modeling for consecutive k-out-of-n: F systems with local load-sharing components subject to dependent degradation and shock processes, Quality and Reliability Engineering International, 36(5), 1553–1569.
  • R. E. Barlow, K. D. Heidtmann, 1984, Computing k-out-of-n system reliability, IEEE Transactions on Reliability, 33(4), 322–323.
  • W. S. Griffith, 1986, On consecutive-k-out-of-n failure systems and their generalizations, Reliability and Quality Control, A. P. Basu, (eds.), Elsevier, Amsterdam. s. 157–165.
  • L. Cui, M. Xie, 2005, On a generalized k-out-of-n system and its reliability, International Journal of Systems Science, 36(5), 267–274.
  • M. J. Zuo, Z. Tian, 2006, Performance evaluation of generalized multi-state k-out-of-n systems, IEEE Transactions on Reliability, 55(2), 319–327.
  • S. Eryilmaz, B. Mahmoud, 2012, Linear m -consecutive-k , l-Out-of-n: F system, IEEE Transactions on Reliability, 61(3), 787–791.
  • K. K. Kamalja, 2017, Reliability computing method for generalized k-out-of-n system, Journal of Computational and Applied Mathematics, 323, 111–122.
  • C. Kan, 2018, A Note on circular m-consecutive-k-out-of-n: F systems, Trends and Perspectives in Linear Statistical Inference, M. Tez, D. Rosen, (eds.), Springer International Publishing, Cham, s. 131–142.
  • J. S. Wu, R. J. Chen, 1994, An Algorithm for computing the reliability of weighted-k-out-of-n systems, IEEE Transactions on Reliability, 43(2), 327–328.
  • Y. Higashiyama, 2001, A factored reliability formula for weighted-k-out-of-n system, Asia-Pacific Journal of Operational Research, 18(1), 61–66.
  • S. Eryilmaz, G. Y. Tutuncu, 2009, Reliability evaluation of linear consecutive-weighted-k-out-of-n:F system, Asia-Pacific Journal of Operational Research, 26(6), 805–816.
  • F. J. Samaniego, 1985, On closure of the IFR class under formation of coherent systems, IEEE Transactions on Reliability, 34(1), 69–72.
  • S. Eryilmaz, 2010, Review of recent advances in reliability of consecutive k-out-of-n and related systems, Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 224(3), 225–237.
  • S. Eryilmaz, A. Tuncel, 2015, Computing the signature of a generalized k-out-of-n system, IEEE Transactions on Reliability, 64(2), 766–771.
  • P. J. Boland, 2001, Signatures of indirect majority systems, Journal of Applied Probability, 38(2), 597–603.

Reliability analysis of linear generalized weighted k-out-of-n F system

Year 2021, Volume 14, Issue 1, 1 - 12, 30.06.2021

Abstract

The structure formed by connecting a certain number of components in parallel is called a module. A generalized k-out-of-n F system consists of a sequence of N ordered modules in a line or circle. In this study, linear generalized weighted k-out-of-n F system is defined. The reliability and system signature of this system have been obtained. Since the coefficient of each component is different in weighted systems, this additive is expressed as component weight. Each component in the system has its own weight and working probability. The total weight of all components in the module is called the module weight. The linear generalized weighted k-out-of-n F system fails when the total weight of consecutive failed modules is at least k or the total weight of the failed components in the system is at least τ

References

  • J. M. Kontoleon, 1980, Reliability determination of a r-successive-out-of-n:F system, IEEE Transactions on Reliability, 29(5), 437.
  • D. T. Chiang, S. C. Niu, 1981, Reliability of consecutive-k-out-of-n : F system, IEEE Transactions on Reliability, 30(1), 87–89.
  • C. Derman, G. J. Lieberman, S. M. Ross, 1982, On the consecutive-k-of-n : F system, IEEE Transactions on Reliability, 31(1), 57–63.
  • M. Lambiris, S. Papastavridis, 1985, Exact reliability formulas for line & circular consecutive-k-out-of-n:F systems, IEEE Transactions on Reliability, 34(2), 124–126.
  • M. T. Chao, J. C. Fu, M. V. Koutras, 1995, Survey of reliability studies of consecutive-k-out-of-n:F & related systems, IEEE Transactions on Reliability, 44(1), 120–127.
  • J. Guan, Y. Wu, 2006, Repairable consecutive-k-out-of-n:F system with fuzzy states, Fuzzy Sets and Systems, 157(1), 121–142.
  • X. Zhu, M. Boushaba, M. Reghioua, 2015, Joint reliability importance in a consecutive-k-out-of-n: F system and an m-consecutive-k-out-of-n:F system for Markov-dependent components, IEEE Transactions on Reliability, 64(2), 784–798.
  • J. Guo, Y. Shen, Z. Lu, H. Che, Z. Liu, S. Zeng, 2020, Reliability modeling for consecutive k-out-of-n: F systems with local load-sharing components subject to dependent degradation and shock processes, Quality and Reliability Engineering International, 36(5), 1553–1569.
  • R. E. Barlow, K. D. Heidtmann, 1984, Computing k-out-of-n system reliability, IEEE Transactions on Reliability, 33(4), 322–323.
  • W. S. Griffith, 1986, On consecutive-k-out-of-n failure systems and their generalizations, Reliability and Quality Control, A. P. Basu, (eds.), Elsevier, Amsterdam. s. 157–165.
  • L. Cui, M. Xie, 2005, On a generalized k-out-of-n system and its reliability, International Journal of Systems Science, 36(5), 267–274.
  • M. J. Zuo, Z. Tian, 2006, Performance evaluation of generalized multi-state k-out-of-n systems, IEEE Transactions on Reliability, 55(2), 319–327.
  • S. Eryilmaz, B. Mahmoud, 2012, Linear m -consecutive-k , l-Out-of-n: F system, IEEE Transactions on Reliability, 61(3), 787–791.
  • K. K. Kamalja, 2017, Reliability computing method for generalized k-out-of-n system, Journal of Computational and Applied Mathematics, 323, 111–122.
  • C. Kan, 2018, A Note on circular m-consecutive-k-out-of-n: F systems, Trends and Perspectives in Linear Statistical Inference, M. Tez, D. Rosen, (eds.), Springer International Publishing, Cham, s. 131–142.
  • J. S. Wu, R. J. Chen, 1994, An Algorithm for computing the reliability of weighted-k-out-of-n systems, IEEE Transactions on Reliability, 43(2), 327–328.
  • Y. Higashiyama, 2001, A factored reliability formula for weighted-k-out-of-n system, Asia-Pacific Journal of Operational Research, 18(1), 61–66.
  • S. Eryilmaz, G. Y. Tutuncu, 2009, Reliability evaluation of linear consecutive-weighted-k-out-of-n:F system, Asia-Pacific Journal of Operational Research, 26(6), 805–816.
  • F. J. Samaniego, 1985, On closure of the IFR class under formation of coherent systems, IEEE Transactions on Reliability, 34(1), 69–72.
  • S. Eryilmaz, 2010, Review of recent advances in reliability of consecutive k-out-of-n and related systems, Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 224(3), 225–237.
  • S. Eryilmaz, A. Tuncel, 2015, Computing the signature of a generalized k-out-of-n system, IEEE Transactions on Reliability, 64(2), 766–771.
  • P. J. Boland, 2001, Signatures of indirect majority systems, Journal of Applied Probability, 38(2), 597–603.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Fahrettin ÖZBEY (Primary Author)
BİTLİS EREN ÜNİVERSİTESİ
0000-0002-7847-739X
Türkiye


Gökhan GÖKDERE
Fırat Üniversitesi
0000-0001-7004-7670
Türkiye

Supporting Institution Yok
Publication Date June 30, 2021
Published in Issue Year 2021, Volume 14, Issue 1

Cite

Bibtex @research article { jssa864655, journal = {İstatistikçiler Dergisi:İstatistik ve Aktüerya}, issn = {1308-0539}, eissn = {1308-0539}, address = {}, publisher = {Aktüerya Derneği}, year = {2021}, volume = {14}, pages = {1 - 12}, doi = {}, title = {Doğrusal genelleştirilmiş ağırlıklı n-den k çıkışlı F sistemin güvenilirlik analizi}, key = {cite}, author = {Özbey, Fahrettin and Gökdere, Gökhan} }
APA Özbey, F. & Gökdere, G. (2021). Doğrusal genelleştirilmiş ağırlıklı n-den k çıkışlı F sistemin güvenilirlik analizi . İstatistikçiler Dergisi:İstatistik ve Aktüerya , Prof. Dr. Hasan Işın DENER özel sayısı , 1-12 . Retrieved from https://dergipark.org.tr/en/pub/jssa/issue/62966/864655
MLA Özbey, F. , Gökdere, G. "Doğrusal genelleştirilmiş ağırlıklı n-den k çıkışlı F sistemin güvenilirlik analizi" . İstatistikçiler Dergisi:İstatistik ve Aktüerya 14 (2021 ): 1-12 <https://dergipark.org.tr/en/pub/jssa/issue/62966/864655>
Chicago Özbey, F. , Gökdere, G. "Doğrusal genelleştirilmiş ağırlıklı n-den k çıkışlı F sistemin güvenilirlik analizi". İstatistikçiler Dergisi:İstatistik ve Aktüerya 14 (2021 ): 1-12
RIS TY - JOUR T1 - Doğrusal genelleştirilmiş ağırlıklı n-den k çıkışlı F sistemin güvenilirlik analizi AU - Fahrettin Özbey , Gökhan Gökdere Y1 - 2021 PY - 2021 N1 - DO - T2 - İstatistikçiler Dergisi:İstatistik ve Aktüerya JF - Journal JO - JOR SP - 1 EP - 12 VL - 14 IS - 1 SN - 1308-0539-1308-0539 M3 - UR - Y2 - 2021 ER -
EndNote %0 Journal of Statisticians: Statistics and Actuarial Sciences Doğrusal genelleştirilmiş ağırlıklı n-den k çıkışlı F sistemin güvenilirlik analizi %A Fahrettin Özbey , Gökhan Gökdere %T Doğrusal genelleştirilmiş ağırlıklı n-den k çıkışlı F sistemin güvenilirlik analizi %D 2021 %J İstatistikçiler Dergisi:İstatistik ve Aktüerya %P 1308-0539-1308-0539 %V 14 %N 1 %R %U
ISNAD Özbey, Fahrettin , Gökdere, Gökhan . "Doğrusal genelleştirilmiş ağırlıklı n-den k çıkışlı F sistemin güvenilirlik analizi". İstatistikçiler Dergisi:İstatistik ve Aktüerya 14 / 1 (June 2021): 1-12 .
AMA Özbey F. , Gökdere G. Doğrusal genelleştirilmiş ağırlıklı n-den k çıkışlı F sistemin güvenilirlik analizi. JSSAS. 2021; 14(1): 1-12.
Vancouver Özbey F. , Gökdere G. Doğrusal genelleştirilmiş ağırlıklı n-den k çıkışlı F sistemin güvenilirlik analizi. İstatistikçiler Dergisi:İstatistik ve Aktüerya. 2021; 14(1): 1-12.
IEEE F. Özbey and G. Gökdere , "Doğrusal genelleştirilmiş ağırlıklı n-den k çıkışlı F sistemin güvenilirlik analizi", İstatistikçiler Dergisi:İstatistik ve Aktüerya, vol. 14, no. 1, pp. 1-12, Jun. 2021