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Ardıl-k Sistemler için Önerilen Güvenilirlik Sınırlarının Karşılaştırılması

Year 2021, Volume: 10 Issue: 3, 877 - 890, 17.09.2021

Ahmet Demiralp Mehmet Güngör

https://doi.org/10.17798/bitlisfen.942517

Abstract

Hızla gelişen teknolojik gelişmeler, birçok karmaşık yapıya sahip sistemlerin ortaya çıkmasına neden olmuştur. Ortaya çıkan bu sistemler, hem karmaşık yapıda hem de yüksek boyutlu bileşenlerden oluştuğu için bu sistemlerin tam güvenilirliklerini hesaplamak her zaman kolay olmamaktadır. Tam güvenilirlik değerlerinin hesaplanması zor ya da mümkün olmayan bu sistemlerin güvenilirliklerinin belirlenmesi için araştırmacılar, güvenilirlik sınırları kavramını geliştirmişlerdir. Bu çalışmada, ardıl-k sistemler olarak bilinen n-den ardıl k-çıkışlı sistemler için önerilen sınır yaklaşım yöntemlerinin karşılaştırılması amaçlanmıştır. Bu doğrultuda hem söz konusu sistemleri oluşturan bileşenlerin diziliş şekillerine göre doğrusal ve dairesel olarak hem de başarılı ve hatalı olma durumlarına göre adlandırılan sistemler incelenmiştir. Önerilen yöntemlerin belli n, k ve p (q) değerleri için elde edilen sonuçları, tam güvenilirlik değerleriyle karşılaştırılarak tablolar halinde verilmiştir. Buradan elde edilen sonuçlardan güvenilirlik sınırlarının ne kadar doğru olduğu, sadece n ve k değerlerine bağlı olmayıp aynı zamanda p’nin seçildiği aralığa da bağlı olduğu belirlenmiştir.

Keywords

Doğrusal (dairesel) n-den ardıl k-çıkışlı sistem Başarılı ve hatalı sistem Sistem güvenilirliği Sınır yaklaşımları

Supporting Institution

İnönü Üniversitesi Bilimsel Araştırma Projeleri Birimi

Project Number

SDK-2018-991

Thanks

Bu çalışma, Ahmet DEMİRALP’in Doktora Tezi’nden özetlenmiş olup, İnönü Üniversitesi Bilimsel Araştırma Projeleri Birimi tarafından SDK-2018-991 proje numarası ile desteklenmiştir.

References

  • [1] Kuo, W., Zuo, M. J. 2003. Optimal Reliability Modeling: Princeples and Applications. New Jersey: John Wiley & Sons, Inc., 1-544.
  • [2] Tong, Y. L. 1985. A Rearrangement Inequality for the Longest Run, With an Application to Network Reliability. Journal of Applied Probability, 22(2), 386-393.
  • [3] Kuo, W., Zhang, W., Zuo, M. 1990. A Consecutive-k-out-of-n:G System: The Mirror Image of a Consecutive-k-out-of-n:F System. IEEE Transactions on Reliability, 39(2), 244-253.
  • [4] Kontoleon, J. M. 1980. Reliability determination of a r-successive-out-of-n: F system. IEEE Transactions on Reliability, 29(5), 437-437.
  • [5] Chiang, D. T., Niu, S. C. 1981. Reliability of consecutive-k-out-of-n: F system. IEEE Transactions on Reliability, 30(1), 87-89.
  • [6] Zuo, M., Kuo, W. 1990. Design and performance analysis of consecutive-k-out-of-n structure. Naval Research Logistics, 37(2), 203-230.
  • [7] Shanthikumar, J. G. 1982. Recursive algorithm to evaluate the reliability of a consecutive-k-out-of-n: F system. IEEE Transactions on Reliability, 31(5), 442-443.
  • [8] Derman, C., Lieberman, G. J., Ross, S. M. 1982. On the consecutive-k-of-n: F system. IEEE Transactions on Reliability, 31(1), 57-63.
  • [9] Bollinger, R. C., Salvia, A. A. 1982. Consecutive-k-out-of-n: F networks. IEEE Transactions on Reliability, 31(1), 53-56.
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  • [11] Chao, M. T., Lin, G. D. 1984. Economical design of large consecutive-k-out-of-n: F systems. IEEE Transactions on Reliability, 33(5), 411-413.
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  • [13] Fu, J. C. 1985. Reliability of a large consecutive-k-out-of-n: F system. IEEE transactions on reliability, 34(2), 127-130.
  • [14] Antonopoulou, I., Papastavridis, S. 1987. Fast recursive algorithm to evaluate the reliability of a circular consecutive-k-out-of-n: F system. IEEE Transactions on Reliability, 36(1), 83-84.
  • [15] Chan, F. Y., Chan, L. K., Lin, G. D. 1988. On consecutive-k-out-of-n: F systems. European journal of operational research, 36(2), 207-216.
  • [16] Peköz, E. A., Ross, S. M. 1995. A Simple Derivation of Exact Reliability Formulas For Linear and Circular Consecutive-k-out-of-n:F Systems. J. Appl. Prob., 32(2), 554-557.
  • [17] Cluzeau, T., Keller, J., Schneeweiss, W. 2008. An efficient algorithm for computing the reliability of consecutive-k-out-of-n:F systems. IEEE Transactıons On Relıabılıty, 57(1), 84-87.
  • [18] Gökdere, G., Gürcan, M., Kılıç, M. B. 2016. A new method for computing the reliability of consecutive k-out-of-n: F systems. Open Physics, 14(1), 166-170.
  • [19] Gökdere, G., Güral, Y. 2018. Birnbaum Önem Tabanlı Genetik Algoritma ve Doğrusal Ardışık n-den k-çıkışlı Sistemlerin Optimizasyonunda Uygulaması. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, 7(2), 276-283.
  • [20] Özbey, F., Gökdere, G. 2021. Analysis of Linear Consecutive-2-out-of-n:F Repairable System with Different Failure Rate. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, 10(1), 91-99.
  • [21] Özbey, F., Gökdere, G. 2021. Doğrusal genelleştirilmiş ağırlıklı n-den k-çıkışlı F sistemin güvenilirlik analizi. İstatistikçiler Dergisi: İstatistik ve Aktüerya, 14(1), 1-13.
  • [22] Hwang, F. K. 1982. Fast Solutions for Consecutive-k-out-of-n: F System. IEEE Transactions On Reliability, R-31(5), 447-448.
  • [23] Zuo, M. 1993. Reliability and component importance of a consecutive-k-out-of-n system. Microelectronics Reliability, 33(2), 243-258.
  • [24] Salvia, A. A. 1982. Simple Inequalities for Consecutive-k-out-of-n:F Networks. IEEE Transactions On Reliability, R-31(5), 450.
  • [25] Fu, J. C. 1986. Bounds for Reliability of Large Consecutive-k-out-of-n:F Systems with Unequal Component Reliability. IEEE Transactions On Reliability, 35(3), 316-319.
  • [26] Papastavridis, S. 1986. Upper and Lower Bounds for the Reliability of a Consecutive-k-out-of-n:F System. IEEE Transactions On Reliability, 35(5), 607-610.
  • [27] Papastavridis, S. 1986. Algorithms for strict consecutive-k-out-of-n:F systems. IEEE Trans.On Reliability, 35(5), 613-615.
  • [28] Chrysaphinou, O., Papastavridis, S. 1990. Reliability of a Consecutive-k-out-of-n System in a Random Environment. Journal of Applied Probability, 27(2), 452-458.
  • [29] Barbour, A. D., Holst, L., Janson, S. 1992. Poisson approximation (Vol. 2). The Clarendon Press Oxford University Press.
  • [30] Papastavridis, S. G., Koutras, M. V. 1993. Bounds for Reliability of Consecutive k-within-m-out-of-n:F Systems. IEEE Transactions On Reliability, 42(1), 156-160.
  • [31] Barbour, A. D., Chrysaphinou, O., Ross, M. 1995. Compound Poisson Approximation in Reliability Theory. IEEE Transactions On Reliability, 44(3), 398-402.
  • [32] Muselli, M. 1997. On Convergence Properties of pocket Algorithm. IEEE Transactıons On Neural Networks, 8(3), 623-629.
  • [33] Xie, M., Lai, C. D. 1998. On Reliability Bounds via Conditional Inequalities. Journal of Applied Probability, 35(1), 104-114.
  • [34] Muselli, M. 2000. New Improved Bounds For Reliability of Consecutive-k-out-of-n:F Systems. Journal of Applied Probability, 37(4), 1164-1170.
  • [35] Muselli, M. 2000. Useful Inequalities for the Longest Run Distribution. Statistics &Probability Letters, 46(3), 239-249.
  • [36] Dauş, L., Beiu, V. 2015. Lower and Upper Reliability Bounds for Consecutive-k-out-of-n:F Systems. IEEE Transactions on Reliability, 64(3), 1128-1135.
  • [37] Makri, F. S., Psillakis, Z. M. 2011. On success runs of a fixed length in Bernoulli sequences:Exact and asymptotic results. Computational Mathematics Appl., 61(4), 761-772.
  • [38] Saenz-de-Cabezon, E., Wynn, H. P. 2011. Computational algebraic algorithms for the reliability of generalized k-out-of-n and related systems. Math. Comput. Simul., 82(1), 68-78.

Year 2021, Volume: 10 Issue: 3, 877 - 890, 17.09.2021

Ahmet Demiralp Mehmet Güngör

https://doi.org/10.17798/bitlisfen.942517

Abstract

Project Number

SDK-2018-991

References

  • [1] Kuo, W., Zuo, M. J. 2003. Optimal Reliability Modeling: Princeples and Applications. New Jersey: John Wiley & Sons, Inc., 1-544.
  • [2] Tong, Y. L. 1985. A Rearrangement Inequality for the Longest Run, With an Application to Network Reliability. Journal of Applied Probability, 22(2), 386-393.
  • [3] Kuo, W., Zhang, W., Zuo, M. 1990. A Consecutive-k-out-of-n:G System: The Mirror Image of a Consecutive-k-out-of-n:F System. IEEE Transactions on Reliability, 39(2), 244-253.
  • [4] Kontoleon, J. M. 1980. Reliability determination of a r-successive-out-of-n: F system. IEEE Transactions on Reliability, 29(5), 437-437.
  • [5] Chiang, D. T., Niu, S. C. 1981. Reliability of consecutive-k-out-of-n: F system. IEEE Transactions on Reliability, 30(1), 87-89.
  • [6] Zuo, M., Kuo, W. 1990. Design and performance analysis of consecutive-k-out-of-n structure. Naval Research Logistics, 37(2), 203-230.
  • [7] Shanthikumar, J. G. 1982. Recursive algorithm to evaluate the reliability of a consecutive-k-out-of-n: F system. IEEE Transactions on Reliability, 31(5), 442-443.
  • [8] Derman, C., Lieberman, G. J., Ross, S. M. 1982. On the consecutive-k-of-n: F system. IEEE Transactions on Reliability, 31(1), 57-63.
  • [9] Bollinger, R. C., Salvia, A. A. 1982. Consecutive-k-out-of-n: F networks. IEEE Transactions on Reliability, 31(1), 53-56.
  • [10] Bollinger, R. C. 1982. Direct computation for consecutive-k-out-of-n: F systems. IEEE Transactions on Reliability, 31(5), 444-446.
  • [11] Chao, M. T., Lin, G. D. 1984. Economical design of large consecutive-k-out-of-n: F systems. IEEE Transactions on Reliability, 33(5), 411-413.
  • [12] Lambiris, M., Papastavridis, S. 1985. Exact reliability formulas for linear & circular consecutive-k-out-of-n: F systems. IEEE Transactions on Reliability, 34(2), 124-126.
  • [13] Fu, J. C. 1985. Reliability of a large consecutive-k-out-of-n: F system. IEEE transactions on reliability, 34(2), 127-130.
  • [14] Antonopoulou, I., Papastavridis, S. 1987. Fast recursive algorithm to evaluate the reliability of a circular consecutive-k-out-of-n: F system. IEEE Transactions on Reliability, 36(1), 83-84.
  • [15] Chan, F. Y., Chan, L. K., Lin, G. D. 1988. On consecutive-k-out-of-n: F systems. European journal of operational research, 36(2), 207-216.
  • [16] Peköz, E. A., Ross, S. M. 1995. A Simple Derivation of Exact Reliability Formulas For Linear and Circular Consecutive-k-out-of-n:F Systems. J. Appl. Prob., 32(2), 554-557.
  • [17] Cluzeau, T., Keller, J., Schneeweiss, W. 2008. An efficient algorithm for computing the reliability of consecutive-k-out-of-n:F systems. IEEE Transactıons On Relıabılıty, 57(1), 84-87.
  • [18] Gökdere, G., Gürcan, M., Kılıç, M. B. 2016. A new method for computing the reliability of consecutive k-out-of-n: F systems. Open Physics, 14(1), 166-170.
  • [19] Gökdere, G., Güral, Y. 2018. Birnbaum Önem Tabanlı Genetik Algoritma ve Doğrusal Ardışık n-den k-çıkışlı Sistemlerin Optimizasyonunda Uygulaması. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, 7(2), 276-283.
  • [20] Özbey, F., Gökdere, G. 2021. Analysis of Linear Consecutive-2-out-of-n:F Repairable System with Different Failure Rate. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, 10(1), 91-99.
  • [21] Özbey, F., Gökdere, G. 2021. Doğrusal genelleştirilmiş ağırlıklı n-den k-çıkışlı F sistemin güvenilirlik analizi. İstatistikçiler Dergisi: İstatistik ve Aktüerya, 14(1), 1-13.
  • [22] Hwang, F. K. 1982. Fast Solutions for Consecutive-k-out-of-n: F System. IEEE Transactions On Reliability, R-31(5), 447-448.
  • [23] Zuo, M. 1993. Reliability and component importance of a consecutive-k-out-of-n system. Microelectronics Reliability, 33(2), 243-258.
  • [24] Salvia, A. A. 1982. Simple Inequalities for Consecutive-k-out-of-n:F Networks. IEEE Transactions On Reliability, R-31(5), 450.
  • [25] Fu, J. C. 1986. Bounds for Reliability of Large Consecutive-k-out-of-n:F Systems with Unequal Component Reliability. IEEE Transactions On Reliability, 35(3), 316-319.
  • [26] Papastavridis, S. 1986. Upper and Lower Bounds for the Reliability of a Consecutive-k-out-of-n:F System. IEEE Transactions On Reliability, 35(5), 607-610.
  • [27] Papastavridis, S. 1986. Algorithms for strict consecutive-k-out-of-n:F systems. IEEE Trans.On Reliability, 35(5), 613-615.
  • [28] Chrysaphinou, O., Papastavridis, S. 1990. Reliability of a Consecutive-k-out-of-n System in a Random Environment. Journal of Applied Probability, 27(2), 452-458.
  • [29] Barbour, A. D., Holst, L., Janson, S. 1992. Poisson approximation (Vol. 2). The Clarendon Press Oxford University Press.
  • [30] Papastavridis, S. G., Koutras, M. V. 1993. Bounds for Reliability of Consecutive k-within-m-out-of-n:F Systems. IEEE Transactions On Reliability, 42(1), 156-160.
  • [31] Barbour, A. D., Chrysaphinou, O., Ross, M. 1995. Compound Poisson Approximation in Reliability Theory. IEEE Transactions On Reliability, 44(3), 398-402.
  • [32] Muselli, M. 1997. On Convergence Properties of pocket Algorithm. IEEE Transactıons On Neural Networks, 8(3), 623-629.
  • [33] Xie, M., Lai, C. D. 1998. On Reliability Bounds via Conditional Inequalities. Journal of Applied Probability, 35(1), 104-114.
  • [34] Muselli, M. 2000. New Improved Bounds For Reliability of Consecutive-k-out-of-n:F Systems. Journal of Applied Probability, 37(4), 1164-1170.
  • [35] Muselli, M. 2000. Useful Inequalities for the Longest Run Distribution. Statistics &Probability Letters, 46(3), 239-249.
  • [36] Dauş, L., Beiu, V. 2015. Lower and Upper Reliability Bounds for Consecutive-k-out-of-n:F Systems. IEEE Transactions on Reliability, 64(3), 1128-1135.
  • [37] Makri, F. S., Psillakis, Z. M. 2011. On success runs of a fixed length in Bernoulli sequences:Exact and asymptotic results. Computational Mathematics Appl., 61(4), 761-772.
  • [38] Saenz-de-Cabezon, E., Wynn, H. P. 2011. Computational algebraic algorithms for the reliability of generalized k-out-of-n and related systems. Math. Comput. Simul., 82(1), 68-78.
There are 38 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Araştırma Makalesi
Authors

Ahmet Demiralp 0000-0002-0981-7215

Mehmet Güngör 0000-0001-6869-4043

Project Number SDK-2018-991
Publication Date September 17, 2021
Submission Date May 25, 2021
Acceptance Date August 12, 2021
Published in Issue Year 2021 Volume: 10 Issue: 3

Cite

IEEE A. Demiralp and M. Güngör, “Ardıl-k Sistemler için Önerilen Güvenilirlik Sınırlarının Karşılaştırılması”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 10, no. 3, pp. 877–890, 2021, doi: 10.17798/bitlisfen.942517.
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Bitlis Eren University
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Bitlis Eren University Graduate Institute
Bes Minare Mah. Ahmet Eren Bulvari, Merkez Kampus, 13000 BITLIS