Analysis of Linear Consecutive-2-out-of-n: F Repairable System with Different Failure Rate

Özbey, Fahrettin; Gökdere, Gökhan

Analysis of Linear Consecutive-2-out-of-n: F Repairable System with Different Failure Rate

Fahrettin ÖZBEY, (Bitlis Eren Üniversitesi, Fen Edebiyat Fakültesi, İstatistik Bölümü)

Gökhan GÖKDERE (Fırat Üniversitesi, Fen Fakültesi, İstatistik Bölümü)

Bitlis Eren Üniversitesi Fen Bilimleri Dergisi

4 0

Yıl: 2021 Cilt: 10 Sayı: 1 Sayfa Aralığı: 91 - 99 Metin Dili: İngilizce İndeks Tarihi: 08-06-2021

Analysis of Linear Consecutive-2-out-of-n: F Repairable System with Different Failure Rate

Öz:

In the reliability analysis, when the reliability of a repairable consecutive-k-out-of-n system is considered, thecomponents are generally supposed to have an equal failure rate. In practice, this assumption may fail. Therefore,in this paper it is adopted that the lifetime of each component are random variables, exponentially distributed, withdifferent failure rates. The time required to repair is an exponential random variable and each component afterrepair is as durable as new. In this paper, we proposed a model for the state transition probability of this repairablesystem when components have unequal failure rates. The system mean time to first failure was also studied.

Anahtar Kelime:

Farklı Hata Oranlı Doğrusal Ardışık n-den 2 Çıkışlı Tamir Edilebilir F Sistemin Analizi

Öz:

Güvenilirlik analizinde, tamir edilebilir ardışık n-den k-çıkışlı sistemin güvenilirliği elde edilirken genellikle bileşenlerin eşit hata oranlarına sahip olduğu varsayılır. Uygulamada bu varsayım hatalı olabilir. Bu nedenden dolayı bu çalışmada her bir bileşenin ömrü farklı hata oranlarına sahip üstel tesadüfi değişken olarak ele alınmıştır. Tamir için gerekli süre üstel tesadüfi değişken olarak tanımlanmıştır ve tamirden sonra her bir bileşen yeni bir bileşen kadar iyi durumdadır. Bu çalışmada, bileşenlerin eşit olamayan hata olasılıklarına sahip olduklarında bu tamir edilebilir sistemin durum geçiş olasılıkları için bir model önerilmiştir. Ayrıca sistemin ilk ortalama arızalanma süresi de incelenmiştir.

Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Kontoleon J.M. 1980. Reliability determination of a r-successive-out-of-n: F system. IEEE Trans Reliability, 29: 437.
[2] Chiang D.T., Niu S.C. 1981. Reliability of consecutive-k-out-of-n: F system. IEEE Trans Reliability, 30: 87-89.
[3] Bollinger R.C., Salvia A.A. 1982. Consecutive-k-out-of-n: F networks. IEEE Trans Reliability, 31: 53-56.
[4] Derman C., Lieberman G.J., Ross S.M. 1982. On the consecutive-k-out-of-n: F system. IEEE Trans Reliability, 31: 57-63.
[5] Zuo M.J., Kuo W. 1990. Design and performance analysis of consecutive-k-out-of-n structure. Naval Research Logistics; 37: 203-230.
[6] Chang G.J., Cui L., Hwang F.K. 2000. Reliabilities of consecutive-k systems. Kluwer Academic Publishers, Dordrecht, 1-208.
[7] Kuo W., Zuo M.J. 2003. Optimal Reliability Modeling: Principles and Applications. John Wiley & Sons, New Jersey, 1-544.
[8] Eryilmaz S. 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: 225-237.
[9] Zhang Y.L., Wang T.P. 1996. Repairable consecutive-2-out-of-n: F system. Microelectronic Reliability, 36: 605-608.
[10] Zhang Y.L., Wang T.P., Jia J.S. 1998. Reliability analysis of consecutive-(n-1)-out-of-n: G repairable system. Chinese Journal of Automation, 10: 181-186.
[11] Zhang Y.L., Lam Y. 1998. Reliability of consecutive-k-out-of-n: G repairable system. International Journal of Systems Science, 29: 1375-1379.
[12] Zhang Y.L., Zuo M.J., Yam R.C.M. 2000. Reliability analysis for a circular consecutive-2-outof-n: F repairable system with priority in repair. Reliability Engineering and System Safety, 68: 113-120.
[13] Cheng K., Zhang Y.L. 2001. Analysis for a consecutive-k-out-of-n: F repairable system with priority in repair. International Journal of Systems Science, 32: 591-598.
[14] Navas Á. M. Á., Ibáñez J. C., Sancho M. C. 2021. Reliability assessment of repairable systems using simple regression models. International Journal of Mathematical, Engineering and Management Sciences, 6: 180-192.
[15] Wang J., Xie N., Yang N. 2021. Reliability analysis of a two-dissimilar-unit warm standby repairable system with priority in use. Communications in Statistics - Theory and Methods, 50: 792-814.
[16] 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: 276-283.
[17] 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: 166-170.
[18] Lam Y., Zhang Y.L. 1999. Analysis of repairable consecutive-2-out-of-n: F repairable systems with Markov dependence. International Journal of Systems Science, 30: 799-809.
[19] Lam Y., Zhang Y.L. 2000. Repairable consecutive-k-out-of-n: F system with Markov dependence. Naval Research Logistics, 47: 18-39.
[20] Lam Y., Ng H.K.T. 2001. A general model for consecutive-k-out-of-n: F repairable system with exponential distribution and (k-1)-step Markov dependence. European Journal of Operational Research, 129: 663-682.

APA	Özbey F, Gökdere G (2021). Analysis of Linear Consecutive-2-out-of-n: F Repairable System with Different Failure Rate. , 91 - 99.
Chicago	Özbey Fahrettin,Gökdere Gökhan Analysis of Linear Consecutive-2-out-of-n: F Repairable System with Different Failure Rate. (2021): 91 - 99.
MLA	Özbey Fahrettin,Gökdere Gökhan Analysis of Linear Consecutive-2-out-of-n: F Repairable System with Different Failure Rate. , 2021, ss.91 - 99.
AMA	Özbey F,Gökdere G Analysis of Linear Consecutive-2-out-of-n: F Repairable System with Different Failure Rate. . 2021; 91 - 99.
Vancouver	Özbey F,Gökdere G Analysis of Linear Consecutive-2-out-of-n: F Repairable System with Different Failure Rate. . 2021; 91 - 99.
IEEE	Özbey F,Gökdere G "Analysis of Linear Consecutive-2-out-of-n: F Repairable System with Different Failure Rate." , ss.91 - 99, 2021.
ISNAD	Özbey, Fahrettin - Gökdere, Gökhan. "Analysis of Linear Consecutive-2-out-of-n: F Repairable System with Different Failure Rate". (2021), 91-99.

APA	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.
Chicago	Özbey Fahrettin,Gökdere Gökhan Analysis of Linear Consecutive-2-out-of-n: F Repairable System with Different Failure Rate. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 10, no.1 (2021): 91 - 99.
MLA	Özbey Fahrettin,Gökdere Gökhan Analysis of Linear Consecutive-2-out-of-n: F Repairable System with Different Failure Rate. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol.10, no.1, 2021, ss.91 - 99.
AMA	Özbey F,Gökdere G Analysis of Linear Consecutive-2-out-of-n: F Repairable System with Different Failure Rate. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2021; 10(1): 91 - 99.
Vancouver	Özbey F,Gökdere G Analysis of Linear Consecutive-2-out-of-n: F Repairable System with Different Failure Rate. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2021; 10(1): 91 - 99.
IEEE	Özbey F,Gökdere G "Analysis of Linear Consecutive-2-out-of-n: F Repairable System with Different Failure Rate." Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, 10, ss.91 - 99, 2021.
ISNAD	Özbey, Fahrettin - Gökdere, Gökhan. "Analysis of Linear Consecutive-2-out-of-n: F Repairable System with Different Failure Rate". Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 10/1 (2021), 91-99.