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

Year 2021, , 91 - 99, 21.03.2021

Fahrettin Özbey , Gökhan Gökdere

https://doi.org/10.17798/bitlisfen.849725

Cited By: 3

Abstract

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 geliştirilmiştir. Ayrıca sistemin ilk ortalama arızalanma süreside incelenmiştir.

Keywords

Tamir edilebilir ardışık sistem,, Markov süreci,, İlk ortalama arızalanma süresi.

Supporting Institution

Yok

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

Abstract

In the reliability analysis, when it is obtained the reliability of repairable consecutive-k-out-of-n system, the components 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, with different failure rates. The time required to repair is an exponential random variable and each component after fix is as durable as new. In this paper, we improved a model for the state transition probability of this repairable system when components have unequal probability of failure. The system mean time to first failure was also studied.

Keywords

Repairable consecutive system, Markov process, Mean time to first failure

References

• Kontoleon J.M. 1980. Reliability determination of a r-successive-out-of-n: F system. IEEE Trans Reliability, 29: 437.
• Chiang D.T., Niu S.C. 1981. Reliability of consecutive-k-out-of-n: F system. IEEE Trans Reliability, 30: 87-89.
• Bollinger R.C., Salvia A.A. 1982. Consecutive-k-out-of-n: F networks. IEEE Trans Reliability, 31: 53-56.
• Derman C., Lieberman G.J., Ross S.M. 1982. On the consecutive-k-out-of-n: F system. IEEE Trans Reliability, 31: 57-63.
• Zuo M.J., Kuo W. 1990. Design and performance analysis of consecutive-k-out-of-n structure. Naval Research Logistics; 37: 203-230.
• Chang G.J., Cui L., Hwang F.K. 2000. Reliabilities of consecutive-k systems. Kluwer Academic Publishers, Dordrecht, 1-208.
• Kuo W., Zuo M.J. 2003. Optimal Reliability Modeling: Principles and Applications. John Wiley & Sons, New Jersey, 1-544.
• 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.
• Zhang Y.L., Wang T.P. 1996. Repairable consecutive-2-out-of-n: F system. Microelectronic Reliability, 36: 605-608.
• 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.
• Zhang Y.L., Lam Y. 1998. Reliability of consecutive-k-out-of-n: G repairable system. International Journal of Systems Science, 29: 1375-1379.
• Zhang Y.L., Zuo M.J., Yam R.C.M. 2000. Reliability analysis for a circular consecutive-2-out-of-n: F repairable system with priority in repair. Reliability Engineering and System Safety, 68: 113-120.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• Lam Y., Zhang Y.L. 2000. Repairable consecutive-k-out-of-n: F system with Markov dependence. Naval Research Logistics, 47: 18-39.
• 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.