Performance assessment of a complex repairable system with k-out-of-n: G operational scheme and copula repair approach

محورهای موضوعی : Reliability Engineering

Dhruv Raghav ¹ , Suresh Sahani ² , Vijay Singh ³ , Shakeeludeen Chaudhary ⁴

1 - Software Engineer, MapmyIndia Okhla Industrial Estate, New Delhi, India
2 - Department of Mathematics, Rajarshi Janak Campus, Tribhuvan University, Nepal
3 - Department of Mathematics, Yusuf Maitama Sule University, Kano, Nigeria
4 - Department of Mathematics, Amity University, Greater Noida, UP, India

تاریخ دریافت : 1400/12/07 تاریخ پذیرش : 1402/05/06 تاریخ انتشار : 1401/06/10

کلید واژه: Availability, Cost analysis, Gumbel- Hougaard family copula, MTTF, Reliability,

چکیده مقاله :

The present study is a complex system with three subsystems connected in a series configuration. The first subsystem has n identical units and is ascribed to be operable by a k-out-of-n: G scheme, and the second subsystem, which has three indistinguishable parts, is capable of being operational if at least two of them are operable. The third subsystem has an independent unit and all subsystems are connected in a series in the sequence of subsystem 1, subsystem 2, and subsystem 3. The units of subsystem 1 and subsystem 2 are controlled by the auto changeover switches and the switch failure led to the complete failed state. The units' failure rates of subsystems are constant and follow an exponential distribution, however, there are two types of repair facilities: general and copula repair. Minor repair dealt with the general repair but complete failure needs copula repair. Traditional reliability measures have been studied for different values of failure and repair through supplementary variable and copula approaches.

منابع و مأخذ:

[1] Gahlot, M, Singh, V. V., Ayagi H. Ismail, Abdullahi, I. (2020), Stochastic Analysis of a two units’ complex repairable system with Switch and Human failure using Copula Approach, Life Cycle Reliability and Safety Engineering, Vol. 9(1), pp. 1-11, 2020.

[2] Gahlot, M, Singh, V. V., Ayagi H. Ismail, Goel, C. K. (2018), Performance assessment of repairable system in the series configuration under different types of failure and repair policies using Copula Linguistics, International Journal of Reliability and Safety. Vol.12(4), pp.348-374.

[3] Gokdere, G., Gurcan, M, Kilic, M. B, (2016), A new method for computing the reliability of consecutive k-out-of-n: F systems, Open Physics, Volume 14(1), pp.166-170.

[4] Maktabi, H., Tohidi, H. & Seyedaliakbar, S.M. (2011). An Application of Linear Programming for Efficient Resource Allocation Case Study of University Education. Australian Journal of Basic and Applied Sciences, 5(12): 703-706


[5] Namdari, A., Drzymalski, J., Tohidi, H. (2017). Labor Productivity and Optimal Team Size in an Inspection Process. IIE Annual Conference. Proceedings, 854-859

[6] Nelsen R. B. (2006), An Introduction to Copulas. 2nd edition. New York, Springer.
[7] Niaki, S. T., Yaghoubi, A. (2021), Exact equations for the reliability and mean time to failure of 1-out-of-n cold standby system with imperfect switching, Journal of Optimization of industrial Engineering, Vol.14(2), pp. 197-203.
[8] Poonia, P K., Sirohi, A. (2020), Cost-benefit analysis of a k-out-of-n: G type of warm standby series system under catastrophic failure using copula linguistic. Int. J Reliab Risk Safety Theory and Applications, Vol 3(1), pp. 35-44.
[9] Poonia, P K., Sirohi, A., Kumar, A. (2021), Cost analysis of a reparable warm standby k-out-of-n: G and 2-out-of-4: G system in the series configuration under catastrophic failure using copula repair, Life Cycle Reliab Saf Eng., Vol. 10(2), pp. 121-133.
[10] Poonia, P. K, (2021); Performance assessment of multi-state computer network system in the series configuration using copula repair, Int. J. Reliability and Safety, Vol 12(1/2), pp. 68-88.
[11] Raghav, D., Poonia, P. K., Gahlot, M., Monika Gahlot, Singh, V. V., Ayagi, H. I, Abdullahi, A. H. (2020), Probabilistic analysis of a system consisting of two subsystems in the series configuration under copula repair approach, Journal of Korean Mathematical Educational Society: Series B Pure and Applied Mathematics, Vol. 27(3), pp. 135- 155.
[12] Raghav, D., Poonia, P. K., Singh, V. V. (2021), Probabilistic analysis of complex repairable system involving two subsystems in a series arrangement with (k- out- of- n): G operation Scheme and copula repair approach, Reliability Theory & Applications, Vol. 16(2), pp.1-18.
[13] Singh, V. V, Poonia, P. K, Labran, U. J, Abdullahi, I. (2021), Probabilistic analysis of a multi-state warm standby k-out-of-n: G; system in a series configuration using copula Linguists. Reliability Theory & Applications, Vol. 16(2), pp.22-39, 2021.
[14] Singh, V. V, Ram, M, Rawal, D. K. (2013), Cost analysis of an engineering system involving subsystems in a series configuration, IEEE Transactions on Automation Science and Engineering, Vol. 10(4), pp.1124-1130.
[15] Singh, V. V, Ram, M. (2014), multi-state k-out-of-n-type system analysis, Mathematics in Engineering, Science and Aerospace, Vol. 5(3), pp. 281- 292.
[16] Singh, V. V, Singh, S. B, Ram, M, Goel, C. K. (2013), Availability, MTTF and cost analysis of a system having two units in a series configuration with the controller, International
[17] Farahani, A., Tohidi, H., Shoja, A. (2019). An integrated optimization of quality control chart parameters and preventive maintenance using Markov chain. Advances in Production Engineering & Management. 14(1), pp 5–14. https://doi.org/10.14743/apem2019.1.307
[18] Journal of System Assurance and Management, Vol. 4(4), pp 341-352.
[19] Singh, V. V., Lado, A. K., Yusuf, I., Abdullahi, A. H. (2020), Probabilistic Assessment of Computer-Based Test (CBT) Network System Using Copula Linguistic Approach. Journal of Reliability and Statistical Studies, Vol. 13(2), pp. 401-428.
[20] Singh, V. V., Mohammad, A. I., Ibrahim, K. H., Yusuf, I. (2021), Performance assessment of the complex repairable system with n-identical units under (k-out-of-n: G) scheme and copula linguistic repair approach. International Journal of Quality Reliability and Management, Vol. 39(2), pp. 367-386.
[21] Singh, V. V., Poonia, P. K., Abdullahi, A. H. (2020), Performance analysis of a complex repairable system with two subsystems in a series configuration with an imperfect switch, Journal of Mathematics & Computational Science, Vol. 10(2). pp. 359-383.
[22] Singh, V. V., Rawal, D. K., Kumar, P. (2020), Performance Assessment of Linux Operating System Employing Copula Distribution Approach. Life Cycle Reliability and Safety Engineering, Vol.9(4), pp.389-403.
[23] Singh, V. V., Rawal, D. K. (2011), Availability analysis of a system having two units in a series configuration with the controller and human failure under different repair policies, International J. of Scientific and Engineering Research, Vol. 2 (10), pp. 1- 9.
[24] Singh, V. V., Rawal, D. K. (2015), Stochastic analysis of N-unit plant with different types of failure and repair policy using copula distribution, Journal of Reliability and Statistical Studies. Vol. 8(2), pp. 119-133.
[25] Tohidi, H., Jabbari, M.M., (2012). “Decision role in management to increase effectiveness of an organization”. Procedia-social and behavioral sciences, 32: 825-828.
[26] Singh, V. V., Rawal, D. K., Sahani, S. K., Jibril, B. A, (2022), Reliability Assessment of Multi-Computer System Consisting n clients and the kout-of- n: G operation scheme with Copula Repair Policy, Life Cycle Reliability and Safety Engineering, Vol. 11 (2), pp. 163-175.
[27] Tukur, I., Ibrahim, K. H, Isa, M. S, Yusuf, I. (2021), Availability and performance of computer network with a dual server using Gumbel Hougaard family Copula distribution, Vol. 63(3), pp. 183-194.
[28] Yusuf, I., Yusuf, B., Babagana, M., Sani, B., Lawan, A. M, (2018), Some reliability chrematistics of linear consecutive 2-out-of-4 supporting device for operation, Int. Journal of Engg & Technology, Vol. 7(1), pp. 135-139.