Linear Consecutive-k-out-of-n: G System Reliability Analysis
Keywords:Consecutive-k-out-of-n: G system, SVT, common cause failure, copula, reliability measures
The concerned study pertains to the development of a new stochastic model for the reliability analysis of linear consecutive-k-out-of-n: G system, where k>n2. In the developed model, system may collapse as a result of common cause failure or hardware failure in its units. The system has exponentially distributed failure rates, and in case of breakdown, it is repaired with the copula method. The developed model has been examined through supplementary variable technique (SVT) along with Laplace transform. The current paper has specifically studied consecutive-(n-1)-out-of-n: G system. The performance of such system having ten components is explored and its various reliability measures have been obtained and discussed with the help of graphs. The originality of this work lies in incorporating common cause failure in conjunction with copula repair in the reliability modeling of consecutive systems through the SVT. The study confirms that an increase in failure rates and the number of components of the concerned system decreases mean time to failure (MTTF). The profit of linear consecutive-9-out-of-10: G system is examined with the help of a numerical example.
Cheng, K., and 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(5), 591–598.
Chopra, G., and Ram, M. (2019). Reliability measures of two dissimilar units parallel system using Gumbel-Hougaard family copula. International Journal of Mathematical, Engineering and Management Sciences, 4(1), 116–130.
Cox, D. R. (1955). The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables. In Mathematical Proceedings of the Cambridge Philosophical Society, 51(3), 433–441. Cambridge University Press.
Gökdere, G., and Tony Ng, H. K. (2022). Time-dependent reliability analysis for repairable consecutive-k-out-of-n: F system. Statistical Theory and Related Fields, 6(2), 139–147.
Goyal, N., Ram, M., Amoli, S., and Suyal, A. (2017). Sensitivity analysis of a three-unit series system under k-out-of-n redundancy. International Journal of Quality and Reliability Management, 34(6), 770–784.
Guan, J., and Wu, Y. (2006). Repairable consecutive k-out-of-n: F system with fuzzy states. Fuzzy sets and systems, 157(1), 121–142.
Gupta, R., and Goel, L. R. (1992). Profit analysis of a k-out-of-n trichotomous system. Reliability Engineering and System Safety, 37(1), 39–44.
Kontoleon, J. M. (1980). Reliability determination of a r-successive-out-of-n: F system. IEEE Transactions on Reliability, 29(5), 437–437.
Kossow, A., and Preuss, W. (1989). Reliability of consecutive-k-out-of-n: F systems with nonidentical component reliabilities. IEEE Transactions on Reliability, 38(2), 229–233.
Krishnan, R., and Somasundaram, S. (2011). Reliability analysis of repairable consecutive-k-out-of-n: G systems with sensor and repairmen. International Journal of Quality and Reliability Management, 28(8), 894–908.
Kumar, V., Singh, L., and Tripathi, A. K. (2018). Reliability analysis of safety-critical and control systems: a state-of-the-art review. IET Software, 12(1), 1–18.
Kuo, W., Zhang, W., and 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.
Linton, D. G., and Saw, J. G. (1974). Reliability analysis of the k-out-of-n: F system. IEEE Transactions on Reliability, 23(2), 97–103.
Mishra, A., and Jain, M. (2013). Availability of k-out-of-n: F secondary subsystem with general repair time distribution.
Özbey, F., and 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.
Poonia, P. K. (2021). Performance assessment of a multi-state computer network system in series configuration using copula repair. International Journal of Reliability and Safety, 15(1–2), 68–88.
Poonia, P. K. (2022). Performance Assessment and Sensitivity Analysis of a Computer Lab Network Through Copula Repair with Catastrophic Failure. Journal of Reliability and Statistical Studies, 105–128.
Ram, M., and Kumar, A. (2014). Performance of a structure consisting a 2-out-of-3: F substructure under human failure. Arabian Journal for Science and Engineering, 39(11), 8383–8394.
Ram, M., and Kumar, A. (2015). Performability analysis of a system under 1-out-of-2: G scheme with perfect reworking. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 37(3), 1029–1038.
Ram, M., and Singh, S. B. (2010). Availability, MTTF and cost analysis of complex system under preemptive-repeat repair discipline using Gumbel-Hougaard family copula. International Journal of Quality & Reliability Management, 27(5), 576–595.
Rawal, D. K., Ram, M., and Singh, V. V. (2015). Study of reliability measures of a local area network via copula linguistics approach. International Journal of Quality & Reliability Management, 33(1), 97–111.
Rawal, D. K., Sahani, S. K., Singh, V. V., and Jibril, A. (2022). Reliability assessment of multi-computer system consisting n clients and the k-out-of-n: G operation scheme with copula repair policy. Life Cycle Reliability and Safety Engineering, 11, 163–175.
Sanusi, A., Yusuf, I., and Yusuf, H. A. (2022). Evaluation of reliability characteristics of automated teller machine system using Gumbel–Hougaard family copula repair policies. Life Cycle Reliability and Safety Engineering, 11, 367–375.
Singh, J., and Dayal, B. (1991). A 1-out-of-N: G system with common-cause failures and critical human errors. Microelectronics Reliability, 31(5), 847–849.
Singh, V. V., and Poonia, P. K. (2022). Stochastic analysis of k-out-of-n: G type of repairable system in combination of subsystems with controllers and multi repair approach. Journal of Optimization in Industrial Engineering, 15(1), 121–130.
Singh, V. V., Ismail, A. L., Chand, U., and Maiti, S. S. (2022). Performance Assessment of Complex System Under the k-out-of-n: G Type Configuration with k Consecutive Degraded States through the Copula Repair Approach. International Journal of Reliability, Quality and Safety Engineering, 29(2), 2150047.
Wang, Y., Hu, L., Yang, L., and Li, J. (2022). Reliability modeling and analysis for linear consecutive-k-out-of-n: F retrial systems with two maintenance activities. Reliability Engineering & System Safety, 226, 108665.
Wu, W., Tang, Y., Yu, M., and Jiang, Y. (2014). Reliability analysis of a k-out-of-n: G repairable system with single vacation. Applied Mathematical Modelling, 38(24), 6075-6097.
Wu, C., Zhao, X., Wang, S., and Song, Y. (2022). Reliability analysis of consecutive-k-out-of-r-from-n subsystems: F balanced systems with load sharing. Reliability Engineering & System Safety, 228, 108776.
Yam, R. C., Zuo, M. J., and Zhang, Y. L. (2003). A method for evaluation of reliability indices for repairable circular consecutive-k-out-of-n: F systems. Reliability engineering and System safety, 79(1), 1–9.
Yuan, L., and Cui, Z. D. (2013). Reliability analysis for the consecutive-k-out-of-n: F system with repairmen taking multiple vacations. Applied mathematical modelling, 37(7), 4685–4697.
Yusuf, I., Ismail, A. L., Lawan, M. A., Ali, U. A., and Nasir, S. (2021). Reliability modelling and analysis of client–server system using Gumbel–Hougaard family copula. Life Cycle Reliability and Safety Engineering, 10(3), 235–248.
Zhang, Y. L., and Wang, T. P. (1996). Repairable consecutive-2-out-of-n: F system. Microelectronics Reliability, 36(5), 605–608.
Zhang, Y. L., and Lam, Y. (1998). Reliability of consecutive-k-out-of-n: G repairable system. International Journal of Systems Science, 29(12), 1375–1379.
Zhang, Y. L., Zuo, M. J., and Yam, R. C. (2000). Reliability analysis for a circular consecutive-2-out-of-n: F repairable system with priority in repair. Reliability Engineering and System Safety, 68(2), 113–120.
Zhou, L., Yamamoto, H., Nakamura, T., and Xiao, X. (2020). Optimization problems for consecutive-2-out-of-n: G system. Communications in Statistics-Theory and Methods, 49(15), 3792–3807.