Signature reliability of linear consecutive k-out-of-n:Gsystemusing universal generating function approach
DOI: https://doi.org/10.33003/jobasr
Lurwanu Surajo Mustapha
Hamisu Ismail Ayagi
Kabiru Suleiman
Alhassan Nazifi Abubakar
Muhammad Shitu
Ashiru Umar
Abstract
This paper investigates the signature reliability of a linear consecutive k-out-of-n:G system using the universal generating function (UGF) technique. The system comprises n components, where only k consecutive ones need to function for the entire system to operate. As a starting point, a linear consecutive 4-out-of-7: G system is modeled to derive its reliability function, which is then converted into polynomial form. The study next analyzes the system’s tail-signature to support the evaluation of its signature reliability. facilitate the evaluation of its signature reliability. The Barlow-Proschan index is applied to assess the system's overall reliability. Finally, the study derives key performance metrics including the minimal signature, expected lifespan, and actual cost rate for the proposed configuration.
References
Bennour, B., &Belaloui, S. (2015). Reliability of linear and circular consecutive-k-out-of-n systems with shock model. Afrika Statistika, 10(1), 795–805.
Boland, P. J. (2001). Signatures of indirect majority systems. Journal of Applied Probability, 38(2), 597–603.
Bollinger, R., & Salvia, A. (1982). Consecutive-k-out-of-n:F networks. IEEE Transactions on Reliability, 31, 53–55.
Chang, J., Chen, R., & Hwang, F. (1998). A fast reliability algorithm for the circular consecutive weighted k-out-of-n:F system. IEEE Transactions on Reliability, 47, 472–474.
Chiang, D., & Chiang, R.-F. (1986). Relayed communication via consecutive-k-out-of-n:F system. IEEE Transactions on Reliability, 35, 65–67. https://doi.org/10.1109/TR.1986.4335348
Chiang, D. T., & Niu, S.-C. (1981). Reliability of consecutive-k-out-of-n:F system. IEEE Transactions on Reliability, 30, 87. https://doi.org/10.1109/TR.1981.5220981
Cui, L., & Hawkes, A. (2008). A note on the proof for the optimal consecutive k-out-of-n:G line. “Journal of Statistical Planning and Inference, 138”(6), 1516–1520. https://doi.org/10.1016/j.jspi.2007.07.003
Da, G., Xu, M., & Chan, P. S. (2018). An efficient algorithm for computing the signatures of systems with exchangeable components and applications. IISE Transactions, 50(8), 735–746. https://doi.org/10.1080/24725854.2018.1429694
Derman, C., Lieberman, G. J., & Ross, S. M. (1972). On optimal assembly of systems. Naval Research Logistics Quarterly, 19(4), 569–574. https://doi.org/10.1002/nav.3800190402
Goyal, N., Tyagi, S., & Ram, M. (2021). Reliability analysis of a system using universal generating function. Advances in Interdisciplinary Research in Engineering and Business.
Hwang, F. (1982). Fast solutions for consecutive-k-out-of-n:F system. IEEE Transactions on Reliability, 31, 447–448.
Hwang, F. (1986). Simplified reliabilities for consecutive-k-out-of-n:F systems. SIAM Journal on Algebraic and Discrete Methods, 7(2), 258–264.
Jafary, B., & Fiondella, L. (2016). A universal generating function-based multi-state system performance model subject to correlated failures. Reliability Engineering & System Safety, 152, 16–27.
Jalali, A., Hawkes, A., Cui, L., & Hwang, F. (2005). The optimal consecutive k-out-of-n:G line. Journal of Statistical Planning and Inference, 128(1), 281–287. https://doi.org/10.1016/j.jspi.2003.09.018
Kontoleon, J. (1980). Reliability determination of a r-successive-out-of-n:F system. IEEE Transactions on Reliability, 29(4), 437.
Kumar, A., Tyagi, S., & Ram, M. (2020). Signature of bridge structure using universal generating function.
Proceedings of the Society for Reliability Engineering, Quality and Operations Management (SREQOM), India, and Luleå University of Technology, Sweden.
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. https://doi.org/10.1109/24.55888
Kuo, W., & Zhu, X. (2012). Importance measures in reliability, risk, and optimization. Wiley. https://doi.org/10.1002/9781118314593
Levitin, G. (2005). The universal generating function in reliability analysis and optimization (Vol. 6). Springer.
Levitin, G., &Lisnianski, A. (2001). A new approach to solving problems of multi-state system reliability optimization. Quality and Reliability Engineering International, 17(2), 93–104.
Marichal, J.-L. (2015). Algorithms and formulae for conversion between system signatures and reliability functions. Journal of Applied Probability, 52(2), 490–507.
Marichal, J.-L., &Mathonet, P. (2013). Computing system signatures through reliability functions. Statistics & Probability Letters, 83(3), 710–717.
Mutar, E. K. (2022). Path tracing method to evaluate the signature reliability function of a complex system. University of Babylon, Iraq. https://doi.org/10.1590/jatm.v14.1284
Navarro, J., & Rubio, R. (2009). Computations of signatures of coherent systems with five components. Communications in Statistics—Simulation and Computation, 39(1), 68–84.
Owen, G. (1972). Multilinear extensions of games. Management Science, 18(5–2), 64–79. https://doi.org/10.1287/mnsc.18.5.64
Sadiya, Akshay, K., & Ram, M. (2024). Consecutive k-out-of-n:W system signature reliability appraisal via structure function approach and U-function approach. Life Cycle Reliability and Safety Engineering. https://doi.org/10.1007/s41872-024-00260
Shapley, L. S. (1953). A value for n-person games. In H. W. Kuhn & A. W. Tucker (Eds.), Contributions to the theory of games (Vol. 2, pp. 307–317). Princeton University Press.
Shen, J., & Zuo, M. (1994). A necessary condition for optimal consecutive k-out-of-n:G system design. Microelectronics Reliability, 34, 485. https://doi.org/10.1016/0026-2714(94)90087-6
Wang W., Fu Y., Si P., & Lin M. (2020). Reliability analysis of circular multi-state sliding window system with sequential demands. Reliab Eng Syst Saf;198
Yin, J., & Cui, L. (2021). Reliability for consecutive-k-out-of-n:F system with shared components between adjacent subsystems. Reliability Engineering & System Safety, 213, 107532. https://doi.org/10.1016/j.ress.2021.107532
Uan L., Zhen-Dong C. (2013). Reliability analysis for the consecutive k-out-of-n:F system with repairmen taking multiple vacations Applied mathematical modelling 37(7):4685-4697 https://DOI:10.1016/j.apm.2012.09.008
Zhao, J., Si, S., & Cai, Z. (2019). A multi-objective reliability optimization for reconfigurable systems considering components degradation. Reliability Engineering & System Safety, 183, 104–115. https://doi.org/10.1016/j.ress.2018.11.001
Zuo, M., & Kuo, W. (1990). Design and performance analysis of consecutive k-out-of-n structure. Naval Research Logistics, 37(2), 203–230. https://doi.org/10.1002/1520-6750(199004)37:2<203::AID-NAV3220370203>3.0.CO;2-X
PDF