Introducing Copula Functions to Estimate the Reliability of Dependent Mechanical Systems
DOI:
https://doi.org/10.26593/jrsi.v13i2.7219.103-112Keywords:
Reliability, Copula Functions, Mechanical system, Dependent case, CorrelationAbstract
This paper addresses the challenge of assessing the reliability of complex mechanical systems where components are inherently correlated in their failure modes. Traditionally, the assumption of independence among these components has been employed, but it often fails to capture the real-world complexities. To overcome this limitation, copula functions are introduced as a robust methodology for modeling the dependent relationships between correlated variables within mechanical systems. This paper aims to demonstrate the utility of copulas in estimating system reliability while accounting for these dependencies. The results reveal that the Clayton copula emerges as the most suitable model for representing dependence in such systems. Importantly, the reliability estimates obtained through copula-based methods not only reflect the complex interdependencies accurately but also align with the principles of the boundary theory of reliability. This research underscores the potential of copula-based reliability estimation as a valuable alternative, offering a more comprehensive and precise assessment of reliability in complex mechanical systems and holding significant promise for practical engineering applications. This framework allows the consideration of dependence among the observed variables that is usually overlooked in engineering practice.
References
Amini, A., Abdollahi, A., Hariri-Ardebili, M. A., & Lall, U. (2021). Copula-based reliability and sensitivity analysis of aging dams: Adaptive Kriging and polynomial chaos Kriging methods. Applied Soft Computing, 109, 107524. https://doi.org/10.1016/j.asoc.2021.107524
An, H., Yin, H., & He, F. (2016). Analysis and Application of Mechanical System Reliability Model Based on Copula Function. Polish Maritime Research, 23(s1), 187–191. https://doi.org/10.1515/pomr-2016-0064
Aritonang, Y. M. K. (2023). Pengembangan Pendekatan Matematis dan Penyelesaiannya untuk Reliabilitas Sistem Dengan Distribusi Kegagalan Berbeda. Jurnal Rekayasa Sistem Industri, 12(1), 35–42. https://doi.org/10.26593/jrsi.v12i1.6318.35-42
Avontuur, G. C., & van der Werff, K. (2002). Systems reliability analysis of mechanical and hydraulic drive systems. Reliability Engineering & System Safety, 77(2), 121–130. https://doi.org/10.1016/S0951-8320(02)00039-X
Bian, L., Wang, G., & Liu, P. (2023). Reliability analysis for k -out-of- n (G) systems subject to dependent competing failure processes. Computers & Industrial Engineering, 177, 109084. https://doi.org/10.1016/j.cie.2023.109084
Chen, R., Zhang, C., Wang, S., & Qian, Y. (2021). Reliability estimation of mechanical seals based on bivariate dependence analysis and considering model uncertainty. Chinese Journal of Aeronautics, 34(5), 554–572. https://doi.org/10.1016/j.cja.2020.12.001
de Reffye, J., & Dersin, P. (2010). Mechanical Reliability of a point system. IFAC Proceedings Volumes, 43(3), 86–91. https://doi.org/10.3182/20100701-2-PT-4012.00016
Feizabadi, M., & Jahromi, A. E. (2017). A new model for reliability optimization of series-parallel systems with non-homogeneous components. Reliability Engineering & System Safety, 157, 101–112. https://doi.org/10.1016/j.ress.2016.08.023
Gu, Y.-K., Fan, C.-J., Liang, L.-Q., & Zhang, J. (2022). Reliability calculation method based on the Copula function for mechanical systems with dependent failure. Annals of Operations Research, 311(1), 99–116. https://doi.org/10.1007/s10479-019-03202-5
Hu, Y., Ding, Y., Wen, F., & Liu, L. (2019). Reliability Assessment in Distributed Multi-State Series-Parallel Systems. Energy Procedia, 159, 104–110. https://doi.org/10.1016/j.egypro.2018.12.026
Jiang, D., Chen, T., Xie, J., Cui, W., & Song, B. (2023). A mechanical system reliability degradation analysis and remaining life estimation method——With the example of an aircraft hatch lock mechanism. Reliability Engineering & System Safety, 230, 108922. https://doi.org/10.1016/j.ress.2022.108922
Li, H., Huang, H.-Z., Li, Y.-F., Zhou, J., & Mi, J. (2018). Physics of failure-based reliability prediction of turbine blades using multi-source information fusion. Applied Soft Computing, 72, 624–635. https://doi.org/10.1016/j.asoc.2018.05.015
Li, Y., Xia, T., Chen, Z., & Pan, E. (2023). Multiple degradation-driven preventive maintenance policy for serial-parallel multi-station manufacturing systems. Reliability Engineering & System Safety, 230, 108905. https://doi.org/10.1016/j.ress.2022.108905
Liu, Z., Tao, F. H., & Jia, C. Z. (2012). Application of Copula in Reliability Theory. Applied Mechanics and Materials, 217–219, 2746–2749. https://doi.org/10.4028/www.scientific.net/AMM.217-219.2746
Louzada, F., Tomazella, V. L. D., Gonzatto, O. A., Bochio, G., Milani, E. A., Ferreira, P. H., & Ramos, P. L. (2022). Reliability assessment of repairable systems with series–parallel structure subjected to hierarchical competing risks under minimal repair regime. Reliability Engineering & System Safety, 222, 108364. https://doi.org/10.1016/j.ress.2022.108364
Maukar, A. L., Sosodoro, I. W., & Adiprabowo, R. (2016). Scheduling Preventive Maintenance on Auto Rooting Machine at Toys Manufacturer Company. Jurnal Rekayasa Sistem Industri, 5(1), 26. https://doi.org/10.26593/jrsi.v5i1.1910.26-30
Mustaqim, F., Kosasih, W., & Ahnad, A. (2020). Pemeliharaan Mesin Hydraulic Shear Menggunakan Pendekatan Reliability Centered Maintenance dan Manajemen Suku Cadang. Jurnal Rekayasa Sistem Industri, 9(3), 153–162. https://doi.org/10.26593/jrsi.v9i3.4023.153-162
Nelsen, R. B. (2006). An Introduction to Copulas. Springer New York. https://doi.org/10.1007/0-387-28678-0
Pranowo, W., & Ramadhani, A. R. (2023). A Comparison of Python-Based Copula Parameter Estimation for Archimedean-Based Asymmetric Copulas. SN Computer Science, 4(2), 207. https://doi.org/10.1007/s42979-023-01674-8
Ramadhani, A., Khan, F., Colbourne, B., Ahmed, S., & Taleb-Berrouane, M. (2021). Environmental load estimation for offshore structures considering parametric dependencies. Safety in Extreme Environments. https://doi.org/10.1007/s42797-021-00028-y
Ramadhani, A., Khan, F., Colbourne, B., Ahmed, S., & Taleb-Berrouane, M. (2022a). Resilience assessment of offshore structures subjected to ice load considering complex dependencies. Reliability Engineering & System Safety, 222, 108421. https://doi.org/10.1016/j.ress.2022.108421
Ramadhani, A., Khan, F., Colbourne, B., Ahmed, S., & Taleb-Berrouane, M. (2022b). Resilience assessment of offshore structures subjected to ice load considering complex dependencies. Reliability Engineering & System Safety, 222, 108421. https://doi.org/10.1016/j.ress.2022.108421
Stern, R. E., Song, J., & Work, D. B. (2017). Accelerated Monte Carlo system reliability analysis through machine-learning-based surrogate models of network connectivity. Reliability Engineering & System Safety, 164, 1–9. https://doi.org/10.1016/j.ress.2017.01.021
Tang, X.-S., Li, D.-Q., Zhou, C.-B., & Zhang, L.-M. (2013). Bivariate distribution models using copulas for reliability analysis. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 227(5), 499–512. https://doi.org/10.1177/1748006X13481928
Wang, F., & Li, H. (2019). A non-parametric copula approach to dependence modelling of shear strength parameters and its implications for geotechnical reliability under incomplete probability information. Computers and Geotechnics, 116, 103185. https://doi.org/10.1016/j.compgeo.2019.103185
Wei, Y., & Liu, S. (2023). Reliability analysis of series and parallel systems with heterogeneous components under random shock environment. Computers & Industrial Engineering, 179, 109214. https://doi.org/10.1016/j.cie.2023.109214
Woo, S., & O’Neal, D. L. (2019). Reliability design and case study of mechanical system like a hinge kit system in refrigerator subjected to repetitive stresses. Engineering Failure Analysis, 99, 319–329. https://doi.org/10.1016/j.engfailanal.2019.02.015
Wu, X. Z. (2015). Modelling dependence structures of soil shear strength data with bivariate copulas and applications to geotechnical reliability analysis. Soils and Foundations, 55(5), 1243–1258. https://doi.org/10.1016/j.sandf.2015.09.023
Xiahou, T., Zheng, Y.-X., Liu, Y., & Chen, H. (2023). Reliability modeling of modular k-out-of-n systems with functional dependency: A case study of radar transmitter systems. Reliability Engineering & System Safety, 233, 109120. https://doi.org/10.1016/j.ress.2023.109120
Xiao, N.-C., Yuan, K., & Zhan, H. (2022). System reliability analysis based on dependent Kriging predictions and parallel learning strategy. Reliability Engineering & System Safety, 218, 108083. https://doi.org/10.1016/j.ress.2021.108083
Yu, S., & Wang, Z. (2018). A Novel Time-Variant Reliability Analysis Method Based on Failure Processes Decomposition for Dynamic Uncertain Structures. Journal of Mechanical Design, 140(5). https://doi.org/10.1115/1.4039387
