Prediction of the Mean Time to Failures of a Complex System Using the Monte Carlo Simulation Method
DOI:
https://doi.org/10.13052/jrss0974-8024.1721Keywords:
Reliability, mean time to failure, tie set methodAbstract
This paper presents a Monte Carlo-based algorithm for predicting the Mean Time to Failure (MTTF) of complex structures, specifically a “Bridge-type network” with five elements exhibiting various failure distributions. The proposed algorithm involves generating element lifetimes through the inverse of their failure distribution functions, providing a robust approach to evaluating MTTF for systems beyond traditional series or parallel configurations.
The approach was implemented in MATLAB, and the software underwent extensive testing across different scenarios, including both exponential and Weibull distributions. The results demonstrated the method’s accuracy and its capability to handle diverse failure distributions with minimal error. This tool offers reliability engineers a versatile solution for predicting and improving the reliability of complex systems.
In summary, the proposed method and software significantly advance the reliability assessment of intricate structures and offer a solid foundation for further research and practical applications in the field of reliability engineering.
Downloads
References
Dong, Qinglai, Pin Liu, and Xujie Jia. “Reliability analysis of k-out-of-n: G repairable systems considering common cause failure and multi-level maintenance strategy.” Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 238, no. 1, 2024.
Julian Salomon, Niklas Winnewisser, Pengfei Wei, Matteo Broggi, Michael Beer, Efficient reliability analysis of complex systems in consideration of imprecision, Reliability Engineering & System Safety, Volume 216, 2021.
Pan, Guangze, Xiaojian Ding, Dan Li, Yaqiu Li, and Yuanhang Wang. “A reliability evaluation method of complex electromechanical products based on the multi-stress coupling acceleration model.” Engineering Failure Analysis 146, 2023.
Q. Qiu, L. Cui, and D. Kong, “Availability and maintenance modeling for a two-component system with dependent failures over a finite time horizon,” Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, vol. 233, no. 2, pp. 200–210, 2019.
S. Yu, Z. Wang, and D. Meng, “Time-variant reliability assessment for multiple failure modes and temporal parameters,” Structural and Multidisciplinary Optimization, vol. 58, no. 4, pp. 1705–1717, 2018.
Tieling Zhang, Min Xie, Michio Horigome. «Availability and reliability of k-out–of–(M+N):G warm standby systems». Reliability Engineering & System Safety 90, 2005.
Lukitosari, Valeriana, Sentot Didik Surjanto, Sena Safarina, Komar Baihaqi, and Sri Irna Solihatun Ummah. “The Predicted Failure on A Two-Dimensional Warranty Using the Bayesian Approach.” Journal of Reliability and Statistical Studies (2023): 171–196.
Jia-Qi, Liu, Feng Yun-Wen, Lu Cheng, and Pan Wei-Huang. “Decomposed-coordinated framework with intelligent extremum network for operational reliability analysis of complex system.” Reliability Engineering & System Safety 242, 2024.
He, Jun, Zhijun Yuan, Xiaoling Yang, Wentao Huang, Yicong Tu, and Yi Li. “Reliability modeling and evaluation of urban multi-energy systems: A review of the state of the art and future challenges.” IEEE Access 8, 2020.
Mi, Jinhua, Michael Beer, Yan-Feng Li, Matteo Broggi, and Yuhua Cheng. “Reliability and importance analysis of uncertain system with common cause failures based on survival signature.” Reliability Engineering & System Safety 201, 2020.
Martyushev, Nikita V., Boris V. Malozyomov, Svetlana N. Sorokova, Egor A. Efremenkov, Denis V. Valuev, and Mengxu Qi.” Review models and methods for determining and predicting the reliability of technical systems and transport.” Mathematics 11, no. 15, 2023.
Maurya, Ankur, and Divya Kumar. “Reliability of safety-critical systems: A state-of-the-art review.” Quality and Reliability Engineering International 36, no. 7, 2020.
Guesmi, Hedi A., and Sayed O. Madbouly. “Evaluation of the Reliability of a Standby Redundancy System Under Real Conditions.” Journal of Reliability and Statistical Studies (2023): 357–372.
Singh, V. V., Abubakkar Idris Mohhammad, Kabiru Hamisu Ibrahim, and Ibrahim Yusuf. “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 Management 39, no. 2, 2022.
Yuan, Kai, Ning-Cong Xiao, Zhonglai Wang, and Kun Shang. “System reliability analysis by combining structure function and active learning kriging model.” Reliability Engineering & System Safety 195, 2020.
Gao, Shan. “Reliability analysis and optimization for a redundant system with dependent failures and variable repair rates.” Mathematics and Computers in Simulation 208, 2023.
Edward Korczak, Gregory Levitin, Hanoch Ben Haim. «Survivability of series-parallel systems with multilevel protection». Reliability Engineering & System Safety 90, 2005.
Wang, Rongxi, Zezhou Tang, Jianmin Gao, Zhiyong Gao, and Zhen Wang. “Probabilistic model-checking based reliability analysis for failure correlation of multi-state systems.” Quality Engineering 32, no. 4, 2020.
Jun-Yu Chen, Yun-Wen Feng, Da Teng, Cheng Lu, Cheng-Wei Fei, Selective transmit modeling framework of complex system reliability analysis considering failure correlation, Engineering Failure Analysis, Volume 158, 2024.
Ruiz, Cesar, Edward A. Pohl, and Haitao Liao. “Selective maintenance modeling and analysis of a complex system with dependent failure modes.” Quality Engineering 32, no. 3, 2020
Abba, Badamasi, and Hong Wang. “A new failure times model for one and two failure modes system: A Bayesian study with Hamiltonian Monte Carlo simulation.” Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 2023.
Xiahou, Tangfan, Yi-Xuan Zheng, Yu Liu, and Hong Chen. “Reliability modeling of modular k-out-of-n systems with functional dependency: A case study of radar transmitter systems.” Reliability Engineering & System Safety 233, 2023.
Y.-F. Li, H.-Z. Huang, J. Mi, W. Peng, and X. Han, “Reliability analysis of multi-state systems with common cause failures based on Bayesian network and fuzzy probability,” Annals of Operations Research, pp. 1–15, 2019.
Z. Ye, M. Revie, and L. Walls, “A load sharing system reliability model with managed component degradation,” Reliability, IEEE Transactions on, vol. 63, no. 3, pp. 721–730, 2014.
S. Song, D. W. Coit, Q. Feng, and H. Peng, “Reliability analysis for multi-component systems 34 subject to multiple dependent competing failure processes,” IEEE Transactions on Reliability, vol. 63, no. 1, pp. 331–345, 2014.
S. Song, D. W. Coit, and Q. Feng, “Reliability analysis of multiple-component series systems subject to hard and soft failures with dependent shock effects,” IIE Transactions, no. just-accepted, pp. 00–00, 2016.
Y. M. Ko and E. Byon, “Reliability evaluation of large-scale systems with identical units,” IEEE Transactions on Reliability, vol. 64, no. 1, pp. 420–434, 2015.
Wang, Rongxi, Yufan Li, Jinjin Xu, Zhen Wang, and Jianmin Gao. “F2G: A hybrid fault-function graphical model for reliability analysis of complex equipment with coupled faults.” Reliability Engineering & System Safety 226, 2022.
Yang, Chen, Wanze Lu, and Yuanqing Xia. “Reliability-constrained optimal attitude-vibration control for rigid-flexible coupling satellite using interval dimension-wise analysis.” Reliability Engineering & System Safety 237, 2023.
M. Parsa, A. Di Crescenzo, and H. Jabbari, “Analysis of reliability systems via Gini-type index,” European Journal of operational Research, vol. 264, no. 1, pp. 340–353, 2018.
H. Peng, Q. Feng, and D. W. Coit, “Reliability and maintenance modeling for systems subject to multiple dependent competing failure processes,” IIE Transactions, vol. 43, no. 1, pp. 12–22, 2010.
David, Ikwuoche John, Mathew Stephen, and Eghwerido Joseph Thomas. “Reliability Analysis with New Sine Inverse Rayleigh Distribution.” Journal of Reliability and Statistical Studies (2023): 255–268.
N. Gorjian, L. Ma, M. Mittinty, P. Yarlagadda, and Y. Sun, “A review on degradation models in reliability analysis,” in Engineering Asset Lifecycle Management: Springer, 2010.
X. Huang, L. J. Aslett, and F. P. Coolen, “Reliability analysis of general phased mission systems with a new survival signature,” Reliability Engineering & System Safety, vol. 189, pp. 416–422, 2019.
Misra, Peeyush. “Generalized Estimator of Population Mean Using Auxiliary Information in Presence of Measurement Errors.” Journal of Reliability and Statistical Studies (2023): 269–280.
Lee, Seunggyu. “Monte Carlo simulation using support vector machine and kernel density for failure probability estimation.” Reliability Engineering & System Safety 209, 2021.
Wu, Hao, Yanwen Xu, Zheng Liu, and Pingfeng Wang. “Mean Time to Failure Prediction for Complex Systems with Adaptive Surrogate Modeling.” In International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol. 87301, p. V03AT03A051. American Society of Mechanical Engineers, 2023.
Abubakar, Hamza, and Shamsul Rijal Muhammad Sabri. “A Bayesian Approach to Weibull Distribution with Application to Insurance Claims Data.” Journal of Reliability and Statistical Studies (2023): 1–24.
