On planned time replacement of series-parallel system

Document Type: Original Article

Authors

1 School of Continuing Education, Bayero University Kano, Nigeria

2 Department of Mathematical Sciences, Bayero University, Kano, Nigeria

3 School of Continuing Education, Bayero University, Kano, Nigeria

10.22121/aotp.2020.240152.1033

Abstract

This paper investigate some characteristics of the age replacement model with minimal repair, of series-parallel system with non-uniform failure rates and are subjected to two different types of failures, which are Type I and Type II failures. The six units of the system formed three subsystems, which are subsystems A, B and C. Subsystem A is having three parallel units, subsystem B is having a single unit and subsystem C is having two parallel units. We constructed age replacement model with minimal repair that will determine the optimal replacement time of the series-parallel system. Furthermore, we also considered some modifications of the age replacement model with minimal repair constructed. Finally, some numerical examples are given to illustrate the characteristics of the age replacement models with minimal repair constructed. From the results obtained, it was observed that the optimal replacement time of the system when the three units of A are in parallel is higher than when the three units of A are in series. It was also observed that, the optimal replacement time obtained from the standard age replacement model is higher than the optimal replacement time obtained from standard age replacement model with minimal repair.

Keywords


Aven, T., & Castro, I. T. (2008). A minimal repair replacement model with two types of failure and a safety constraint. European Journal of Operational Research188(2), 506-515.‏
Chauhan, S. K., & Malik, S. C. (2016). Reliability evaluation of series-parallel and parallel-series systems for arbitrary values of the parameters. International Journal of Statistics and Reliability Engineering3(1), 10-19.‏
Chen, M., Zhao, X., & Nakagawa, T. (2019). Replacement policies with general models. Annals of Operations Research277(1), 47-61.‏
Chen, T. (2007). Obtaining the optimal cache document replacement policy for the caching system of an EC website. European Journal of Operational Research181(2), 828-841.‏
Chien, Y. H., & Sheu, S. H. (2006). Extended optimal age-replacement policy with minimal repair of a system subject to shocks. European Journal of Operational Research174(1), 169-181.‏
Coria, V. H., Maximov, S., Rivas-Dávalos, F., Melchor, C. L., & Guardado, J. L. (2015). Analytical method for optimization of maintenance policy based on available system failure data. Reliability Engineering & System Safety135, 55-63.‏
Fallahnezhad, M. S., & Najafian, E. (2017). A model of preventive maintenance for parallel, series, and single-item replacement systems based on statistical analysis. Communications in Statistics-Simulation and Computation46(7), 5846-5859.‏
Jain, M., & Gupta, R. (2013). Optimal replacement policy for a repairable system with multiple vacations and imperfect fault coverage. Computers & Industrial Engineering66(4), 710-719.‏
Khatab, A., Aghezzaf, E. H., Diallo, C., & Djelloul, I. (2017). Selective maintenance optimisation for series-parallel systems alternating missions and scheduled breaks with stochastic durations. International Journal of Production Research55(10), 3008-3024.‏
Ling, X., Wei, Y., & Li, P. (2019). On optimal heterogeneous components grouping in series-parallel and parallel-series systems. Probability in the Engineering and Informational Sciences33(4), 564-578.‏
Malki, Z. Ait, D. A., Ouali, M. S., 2015. Age replacement policies for two-component systems with stochastic dependence. Journal of Quality in Maintenance Engineering. 20(3), 346-357.
Mannai, N., & Gasmi, S. (2018). Optimal design of k-out-of-n system under first and last replacement in reliability theory. Operational Research, 1-16.‏
Mohammadi, M., Mortazavi, S. M., & Karbasian, M. (2018). Developing a method for reliability allocation of series-parallel systems by considering common cause failure. International Journal of Industrial Engineering & Production Research29(2).‏
Mustafa, A. (2017). Improving the Reliability of a Series-Parallel System Using Modified Weibull Distribution. In International Mathematical Forum (Vol. 12, No. 6, pp. 257-269).‏
Nakagawa, T. 2005. Maintenance Theory of Reliability. Springer-Verlag, London Limited.
Ouali, M. S., Yacout, S., 2003. Optional preventive replacement policy for two-component System.  Journal of Decision Systems 12(1), 11-20.
Okamura, H., & Dohi, T. (2017). Moment-based approach for some age-based replacement problems. Journal of Industrial and Production Engineering34(8), 558-567.‏
Peng, R., Zhai, Q., Xing, L., & Yang, J. (2016). Reliability analysis and optimal structure of series-parallel phased-mission systems subject to fault-level coverage. Iie Transactions48(8), 736-746.‏
Pham, H.,  2003. Handbook of Engineering. Springer-Verlag, London Limited.
Sandve, K., & Aven, T. (1999). Cost optimal replacement of monotone, repairable systems. European Journal of Operational Research116(2), 235-248.‏
Sharma, G. C., Kumar, A., & Jain, M. (2002). Maintenance Cost Analysis for Replacement Model with Perfect Minimal Repair. International Journal of Engineering15(2), 161-168.‏
Shen, J., Hu, J., & Ye, Z. S. (2020). Optimal switching policy for warm standby systems subjected to standby failure mode. IISE Transactions, 1-13.‏
Sibai, F. N. (2014). Modelling and output power evaluation of series-parallel photovoltaic modules. International Journal of Advanced Computer Science and Applications (IJACSA)5(1).‏
Wang, J., Ye, J., & Wang, L. (2019). Extended age maintenance models and its optimization for series and parallel systems. Annals of Operations Research, 1-23.‏
Wang, L., Chu, J., & Mao, W. (2008). A condition-based order-replacement policy for a single-unit system. Applied mathematical modelling32(11), 2274-2289.‏
Wang, W., Zhao, F., & Peng, R. (2014). A preventive maintenance model with a two-level inspection policy based on a three-stage failure process. Reliability Engineering & System Safety121, 207-220.‏
Waziri, T. A., Yakasai, B. M., & Yusuf, I. (2019). On some discounted replacement models of a series system. Life Cycle Reliability and Safety Engineering, 1-11.‏‏
Xie, L., Lundteigen, M. A., & Liu, Y. (2020). Reliability and barrier assessment of series–parallel systems subject to cascading failures. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability234(3), 455-469.‏
Xu, M., Chen, T., & Yang, X. (2012). Optimal replacement policy for safety-related multi-component multi-state systems. Reliability Engineering & System Safety99, 87-95.‏
Xu, Q. Z., Guo, L. M., Shi, H. P., & Wang, N. (2016). Selective maintenance problem for series–parallel system under economic dependence. Defence technology12(5), 388-400.‏
Yusuf, I., & Ali, U. A. (2012). Structural dependence replacement model for parallel system of two units. Nigerian Journal of Basic and Applied Sciences20(4), 324-326.‏
Yusuf, I., Sani, B and Yusuf, B. (2019). Profit analysis of a series-parallel system under partial and complete failures, Journal of Applied Sciences, 19(6),565-574.
Zhao, X., Cai, J., Mizutani, S., & Nakagawa, T. (2020). Preventive replacement policies with time of operations, mission durations, minimal repairs and maintenance triggering approaches. Journal of Manufacturing Systems. Online. https://doi.org/10.1016/j.jmsy.2020.04.003.
Zhao, X., Mizutani, S., Chen, M., & Nakagawa, T. (2020). Preventive replacement policies for parallel systems with deviation costs between replacement and failure. Annals of Operations Research, 1-19.‏
Zhu, Z., Xiang, Y., & Coit, D. (2018, June). Redundancy Allocation for Serial-Parallel System Considering Heterogeneity of Components. In International Manufacturing Science and Engineering Conference (Vol. 51371, p. V003T02A049). American Society of Mechanical Engineers.‏