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Optimizations of Replacement Policies for Random $k$ $k$ -out-of- $n$ $n$ Systems

Xiaoning Zhang

College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, P. R. China

E-mail Address: 123823627@qq.com

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and

Junyuan Wang

College of Sciences, China Jiliang, University, Hangzhou 310018, P. R. China

E-mail Address: junyuanyc@163.com

Corresponding author.

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https://doi.org/10.1142/S0218539321410023Cited by:2 (Source: Crossref)

This article is part of the issue:

Special Issue: Reliability Modeling and Applications
Guest Editors: Xufeng Zhao and Cunhua Qian

Abstract

In this paper, a random repairable $k$ $k$ -out-of- $n$ $n$ system is studied when random replacement policies are performed, where $k$ $k$ is a stochastic parameter. It is replaced before failure at a planned time $T$ $T$ or at random working cycle $Y$ $Y$ , whichever occurs last or first. Furthermore, optimal replacement policies are obtained for the extended models with working numbers. This paper aims to find the optimal replacement policies when replacement first and last policies are performed. Expected cost rates for the first and last replacement policies are derived, and their optimal replacement policies are derived analytically. Numerical examples are given to illustrate the theoretical results.

Keywords:

References

1. FAR 25.571 Amendment 45 (1978). Google Scholar
2. T. Nakagawa , Optimization problems in $k$ $k$ -out-of- $n$ $n$ systems, IEEE Trans. Reliab. 34(3) (2009) 248–250. Crossref, Web of Science, Google Scholar
3. W. Wu, Y. Tang, M. Yu and J. Ying , Reliability analysis of a $k$ $k$ -out-of- $n$ $n$ :G repairable system with single vacation, Appl. Math. Model. 38 (2014) 6075–6097. Crossref, Web of Science, Google Scholar
4. A. J. Fernádez , Computing tolerance limits for the lifetime of a $k$ $k$ -out-of- $n$ $n$ :F system based on prior information and censored data, Appl. Math. Model. 38 (2014) 548–561. Crossref, Web of Science, Google Scholar
5. S. Eryilmaz , Mean time to failure of weighted $k$ $k$ -out-of- $n$ $n$ :G systems, Commun. Stat. Simul. Comput. 44(10) (2015) 2705–2713. Crossref, Web of Science, Google Scholar
6. H. A. Khorshidi, I. Gunawan and M. Y. Ibrahim , On reliability evaluation of multistate weighted $k$ $k$ -out-of- $n$ $n$ system using present value, Eng. Econ. 60(1) (2015) 22–39. Crossref, Web of Science, Google Scholar
7. N. Mannai and S. Gasmi , Optimal design of $k$ $k$ -out-of- $n$ $n$ system first and last replacement in reliability theory, Oper. Res. (2018), https://doi.org/10.1007/s12351-018-0357-4. Web of Science, Google Scholar
8. A. J. Endharta and W. Y. Yun , A preventive maintenance of circular consecutive- $k$ $k$ -out-of- $n$ $n$ : F systems, Int. J. Qual. Reliab. Manage. 34 (2017) 752–769. Crossref, Web of Science, Google Scholar
9. S. Eryilmaz , Age-based preventive maintenance for coherent systems with applications to consecutive- $k$ $k$ -out-of- $n$ $n$ and related systems, Reliab. Eng. Syst. Saf. 204 (2020) 1–6. Crossref, Web of Science, Google Scholar
10. S. Eryilmaz and Y. Devrim , Reliability and optimal replacement policy for a $k$ $k$ -out-of- $n$ $n$ system subject to shocks, Reliab. Eng. Syst. Saf. 188 (2019) 393–397. Crossref, Web of Science, Google Scholar
11. I. Yusuf , Reliability modelling of a parallel system with a supporting device and two types of preventive maintenance, Int. J. Oper. Res. 25 (2016) 269–287. Crossref, Google Scholar
12. S. Eryilmaz , The number of failed components in a $k$ $k$ -out-of- $n$ $n$ system consisting of multiple types of components, Reliab. Eng. Syst. Saf. 175 (2018) 246–250. Crossref, Web of Science, Google Scholar
13. R. Peng and H. Xiao , Reliability of linear concecutive- $k$ $k$ -out-of- $n$ $n$ systems with two change points, IEEE Trans. Reliab. 67 (2018) 1019–1029. Crossref, Web of Science, Google Scholar
14. S. Sheu, T. Liu, H. Tsai and Z. Zhang , Optimization issues in $k$ $k$ -out-of- $n$ $n$ systems, Appl. Math. Model. 73 (2019) 563–580. Crossref, Web of Science, Google Scholar
15. D. Katherine and D. Anna , On the number of failed components in a $k$ $k$ -out-of- $n$ $n$ system upon system failure when the lifetimes are discretely distributed, Reliab. Eng. Syst. Saf. 188 (2019) 47–61. Crossref, Web of Science, Google Scholar
16. J. Wang and X. Zhu , Joint optimization of condition-based maintenance and inventory control for a $k$ $k$ -out-of- $n$ $n$ :F system of multi-state degrading components, Eur. J. Oper. Res. 290 (2021) 514–529. Crossref, Web of Science, Google Scholar
17. R. Barlow and L. Hunter , Optimum preventive maintenance policies, Oper. Res. 8(1) (1960) 90–100. Crossref, Web of Science, Google Scholar
18. R. E. Barlow and F. Proschan , Mathematical Theory of Reliability (John Wiley & Sons, New York, 1965). Google Scholar
19. T. Nakagawa , Advanced Reliability Models and Maintenance Policies (Springer, London, 2008). Google Scholar
20. M. S. Fallahnezhad and E. Najafian , A model of preventive maintenance for parallel, series, and single-item replacement systems based on statistical analysis, Commun. Stat. Simul. Comput. 46(7) (2017) 5846–5859. Crossref, Web of Science, Google Scholar
21. J. Wang, J. Ye and L. Wang , Extended age maintenance models and its optimization for series and parallel systems, Ann. Oper. Res. (2019), https://doi.org/10.1007/s10479-019-03355-3. Google Scholar
22. T. Nakagawa, X. Zhao and W. Yun , Optimal age replacement and inspection policies with random failure and replacement times, Int. J. Reliab. Qual. Saf. Eng. 18 (2011) 405–416. Link, Google Scholar
23. X. Zhao and T. Nakagawa , Optimization problems of replacement first or last in reliability theory, Eur. J. Oper. Res. 223 (2012) 141–149. Crossref, Web of Science, Google Scholar
24. M. Hamidi, F. Szidarovszky and M. Szidarovszky , New one cycle criteria for optimizing preventive replacement policies, Reliab. Eng. Syst. Saf. 154 (2016) 42–48. Crossref, Web of Science, Google Scholar
25. H. Okamura and T. Dohi , Moment-based approach for some age-based replacement problems, J. Ind. Prod. Eng. 34 (2017) 558–567. Web of Science, Google Scholar
26. M. Chen, X. Zhao and T. Nakagawa , Replacement policies with general models, Ann. Oper. Res. 277 (2019) 47–61. Crossref, Web of Science, Google Scholar
27. K. Ito, X. Zhao and T. Nakagawa , Random number of units for $k$ $k$ -out-of- $n$ $n$ systems, Appl. Math. Model. 45 (2017) 563–572. Crossref, Web of Science, Google Scholar
28. T. Nakagawa and W. Y. Yun , Note on MTTF of a parallel system, Int. J. Reliab. Qual. Saf. Eng. 18(1) (2011) 43–50. Link, Google Scholar
29. T. Nakagawa and X. Zhao , Optimization problems of a parallel system with a random number of units, IEEE Trans. Reliab. 61(2) (2005) 543–548. Crossref, Web of Science, Google Scholar