Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T18:27:35.534Z Has data issue: false hasContentIssue false
  • English
  • Français

ON OPTIMAL HETEROGENEOUS COMPONENTS GROUPING IN SERIES-PARALLEL AND PARALLEL-SERIES SYSTEMS

Published online by Cambridge University Press:  28 December 2018

Xiaoliang Ling ,
Yinzhao Wei  and
Ping Li
Xiaoliang Ling
Affiliation:
College of Sciences Hebei University of Science and TechnologyShijiazhuang 050018China E-mail: xlling07@126.com
Yinzhao Wei
Affiliation:
College of Sciences Hebei University of Science and TechnologyShijiazhuang 050018China E-mail: xlling07@126.com
Ping Li
Affiliation:
School of Business Hebei Normal UniversityShijiazhuang 050024China
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we consider optimal components grouping in series–parallel and parallel–series systems composed of k subsystems. All components in each subsystem are drawn from a heterogeneous population consisting of m different subpopulations. Firstly, we show that when one allocation vector is majorized by another one, then the series–parallel (parallel–series) system corresponding to the first (second) vector is more reliable than that of the other. Secondly, we study the impact of changes in the number of subsystems on the system reliability. Finally, we study the influence of the selection probabilities of subpopulations on the system reliability.

Keywords

heterogeneous populationmajorization orderparallel–series systemseries–parallel systemstochastic orders
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 33 , Issue 4 , October 2019 , pp. 564 - 578
Copyright
Copyright © Cambridge University Press 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Barlow, R.E. & Proschan, F. (1981). Statistical Theory of Reliability and Life Testing. To Begin with: MD: Silver Spring.Google Scholar
2.Billionnet, A. (2008). Redundancy allocation for series-parallel systems using integer linear programming. IEEE Transactions on Reliability 57(3): 507–516.Google Scholar
3.Cha, J.H. (2011). Comparison of combined stochastic risk processes and its applications. European Journal of Operational Research 215(2): 404–410.Google Scholar
4.Cha, J.H. (2013). Stochastic comparison of generalized combined risk processes. Journal of Statistical Planning and Inference 143(4): 818–826.Google Scholar
5.Coit, D.W. & Smith, A.E. (1996). Reliability optimization of series-parallel systems using a genetic algorithm. IEEE Transactions on Reliability 45(2): 254–260.Google Scholar
6.Di Crescenzo, A. & Pellerey, F. (2011). Stochastic comparisons of series and parallel systems with randomized independent components. Operations Research Letters 39(5): 380–384.Google Scholar
7.Ding, W. & Li, X. (2012). The optimal allocation of active redundancies to k-out-of-n systems with respect to hazard rate ordering. Journal of Statistical Planning and Inference 142(7): 1878–1887.Google Scholar
8.Hazra, N.K., Finkelstein, M., & Cha, J.H. (2017). On optimal grouping and stochastic comparisons for heterogeneous items. Journal of Multivariate Analysis 160: 146–156.Google Scholar
9.Hu, T. & Wang, Y. (2009). Optimal allocation of active redundancies in r-out-of-n systems. Journal of Statistical Planning and Inference 139: 3733–3737.Google Scholar
10.Kuo, W. & Wan, R. (2007). Recent advances in optimal reliability allocation. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans 37(2): 143–156.Google Scholar
11.Levitin, G. & Amari, S.V. (2009). Optimal load distribution in series-parallel systems. Reliability Engineering and System Safety 94(2): 254–260.Google Scholar
12.Li, X. & Ding, W. (2010). Optimal allocation of active redundancies to k-out-of-n systems with heterogeneous components. Journal of Applied Probability 47: 254–263.Google Scholar
13.Li, X. & Ding, W. (2013). On allocation of active redundancies to systems: A brief review. In Li, H., Li, X. (eds.), Stochastic orders in reliability and risk. Lecture Notes in Statistics, Vol. 208; New York, NY: Springer.Google Scholar
14.Marshall, A.W., Olkin, I., & Arnold, B.C. (2011). Inequalities: theory of majorization and its applications. New York: Springer.Google Scholar
15.Misra, N., Dhariyal, I.D., & Gupta, N. (2009). Optimal allocation of active spares in series systems and comparison of component and system redundancies. Journal of Applied Probability 46(1): 19–34.Google Scholar
16.Ramirez-Marquez, J.E., Coit, D.W., & Konak, A. (2004). Redundancy allocation for series-parallel systems using a max-min approach. IIE Transactions 36(9): 891–898.Google Scholar
17.Sarhan, A.M., Al-Ruzaiza, A.S., Alwasel, I.A., & El-Gohary, A.I. (2004). Reliability equivalence of a series-parallel system. Applied Mathematics and Computation 154(1): 257–277.Google Scholar
18.Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders. New York: Springer.Google Scholar
19.Sun, M.X., Li, Y.F., & Zio, E. (2017). On the optimal redundancy allocation for multi-state series-parallel systems under epistemic uncertainty. Reliability Engineering and System Safety. https://doi.org/10.1016/j.ress.2017.11.025.Google Scholar
20.Zhuang, J. & Li, X. (2015). Allocating redundancies to k-out-of-n systems with independent and heterogeneous components. Communications in Statistics-Theory and Methods 44: 5109–5119.Google Scholar