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Reliability analysis of k-out-of-n systems based on a grouping of components

Part of: Distribution theory - Probability Special processes Operations research and management science

Published online by Cambridge University Press:  07 August 2019

Weiyong Ding ,
Rui Fang  and
Peng Zhao
Weiyong Ding*
Affiliation:
Jiangsu Normal University
Rui Fang*
Affiliation:
Shantou University
Peng Zhao*
Affiliation:
Jiangsu Normal University
*
*Postal address: School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China.
**Postal address: Department of Mathematics, Shantou University, Shantou 515063, China.
***Email address: zhaop@jsnu.edu.cn
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Abstract

In this paper we treat a two-stage grouping procedure of building a k-out-of-n system from several clusters of components. We use a static framework in which the component reliabilities are fixed. Under such a framework, we address the impact of the selecting strategies, the sampling probabilities, and the component reliabilities on the constructed system’s reliability. An interesting finding is that the level of component reliabilities could be identified as a decisive factor in determining how the selecting strategies and the component reliabilities affect the system reliability. The new results generalize and extend those established earlier in the literature such as Di Crescenzo and Pellerey (2011), Hazra and Nanda (2014), Navarro, Pellerey, and Di Crescenzo (2015), and Hazra, Finkelstein, and Cha (2017). Several Monte Carlo simulation experiments are provided to illustrate the theoretical results.

Keywords

k-out-of-n structurereliabilitytwo-stage sampling

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60E15: Inequalities; stochastic orderings 60K10: Applications (reliability, demand theory, etc.)
Type
Original Article
Information
Advances in Applied Probability , Volume 51 , Issue 2 , June 2019 , pp. 339 - 357
Copyright
© Applied Probability Trust 2019 

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References

Barlow, R. E. and Proschan, F. (1981). Statistical theory of reliability and life testing: Probability models. To Begin With, Silver Spring, MD.Google Scholar
Boland, P. J. and Proschan, F. (1983). The reliability of k out of n systems. Ann. Prob. 11, 760–764.CrossRefGoogle Scholar
Da, G. and Ding, W. (2016). Component level versus system level k-out-of-n assembly systems. IEEE Trans. Reliab. 65, 425–433.CrossRefGoogle Scholar
Di Crescenzo, A. (2007). A Parrondo paradox in reliability theory. Math. Scientist 32, 17–22.Google Scholar
Di Crescenzo, A. and Pellerey, F. (2011). Stochastic comparisons of series and parallel systems with randomized independent components. Operat. Res. Lett. 39, 380–384.CrossRefGoogle Scholar
Ding, W. and Li, X. (2012). The optimal allocation of active redundancies to k-out-of-n systems with respect to hazard rate. J. Statist. Planning Infer. 142, 1878–1887.CrossRefGoogle Scholar
Fang, R. and Li, X. (2017). On matched active redundancy allocation for coherent systems with statistically dependent component lifetimes. Naval Res. Logistics 64, 580–598.CrossRefGoogle Scholar
Hazra, N. K. and Nanda, A. K. (2014). Some results on series and parallels systems with randomized components. Operat. Res. Lett. 42, 132–136.CrossRefGoogle Scholar
Hazra, N. K., Finkelstein, M. and Cha, J. H. (2017). On optimal grouping and stochastic comparisons for heterogenous items. J. Multivariate Anal. 160, 146–156.CrossRefGoogle Scholar
Kuo, W. and Zuo, M. J. (2003). Optimal Reliability Modeling: Principles and Applications. John Wiley, New York.Google Scholar
Marshall, A. W., Olkin, I. and Arnold, B. C. (2011). Inequalities: Theory of Majorization and its Applications. Springer, New York.CrossRefGoogle Scholar
Misra, N., Dhariyal, I. D. and Gupta, N. (2009). Optimal allocation of active spares in series systems and comparison of component and system redundancies. J. Appl. Prob. 46, 19–34.CrossRefGoogle Scholar
Navarro, J. and Spizzichino, F. (2010). Comparisons of series and parallel systems with components sharing the same copula. Appl. Stoch. Models Business Industry 26, 775–791.CrossRefGoogle Scholar
Navarro, J., Pellerey, F. and Di Crescenzo, A. (2015). Ordering of coherent systems with randomized dependent components. Europ. J. Operat. Res. 240, 127–139.CrossRefGoogle Scholar
Shaked, M. and Shanthikumar, J. G. (1992). Optimal allocation of resources to nodes of series and parallel systems. Adv. Appl. Prob. 24, 894–914.CrossRefGoogle Scholar
Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders. Springer, New York.CrossRefGoogle Scholar
Singh, H. and Singh, R. S. (1997). Note: Optimal allocation of resources to nodes of series systems with respect to failure-rate ordering. Naval Res. Logistics 44, 147–152.3.0.CO;2-A>CrossRefGoogle Scholar