Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2025-01-03T20:54:17.981Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal Allocation of Active Redundancies to k-out-of-n Systems with Heterogeneous Components

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

Published online by Cambridge University Press:  14 July 2016

Xiaohu Li  and
Weiyong Ding
Xiaohu Li*
Affiliation:
Lanzhou University
Weiyong Ding*
Affiliation:
Lanzhou University
*
∗Postal address: School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China.
∗Postal address: School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this note we deal with the allocation of independent and identical active redundancies to a k-out-of-n system with the usual stochastic order among its independent components. The optimal policy is proved both to assign more redundancies to the weaker component and to majorize all other policies. This improves the corresponding one in Hu and Wang (2009) and serves as a nice supplement to that in Misra, Dhariyal and Gupta (2009) as well.

Keywords

MajorizationSchur concavestochastic order

MSC classification

Secondary: 90B25: Reliability, availability, maintenance, inspection 60E15: Inequalities; stochastic orderings 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 1 , March 2010 , pp. 254 - 263
Copyright
Copyright © Applied Probability Trust 2010 

Footnotes

Supported by the National Natural Science Foundation of China (10771090).

References

Cha, J. H., Mi, J. and Yun, W. Y. (2008). Modelling a general standby system and evaluation of its performance. Appl. Stoch. Models Business Industry 24, 159–169.Google Scholar
Hu, T. and Wang, Y. (2009). Optimal allocation of active redundancies in r-out-of-n systems. J. Statist. Planning Infer. 139, 3733–3737.CrossRefGoogle Scholar
Kuo, W. and Zuo, M. J. (2002). Optimal Reliability Modeling: Principles and Applications. John Wiley, Hoboken, NJ.Google Scholar
Li, X., Zhang, Z. and Wu, Y. (2009). Some new results involving general standby systems. Appl. Stoch. Models Business Industry 25, 632–642.Google Scholar
Marshall, A. W. and Olkin, I. (1979). Inequalities: Theory of Majorization and Its Applications. Academic Press, New York.Google 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
Roberts, A. W. and Varberg, D. E. (1973). Convex Functions. Academic Press, New York.Google Scholar
Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders. Springer, New York.Google 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.Google Scholar
Singh, H. and Singh, R. S. (1997). Optimal allocation of resources to nodes of series systems with respect to failure-rate ordering. Naval Res. Logistics 44, 147–152.Google Scholar