Optimal allocation policy of one redundancy in a n-component series system

It is of great importance to optimize system performance by allocating redundancies in a coherent system in reliability engineering and system security. In this paper, we focus on the problem of how to optimally allocate one active [standby] redundancy in a n-component series system in the sense of stochastic ordering. For the active case, it is showed that allocating the redundancy to the relatively weaker component leads to longer system’s lifetime in the likelihood ratio and reversed hazard rate orders, respectively. For the standby case, we show that the redundancy should be allocated to the weakest component of the series system in the likelihood ratio order. Based on these results, two optimal allocation policies are proposed. Also, some numerical examples are presented to explicate the theoretic results established here.

[1]  Xiaohu Li,et al.  On allocating redundancies to k-out-of- n reliability systems , 2014 .

[2]  Xiaohu Li,et al.  On the Allocation of Redundancies in Series and Parallel Systems , 2011 .

[3]  Neeraj Misra,et al.  Standby redundancy allocations in series and parallel systems , 2011 .

[4]  Moshe Shaked,et al.  Optimal allocation of resources to nodes of parallel and series systems , 1992, Advances in Applied Probability.

[5]  Félix Belzunce,et al.  On allocation of redundant components for systems with dependent components , 2013, Eur. J. Oper. Res..

[6]  Neeraj Misra,et al.  Optimal Allocation of Active Spares in Series Systems and Comparison of Component and System Redundancies , 2009, Journal of Applied Probability.

[7]  Peng Zhao,et al.  Optimal allocation of redundancies in series systems , 2012, Eur. J. Oper. Res..

[8]  R. I. Zequeira,et al.  On the optimal allocation of an active redundancy in a two-component series system , 2003 .

[9]  R. I. Zequeira,et al.  Some stochastic comparisons in series systems with active redundancy , 2010 .

[10]  F. Proschan,et al.  Stochastic order for redundancy allocations in series and parallel systems , 1992 .

[11]  Frank Proschan,et al.  Active Redundancy Allocation in Coherent Systems , 1988 .

[12]  Vanderlei da Costa Bueno,et al.  Minimal standby redundancy allocation in a k , 2005, Eur. J. Oper. Res..

[13]  Taizhong Hu,et al.  Optimal allocation of active redundancies in r-out-of-n systems , 2009 .

[14]  Xiaohu Li,et al.  Some new stochastic comparisons for redundancy allocations in series and parallel systems , 2008 .

[15]  R. I. Zequeira,et al.  On the hazard rate and reversed hazard rate orderings in two-component series systems with active redundancies , 2011 .

[16]  Vanderlei da Costa Bueno,et al.  Active redundancy allocation for a k , 2007, Eur. J. Oper. Res..

[17]  Amit Misra,et al.  ACTIVE REDUNDANCY ALLOCATIONS IN SERIES SYSTEMS , 2011 .

[18]  Long Li,et al.  Redundancy allocation at component level versus system level , 2015, Eur. J. Oper. Res..

[19]  Stefan Voß,et al.  An exact algorithm for the reliability redundancy allocation problem , 2015, Eur. J. Oper. Res..

[20]  José E. Valdés,et al.  On the optimal allocation of two active redundancies in a two-component series system , 2006, Oper. Res. Lett..

[21]  Harshinder Singh,et al.  ON REDUNDANCY ALLOCATIONS IN SYSTEMS , 1994 .

[22]  José E. Valdés,et al.  Active-redundancy allocation in systems , 2004, IEEE Transactions on Reliability.

[23]  Harshinder Singh,et al.  On allocation of spares at component level versus system level , 1997 .