Residual Lifetime of Consecutive k -out-of- n Systems Under Double Monitoring

The consecutive k -out-of-n systems are important structures in reliability engineering due to their applications in various real life situations. In this paper, we study the residual lifetime of these systems under the condition that the total number of failed components at time t1 is r , and at time t2 (t2 >; t1) the system is still working. We obtain explicit expressions for the survival function of the corresponding residual life when the components are exchangeably dependent. We also obtain a signature-based mixture representation for a coherent system satisfying a certain property.

[1]  M. Zuo,et al.  Optimal Reliability Modeling: Principles and Applications , 2002 .

[2]  Moshe Shaked,et al.  Ordering conditional lifetimes of coherent systems , 2007 .

[3]  M. H. Poursaeed.  A note on the mean past and the mean residual life of a (n − k + 1)-out-of-n system under multi monitoring , 2010 .

[4]  Majid Asadi,et al.  On the Mean Residual Life Function of Coherent Systems , 2008, IEEE Transactions on Reliability.

[5]  Zhengcheng Zhang,et al.  Ordered properties on the residual life and inactivity time of (n-k+1)-out-of-n systems under double monitoring , 2010 .

[6]  A. R. Nematollahi,et al.  On the Mean Past and the Mean Residual Life Under Double Monitoring , 2008 .

[7]  Selma Gurler,et al.  Parallel and k-out-of-n: G systems with nonidentical components and their mean residual life functions , 2009 .

[8]  Serkan Eryilmaz,et al.  Circular consecutive k-out-of-n systems with exchangeable dependent components , 2011 .

[9]  Serkan Eryilmaz.  Reliability properties of consecutive k-out-of-n systems of arbitrarily dependent components , 2009, Reliab. Eng. Syst. Saf..

[10]  Francisco J. Samaniego,et al.  Mixture Representations of Residual Lifetimes of Used Systems , 2008, Journal of Applied Probability.

[11]  Narayanaswamy Balakrishnan,et al.  On the application and extension of system signatures in engineering reliability , 2008 .

[12]  Zhengcheng Zhang,et al.  Ordering conditional general coherent systems with exchangeable components , 2010 .

[13]  Jorge Navarro,et al.  Reliability and expectation bounds for coherent systems with exchangeable components , 2007 .

[14]  Majid Asadi,et al.  The mean residual life function of a k-out-of-n structure at the system level , 2006, IEEE Transactions on Reliability.

[15]  F. Samaniego,et al.  The signature of a coherent system and its application to comparisons among systems , 1999 .

[16]  Serkan Eryilmaz.  Review of recent advances in reliability of consecutive k-out-of-n and related systems , 2010 .

[17]  F. Samaniego.  On Closure of the IFR Class Under Formation of Coherent Systems , 1985, IEEE Transactions on Reliability.