Conditional residual lifetimes of coherent systems

In this paper, we derive mixture representations for the reliability function of the conditional residual lifetime of a coherent system with n independent and identically distributed (i.i.d.) components under the condition that at least j and at most k−1 (j<k) components have failed by time t. Based on these mixture representations, we then discuss stochastic comparisons of the conditional residual lifetimes of two coherent systems with independent and identical components.

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

[2]  Peng Zhao,et al.  Some Aging Properties of the Residual Life of$k$-out-of-$n$Systems , 2006, IEEE Transactions on Reliability.

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

[4]  Xiaohu Li,et al.  Stochastic Comparison on General Inactivity Time and General Residual Life of k-Out-of-n Systems , 2008, Commun. Stat. Simul. Comput..

[5]  A. R. Nematollahi,et al.  Some aspects of the mean past lifetime of a parallel system under double regularly checking , 2010 .

[6]  Majid Asadi,et al.  A study on the mean past lifetime of the components of (n − k + 1)-out-of-n system at the system level , 2010 .

[7]  Xiaohu Li,et al.  Some stochastic comparisons of conditional coherent systems , 2008 .

[8]  Jorge Navarro,et al.  A note on comparisons among coherent systems with dependent components using signatures , 2005 .

[9]  Narayanaswamy Balakrishnan,et al.  Mixture Representations for the Joint Distribution of Lifetimes of two Coherent Systems with Shared Components , 2013, Advances in Applied Probability.

[10]  N. Balakrishnan,et al.  On the Residual and Inactivity Times of the Components of Used Coherent Systems , 2012, J. Appl. Probab..

[11]  Zhengcheng Zhang,et al.  Mixture Representations of Inactivity Times of Conditional Coherent Systems and their Applications , 2010, Journal of Applied Probability.

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

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

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

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

[16]  N. Balakrishnan,et al.  Stochastic Orderings and Ageing Properties of Residual Life Lengths of Live Components in (n-k+1)-Out-Of-n Systems , 2014, Journal of Applied Probability.

[17]  M. Asadi,et al.  Stochastic Properties of Components in a Used Coherent System , 2014 .

[18]  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 .

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

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