Ordering New Conditional Residual Lifetimes of k-out-of-n Systems

Abstract

This article introduces a new residual life of (n − k + 1)-out-of-n systems consisting of n independent and identically distributed components, given that the total number of failures of components is not less than l at time t, and the system is still working. Some stochastic comparisons of residual lifetimes are conducted, and behaviors of DLR and ILR are given.

Keywords:

• DLR
• Hazard rate order
• ILR
• Likelihood ratio order
• Order statistics
• Stochastic order

2000 Mathematics Subject Classification:

• Primary 62E10
• Secondary 60E05

View correction statement:

Corrigendum

Acknowledgments

The author is grateful to the Editor and referees for their comments and suggestions.