Conditional residual lifetimes of coherent systems under double monitoring

ABSTRACT

In this paper, we obtain a mixture representation for the reliability function of the conditional residual lifetime of a coherent system with n independent and identically distributed (i.i.d.) components under double monitoring. We suppose that at time t₁, j components have failed while at time t₂ the system is still alive. Based on these mixture representation, we then study stochastic comparisons of the conditional residual lifetimes of two coherent systems with independent and identical components.

KEYWORDS:

• Coherent systems
• double monitoring
• hazard rate order
• likelihood ratio order
• residual lifetime
• reversed hazard rate order
• signature

Mathematics Subject Classification:

• Primary 90B25
• Secondary 60K10