## Mean residual lifetimes of consecutive-$$k$$-out-of-$$n$$ systems.(English)Zbl 1135.62084

The authors study some reliability properties of consecutive-$$k$$-out-of-$$n$$ systems with exchangeable component lifetimes. Some monotonicity and asymptotic properties of the associated mean residual life function are derived, and some ordering properties among the lifetimes of such systems are obtained.
For example, the authors show that, under some assumptions, the mean residual life function of a consecutive-$$k$$-out-of-$$n:G$$ system (that is, a system that functions if and only if at least $$k$$ consecutive components function) is asymptotically equivalent to that of a series system of $$k$$ components. When the component lifetimes are independent and identically distributed, the authors show, for $$2k>n$$, that consecutive-$$k$$-out-of-$$n$$ system lifetimes are ordered in the likelihood ratio order.

### MSC:

 62N05 Reliability and life testing 60K10 Applications of renewal theory (reliability, demand theory, etc.) 60E15 Inequalities; stochastic orderings
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### References:

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