## Some stochastic comparisons of the conditional coherent systems.(English)Zbl 1198.62147

For a coherent system with $$n$$ independent and identical components having life times $$X_1,\dots, X_{n}$$, the life time can be expressed as $$T=\tau(X_1,\dots, X_{n})$$, where $$\tau$$ is a structural function. The signature of the system is defined as the probability vector $$(p_1,\dots,p_{n})$$ with $$p_{i}=$$(number of orderings for which the $$i$$ th failure causes the system failure)/$$n!$$. The life time distribution of the residual life and the inactivity time of a coherent system with i.i.d. components depend on the system’s structural design solely through its signature. The authors obtain some stochastic comparisons of residual lives and inactivity times, respectively, between two systems in the hazard rate order and the likelihood ratio order.

### MSC:

 62N05 Reliability and life testing 60E15 Inequalities; stochastic orderings
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### References:

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