## Parallel and $$k$$-out-of-$$n$$: $$G$$ systems with nonidentical components and their mean residual life functions.(English)Zbl 1168.90399

Summary: A system with $$n$$ independent components which has a $$k$$-out-of-$$n: G$$ structure operates if at least $$k$$ components operate. Parallel systems are 1-out-of-$$n: G$$ systems, that is, the system goes out of service when all of its components fail. This paper investigates the mean residual life function of systems with independent and nonidentically distributed components. Some examples related to some lifetime distribution functions are given. We present a numerical example for evaluating the relationship between the mean residual life of the $$k$$-out-of-$$n: G$$ system and that of its components.

### MSC:

 90B25 Reliability, availability, maintenance, inspection in operations research 62N05 Reliability and life testing 60K10 Applications of renewal theory (reliability, demand theory, etc.)
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### References:

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