## Reliability of linear and circular consecutive-$$k$$-out-of-$$n$$ systems with shock model.(English. French summary)Zbl 1327.62495

Summary: A consecutive $$k$$-out-of-$$n$$ system consists of an ordered sequence of $$n$$ components, such that the system functions if and only if at least $$k$$ $$(k\leq n)$$ consecutive components function. The system is called linear ($$L$$) or circular ($$C$$) depending on whether the components are arranged on a straight line or form a circle. In the first part, we use a shock model to obtain the reliability function of consecutve-$$k$$-out-of-$$n$$ systems with dependent and nonidentical components. In the second part, we treat some numerical examples to show the derive results and deduce the failure rate of each component and the system.

### MSC:

 62N05 Reliability and life testing 68M15 Reliability, testing and fault tolerance of networks and computer systems 68M20 Performance evaluation, queueing, and scheduling in the context of computer systems 90B25 Reliability, availability, maintenance, inspection in operations research 60K10 Applications of renewal theory (reliability, demand theory, etc.)
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