Consecutive \(k\) and related models – a survey. (English) Zbl 1536.90065
Li, Quan-Lin (ed.) et al., Stochastic models in reliability, network security and system safety. Essays dedicated to Professor Jinhua Cao on the occasion of his 80th birthday. Singapore: Springer. Commun. Comput. Inf. Sci. 1102, 3-18 (2019).
Summary: As one of the most popular reliability models, the previous several decades have witnessed remarkable developments and extensive applications of consecutive \(k\) systems, and a number of related models have been developed. In the paper, a summary of the state of the arts in the field is provided. After a brief introduction of conventional consecutive \(k\) systems, we focus on variants of the consecutive \(k\) systems by considering failure criteria (single failure criterion and multiple failure criteria), geometric structure of the system, states of components and the system, weight of each component, dependency of components. Finally, several future challenges deserving further studies are highlighted.
For the entire collection see [Zbl 1427.68014].
For the entire collection see [Zbl 1427.68014].
MSC:
| 90B25 | Reliability, availability, maintenance, inspection in operations research |
| 60K10 | Applications of renewal theory (reliability, demand theory, etc.) |
Keywords:
consecutive \(k\)-out-of-\(n\) systems; system reliability; component importance; system signatureReferences:
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