Reliability and Failure Probability Functions of the m-Consecutive-k-out-of-n: F Linear and Circular Systems
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Abstract
The m-consecutive-k-out-of-n: F linear and circular system consists of n sequentially connected components; the components are ordered on a line or a circle; it fails if there are at least m non-overlapping runs of consecutive-k failed components. This paper proposes the reliability and failure probability functions for both linearly and circularly m-consecutive-k-out-of-n: F systems. More precisely, the failure states of the system components are separated into two collections (the working and the failure collections); where each one is defined as a collection of finite mutual disjoint classes of the system states. Illustrative example is provided.
Received 19/3/2020, Accepted 3/11/2020, Published Online First 11/1/2021
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