Abstract
A linear consecutive k-out-of-n:F system is an ordered sequence of n-components that fails if and only if k consecutive components in positions i, (i+1), …, (i+k−1) fail. This modeling paradigm is suitable for several modern systems such as wireless communication, which may be unable to send messages if several adjacent transmission stations fail. Although these systems are susceptible to correlated and dependent failures from geospatial events such as extreme weather, only a handful of consecutive-k-out-of-n:F models in the literature assume failures are not statistically independent and even fewer consider maintenance of consecutive-k-out-of-n:F systems subject to dependent failures. To address this limitation, this paper develops a novel formulation of the linear consecutive-k-out-of-n:F model subject to dependent failures and derives maintenance models. A sequence of illustrative examples demonstrates the ability of the model to explicitly characterize the influence of dependence on several reliability measures and shows how the model enables the identification of optimal age replacement policies to minimize cost or maximize availability despite dependence.
•We present two novel model formulations of a linear consecutive-k-out-of-n:F system.•System components are identical but subject to failure dependence.•The models characterize the impact of dependence on several reliability measures.•Optimal maintenance intervals to minimize cost or maximize availability are derived.