Consecutive-k-out-of-n: G Systems with Stochastically Effective Protection Blocks

In the present work, we study the reliability of consecutive-k-out-of-n: G systems equipped with imperfect protection blocks that enhance the operating probability of protected components only with probability q. This stochastic effectiveness fits to realistic scenarios, where protective actions are not fully reliable. We derive a recurrence scheme for computing the reliability of the aforementioned structure, while asymptotic expressions are also provided. In addition, we investigate the impact of the protection parameters on the asymptotic convergence rate of the reliability for the underlying consecutive-k-out-of-n: G systems equipped with imperfect protection blocks. Several numerical results are produced in order to shed light on how the effectiveness and positioning of stochastic protection affect system reliability. Finally, a DNA sequencing application is described in order to provide some evidence about the applicability of the proposed scheme in real-life situations.