Reliability of a consecutive k-out-of-n: G system under the effect of different shocks

The consecutive k -out-of- n : G ( c / k / n / G ) system is a system consisting of n components, where the system is deemed operational as long as at least k consecutive components are functioning properly, 1 ≤ k ≤ n . In the scope of this article, the reliability of a c / k / n / G system whose components are exposed to two different environments (two different types of shocks) is discussed. There exists a turning point (component B ), say. The shocks that affect components after this turning point differ from those that affect components at or before it. All shocks are assumed to be independent. By considering the shock’s magnitude and its arrival time, the reliability of the system is obtained. The reliability of series and parallel systems are obtained as special cases, as well as the reliability of the unipolar and bipolar c / k / n / G systems. As illustration the exact reliability of the system under the proposed assumptions is obtained under a specific bivariate distribution of the shock’s magnitude and its arrival time. Finally, numerical illustration is introduced to highlight the theoretical results.