The system under consideration has � independent components, and its operation relies on the functioning of at
least � components, 1 ≤ � ≤ �. The system experiences (� + 1) distinct shocks. Shock � impacts the �!" component, � =
1, 2, . . . , �, while shock (� + 1) simultaneously impacts all components. Any shock is lethal if its magnitude is below or
above the component-designed thresholds �# or �$, respectively. A shock is characterized by its magnitude and arrival
time, forming a bivariate random vector. The bivariate random vectors specifying the magnitudes and the arrival times of
the shocks are assumed to be independent and follow non-identical bivariate distributions. The reliability of a �-out-of-�: �
system under the influence of this type of shocks is derived. The reliability of parallel and series systems is obtained as
special situations. The bivariate Pareto type I distribution is applied as an example of the bivariate distribution of the
magnitude and arrival time of the shocks. Furthermore, numerical illustrations are conducted to highlight the theoretical
results obtained. |
