Abstract
Suppose that a system is affected by a sequence of shocks that occur randomly over time, and delta(1), delta(2), eta(1) and eta(2) are critical levels such that 0 < delta(1) < delta(2) and 0 < eta(1) < eta(2). In this paper, a new mixed delta-shock model is introduced for which the system fails with a probability, say theta(1), when the time between two consecutive shocks is lying in [delta(1), delta(2)], and the system fails with a probability, say theta(2), when the magnitude of a shock is lying in [eta(1), eta(2)]. The system fails with probability 1, as soon as the interarrival time between two successive shocks is less than delta(1) or a shock with magnitude greater than eta(2) occurs. The corresponding survival function is derived under two scenarios of independence and dependence between the interarrival times and the magnitude of shocks. The first and second moments are also derived. To illustrate the behavior of the system's lifetime, a simulation study is also conducted. (c) 2021 Elsevier B.V. All rights reserved.
NSTL
Elsevier