Reliability Evaluation of a System Under a Mixed Shock Model

Abstract

A new mixed shock model is introduced and studied. According to the model, for two fixed critical values d(1) and d(2) such that d(1) < d(2), the system under concern fails upon the occurrence of k consecutive shocks of size at least d(1) or a single large shock of size at least d(2). The new model combines run and extreme shock models. Reliability properties of the system are studied under two cases: when the interarrival time X-i between the (i - 1)th and ith shock, and the magnitude of the ith shock Y-i are independent for all i, and when the interarrival time between the (i - 1)th and ith shock, and the magnitude of the ith shock are dependent for all i. (C) 2018 Elsevier B.V. All rights reserved.