Lifetime behavior of a new discrete time shock model

‎In this paper, a new discrete-time shock model is investigated. Under the proposed model, system failure occurs when the inter-arrival time between successive shocks falls below a random critical threshold, denoted by ∆‎. This model can be viewed as a randomized-threshold extension of the classical delta shock model. Assuming that ‎∆‎ follows a uniform distribution, we derive the probability mass function of the system's lifetime and analyze the mean time to failure. Furthermore, the lifetime behavior of the system is examined in a Markovian environment. Illustrative numerical results are presented for both the probability mass function of the system's lifetime and the mean time to failure.

کلیدواژه ها:

Discrete time shock model ، ‎ δ-shock model‎ ، ‎Inter-arrival time ، ‎Random threshold