Lifetime behavior of a new discrete time shock model

Document Type : Original Article

Authors

Hamed Lorvand ¹

Reza Farhadian ²

¹ Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran

² Department of Statistics, Razi University, Kermanshah, Iran

10.22067/smps.2025.93373.1046

Abstract

‎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.
 

Keywords

Discrete time shock model

‎ δ-shock model‎

‎Inter-arrival time

‎Random threshold

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