Lifetime behavior of a new discrete time shock model

Stochastic Models in Probability and Statistics

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 19 آذر 1404   

نوع مقاله: Original Article

شناسه دیجیتال (DOI): 10.22067/smps.2025.93373.1046

نویسندگان

Hamed Lorvand^{* 1}؛ Reza Farhadian²

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

²Department of Statistics, Razi University, Kermanshah, Iran

چکیده

‎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.
 

کلیدواژه‌ها

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

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