A note on a generalization of the δ-shock model
نویسندگان
1 Department of Statistics, Razi University, Kermanshah, Iran
2 Department of Statistics, Razi University, Kermanshah, Iran
doi
10.22034/jsmta.2025.22498.1167چکیده
According to the δ-shock model, a shock-exposed system fails when an intershock time falls below a critical threshold δ. Recently, a generalization of the δ-shock model was introduced by Poursaeed (2019) under which the system fails when the intershock time falls below a threshold δ1>0 and also the system probably fails with probability θ if the intershock time falls in the interval (δ1,δ2] for δ1<δ2. In this paper, we look at this generalized model with new assumptions for intershock times. More precisely, we assume that the intershock times have a discrete distribution, and the chance of their occurrence at a critical time point is significantly high. We investigate some statistical properties of the system's lifetime, and by providing an illustrative example, we examine theoretical results numerically. Numerical results show that when the chance of intershock times occurring at a critical time point increases, the system reliability decreases significantly. Finally, the paper ends with a conclusion.