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.
Farhadian, R. and Jafari, H. (2024). A note on a generalization of the δ-shock model. Journal of Statistical Modelling: Theory and Applications, 5(2), 65-76. doi: 10.22034/jsmta.2025.22498.1167
MLA
Farhadian, R. , and Jafari, H. . "A note on a generalization of the δ-shock model", Journal of Statistical Modelling: Theory and Applications, 5, 2, 2024, 65-76. doi: 10.22034/jsmta.2025.22498.1167
HARVARD
Farhadian, R., Jafari, H. (2024). 'A note on a generalization of the δ-shock model', Journal of Statistical Modelling: Theory and Applications, 5(2), pp. 65-76. doi: 10.22034/jsmta.2025.22498.1167
CHICAGO
R. Farhadian and H. Jafari, "A note on a generalization of the δ-shock model," Journal of Statistical Modelling: Theory and Applications, 5 2 (2024): 65-76, doi: 10.22034/jsmta.2025.22498.1167
VANCOUVER
Farhadian, R., Jafari, H. A note on a generalization of the δ-shock model. Journal of Statistical Modelling: Theory and Applications, 2024; 5(2): 65-76. doi: 10.22034/jsmta.2025.22498.1167
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