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Article Citation - WoS: 23Citation - Scopus: 23Reliability of a Mixed Δ-Shock Model With a Random Change Point in Shock Magnitude Distribution and an Optimal Replacement Policy(Elsevier Sci Ltd, 2023) Chadjiconstantinidis, Stathis; Eryilmaz, SerkanA mixed delta-shock model when there is a change in the distribution of the magnitudes of shocks is defined and studied. Such a model which is a combination of the delta-shock model and the extreme shock model with a random change point (studied by Eryilmaz and Kan, 2019), is useful in practice since a sudden change in environmental conditions may cause a larger shock. In particular, the reliability and the mean time to failure of the system are evaluated by assuming that the random change point has a discrete phase-type distribution. Analytical results for evaluating the reliability function of the system for several joint distributions of the interarrival times and the magnitudes of shocks, are also given. The optimal replacement policy that is based on a control limit is also proposed when the number of shocks until the change point follows geometric distribution. The results are illustrated by numerical examples.Article On 𝜹-Shock Model With a Change Point in Intershock Time Distribution(Statistics & Probability Letters, 2024) Chadjiconstantinidis, Stathis; Eryılmaz, SerkanIn this paper, we study the reliability of a system that works under 𝛿-shock model. That is, the system failure occurs when the time between two successive shocks is less than a given thresh old 𝛿. In a traditional setup of the 𝛿 shock model, the intershock times are assumed to have the same distribution. In the present setup, a change occurs in the distribution of the intershock times due to an environmental effect. Thus, the distribution of the intershock times changes after a random number of shocks. The reliability of the system is studied under this change point setup.Article Citation - WoS: 6Citation - Scopus: 6On δ-shock model with a change point in intershock time distribution(Elsevier, 2024) Chadjiconstantinidis, Stathis; Eryilmaz, SerkanIn this paper, we study the reliability of a system that works under o-shock model. That is, the system failure occurs when the time between two successive shocks is less than a given threshold o. In a traditional setup of the o shock model, the intershock times are assumed to have the same distribution. In the present setup, a change occurs in the distribution of the intershock times due to an environmental effect. Thus, the distribution of the intershock times changes after a random number of shocks. The reliability of the system is studied under this change point setup.
