The Lifetime Behavior of a New Discrete Time Mixed $delta$-shock Model

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Abstract:

In this study, a mixed $delta$-shock model with discrete-time is defined by combining $delta$-shock and extreme shock models. In this model, a system with multiple states fails in two ways: first, when k interarrival times between two consecutive shocks with magnitude larger than the critical threshold $gamma$ are in $[delta_1, delta _2], delta_1 < delta _2$; and second, when the interarrival time between two consecutive shocks is less than $delta_1$. The lifetime of the system and the Markov chain of the system's lifetime under the proposed mixed $delta$-shock model is obtained. Also, the mean lifetime of the system is calculated and a numerical example for validating the analytical results is established here.

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Journal title

volume 17  issue 1

pages  215- 234

publication date 2020-08

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