Life distribution properties of a new δ - shock model

Hamed Lorvand, Alireza Nematollahi and Mohammad Hossien Poursaeed

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 12, 3010-3025

Abstract: In this paper, the mixed δ-shock models for the multi-state systems is generalized to a model for which the system switches to a lower partially working state as soon as the occurrence of each interarrival time between two successive shocks lying in [δ1,δ2]. The system fails in three ways: first, k out of interarrival times between two successive shocks are in [δ1,δ2], second, upon the occurrence of each interarrival time between two successive shocks less than δ1 and third upon the occurrence of each shock with magnitude bigger than the other critical threshold γ. The survival functions of the system’s lifetime, the time used by the system in a perfectly functioning state, and the total time used by the system in partially working states are derived under the proposed model. The first two moments are also calculated. A simulation study is conducted to illustrate the behavior of the survival functions of the system’s lifetime.

Date: 2020
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DOI: 10.1080/03610926.2019.1584316

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