On δ-shock model in a multi-state system

Mohammad Hossein Poursaeed

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 7, 1761-1767

Abstract: Shock models and multi-state systems have both been studied in the reliability literature. Suppose a system experiences shocks that occur randomly and their occurrence causes a change in the system performance. Suppose these shocks occur randomly over discrete time periods, and δ1 and δ2 are two critical thresholds. The system’s efficiency decreases when the time interval between two consecutive shocks falls between [δ1,δ2) and the system fails when the time interval is less than δ1. In this article, the failure time of such a system is studied under two cases. In the first case, the system's failure only depends on the time interval falling below δ1 whereas in the second case, the failure of the system can also occur due to decreasing of system's efficiency. We derive explicit expressions for the distribution and the mean time to failure of the system under the two above mentioned cases.

Date: 2020
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DOI: 10.1080/03610926.2019.1565784

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