A new extended <i>δ</i>-shock model with the consideration of shock magnitude

Abstract

In this article, a new delta$$ \delta $$-shock model that takes into account the magnitude of shocks is introduced and studied from reliability perspective. According to the new model, the system breaks down if either a shock after non-critical shock occurs in a time length less than delta 1$$ {\delta}_1 $$ or a shock after a critical shock occurs in a time length less than delta 2,$$ {\delta}_2, $$ where delta 1<delta 2$$ {\delta}_1<{\delta}_2 $$. The distribution of the system's lifetime is studied for both discrete and continuous intershock time distributions. It is shown that a new model is useful to describe a certain cold standby repairable system.