en عمومى General كاربردي Applicable <span style="font-size:11pt"><span style="line-height:normal"><span style="font-family:Calibri,sans-serif"><span style="font-size:12.0pt"><span new="" roman="" style="font-family:" times="">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&#39;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.</span></span></span></span></span> Discrete time, extreme shocks, interarrival times, lifetime, markov chain, mixed $delta$-shock model. 215 234 http://jsri.srtc.ac.ir/browse.php?a_code=A-10-30-3&slc_lang=en&sid=1 Marjan Entezari مرجان انتظاری me.125n2@gmail.com 10031947532846002411 10031947532846002411 No Yazd University Rasool Roozegar رسول روزگار rroozegar@yazd.ac.ir 10031947532846002412 10031947532846002412 Yes Yazd University