Analyzing the multi-state system under a run shock model

Murat Ozkut*, Cihangir Kan, Ceki Franko

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A system experiences random shocks over time, with two critical levels, d1 and d2, where. k consecutive shocks with magnitudes between d1 and d2 partially damaging the system, causing it to transition to a lower, partially working state. Shocks with magnitudes above d2 have a catastrophic effect, resulting in complete failure. This theoretical framework gives rise to a multi-state system characterized by an indeterminate quantity of states. When the time between successive shocks follows a phase-type distribution, a detailed analysis of the system's dynamic reliability properties such as the lifetime of the system, the time it spends in perfect functioning, as well as the total time it spends in partially working states are discussed.

Original languageEnglish
JournalProbability in the Engineering and Informational Sciences
Publication statusAccepted/In press - 2024


  • mean residual life
  • multi-state system
  • phase-type distribution
  • shock model


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