Reliability monitoring of systems with cumulative shock-based deterioration process

•A new closed-form solution based on Phase-type (PH) distributions is introduced to find the systems reliability and its lifetime distribution.•Performance of the proposed algorithm for finding the solutions is compared to the similar works in reliability estimation.•A control chart for monitoring the time between a fixed number of failures in the system with cumulative shock model deterioration is proposed.•The proposed control chart is evaluated and compared to the average run length (ARL) and the average time to signal (ATS) criteria. Cumulative shock model is one of the shock-based degradation models. For the cumulative shock model, the system failure occurs when the total damages due to shocks exceeds a failure threshold. Control chart is a tool that can be used to monitor and control the reliability of a system. In this work, we propose a control chart based on the time between a fixed number of failures in the system with cumulative shock model deterioration. To this end, Phase-type (PH) distributions are utilized to find system lifetime distribution and to construct the control chart. An illustrative example is provided to assess the efficiency and accuracy of the proposed PH model. The average run length (ARL) and the average time to signal (ATS) criteria are used to evaluate the performance of the suggested control chart. The results show that the proposed control chart is effective in detecting the shifts in system reliability.