Design of control chart for reliability monitoring of systems subjected to cumulative shocks

In shock models, the system will fail as soon as the amount of damages caused by shocks exceeds its failure threshold. In this research, the design of control chart for reliability monitoring of systems with random failure threshold subjected to cumulative random shocks is discussed. In the cumulative shock model, the system fails when the cumulative amount of damage caused by the shocks exceeds the failure threshold of the system. For the analytical solution of the model related to the control chart, there are some complexities such as the existence of unknown distributions, obtaining the convolutions of the distributions and integral calculations. To overcome these problems, phase-type distribution is used for modeling. By presenting a numerical example, the results of the presented analytical model are evaluated and compared with the Monte Carlo simulation method. Also, the performance of the proposed control chart using the average run length and average time to out of control signal criteria is evaluated.