Optimal inspection policy for three-state systems monitored by variable sample size control charts

This paper presents the expected long-run cost per unit time for a system monitored by an adaptive control chart with variable sample sizes: if the control chart signals that the system is out of control, the sampling which follows will be conducted with a larger sample size. The system is supposed to have three states: in-control, out-of-control, and failed. Two levels of repair are applied to maintain the system. A minor repair will be conducted if an assignable cause is confirmed by an inspection, and a major repair will be performed if the system fails. Both the minor and major repairs are assumed to be perfect. We derive the expected long-run cost per unit time, which can be used to obtain the optimal inspection policy. Numerical examples are conducted to validate the derived cost.