CUSUM control charts with variable sampling interval for monitoring the ratio of two normal variables

In many industrial manufacturing processes, the ratio between two normal random variables plays a key role in ensuring quality of products. Thus, monitoring this ratio is an important task that is well worth considering. In this paper, we combine a variable sampling interval (VSI) strategy with a cumulative sum (CUSUM) scheme to create a new type of control chart for purpose of tracking the ratio between two normal variables. The average time to signal ( A T S ) and the expected average time to signal ( E A T S ) criteria are used to evaluate the performance of the new VSI CUSUM RZ control chart. The numerical results show that the proposed control chart has much more attractive performance in comparison with the standard CUSUM‐RZ control chart and the VSI EWMA‐RZ control chart.