Monitoring the Ratio of Two Normal Variables Using EWMA Type Control Charts

In many fields, there is the need to monitor quality characteristics defined as the ratio of two random variables. The design and implementation of control charts directly monitoring the ratio stability is required for the continuous surveillance of these quality characteristics. In this paper, we propose two one‐sided exponentially weighted moving average (EWMA) charts with subgroups having sample size n > 1 to monitor the ratio of two normal random variables. The optimal EWMA smoothing constants, control limits, and ARLs have been computed for different values of the in‐control ratio and correlation between the variables and are shown in several figures and tables to discuss the statistical performance of the proposed one‐sided EWMA charts. Both deterministic and random shift sizes have been considered to test the two one‐sided EWMA charts' sensitivity. The obtained results show that the proposed one‐sided EWMA control charts are more sensitive to process shifts than other charts already proposed in the literature. The practical application of the proposed control schemes is discussed with an illustrative example.