Monitoring the ratio of two normal variables based on double exponentially weighted moving average control charts with fixed and variable sampling intervals

Monitoring the ratio of two normal random variables (RZ) is one of the most important directions in Statistical Process Control (SPC). To enhance the sensitivity of traditional RZ charts in detecting process shifts, especially small and moderate shifts, this paper proposes a new RZ control chart on the basis of the exponentially weighted moving average (EWMA) RZ control chart. Firstly, by smoothing the coefficient of EWMA-RZ control chart twice, the double exponentially weighted moving average (DEWMA) RZ chart is obtained. In particular, the variable sampling interval (VSI) strategy has been adopted to different control charts by researchers. With the application of this strategy, the VSI-DEWMA-RZ chart is then developed to further improve the performance of the proposed DEWMA-RZ chart in detecting process shifts. Secondly, the run length (RL) properties of the proposed DEWMA-RZ charts are obtained by using the Monte-Carlo (MC) simulation. Finally, for different chart parameters, the performance of the proposed VSI-DEWMA-RZ chart is compared with the proposed DEWMA-RZ and the existing VSI-EWMA-RZ charts. The simulation results show that the proposed VSI-DEWMA-RZ chart performs better than the DEWMA-RZ chart and moreover, it has better performance than the VSI-EWMA-RZ chart for small and moderate shifts.