Monitoring the ratio of two normal variables using variable sampling interval exponentially weighted moving average control charts

Quality and Reliability Engineering International , Vol 35, issue 1 (2019): 439-460, https://doi.org/10.1002/qre.2412 

(Q1, IF: 2.885, Ranking 438/2676 (in Engineering Category) in 2020 - Top 20%)

Abstract

We investigate in this paper a new type of control chart called VSI EWMA-RZ by integrating the variable sampling interval feature (VSI) with the exponentially weighted moving average (EWMA) scheme to monitor the ratio of two normal random variables. Because the distribution of the ratio is skewed, we suggest designing two separated one-sided charts instead of one two-sided chart. A new coefficient is introduced allowing us to be free to choose a sampling interval provided that it optimizes the performance of the control chart. We also make a direct comparison between the VSI EWMA-RZ charts and standard EWMA-RZ control charts. The numerical simulations show that the proposed charts outperform the standard EWMA charts in detecting process shifts. An application is illustrated for the implementation of the VSI EWMA-RZ control charts in the food industry.