The Shewhart-type RZ control chart for monitoring the ratio of autocorrelated variables

In many industrial manufacturing processes, the quality of products can depend on relative amount between two characteristics X and Y. Often, this calls for on-line monitoring ratio Z=X/Y as a characteristic itself by means control chart. A large number charts have been investigated in literature under assumption independent normal observations characteristics. practice, due to high frequency sensor data collection, both autocorrelation cross-correlation consecutive exist Y should be modelled protect against false alarm rate inflation when implementing chart Z=X/Y. paper, we tackle problem investigating performance Phase II Shewhart-type RZ variables whose relationship is captured bivariate time series autoregressive model VAR(1), which also account With numerical study, discuss how design statistical change with VAR(1) model's parameters. We provide an example illustrate use furnace process.