Synthetic charts to control bivariate processes with autocorrelated data

•We consider the monitoring of bivariate processes with autocorrelated data.•The use of two side-sensitive X‾ charts compete well with the synthetic T2 chart.•The Markov chain approach was used to obtain the steady-state properties.•The synthetic rules always improve the performance of the control charts.

In this study, we propose the use of simultaneous X‾ charts to control bivariate processes with autocorrelated data. The first set of X‾ charts is side-sensitive with regard to the same variable (SV X‾ charts) and the second one is side-sensitive with regard to both variables (BV X‾ charts). The Markov chain approach was used to obtain the steady-state properties of the X‾ charts. In comparison with the standard synthetic T2 chart, the SV and the BV charts signal faster in a wide variety of disturbances, except when the variables are high correlated. The BV charts are simpler and signal faster than the SV charts.