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 T 2 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.
The RMAX chart was proposed to control the covariance matrix of two quality characteristics. The monitoring statistic of the RMAX chart is the maximum of two standardized sample ranges from bivariate observations of two quality characteristics. In this article, we investigate the performance of two synthetic RMAX charts. The first synthetic chart signals when a second point, not far from the first one, falls beyond the warning limit. The second synthetic chart additionally signals when a sample point falls beyond the control limit. The performance of the synthetic RMAX charts are compared with the performance of the standard RMAX chart and the generalized variance S chart. The proposed charts are the best option to detect moderate or even small changes in the covariance matrix. To detect large changes in the covariance matrix, additional run rules are not necessary.
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