Monitoring bivariate processes with synthetic control charts based on sample ranges

Abstract

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.