The bivariate dispersion control charts for non-normal processes

This article study the performance of the bivariate dispersion control charts, namely the [GRAPHICS] and the [GRAPHICS] charts, for the bivariate normal, bivariate exponential, bivariate t((5)), bivariate Logistic and bivariate Laplace distributions. The asymmetrical probability limits of these charts are proposed for the distributions under study. The estimated factors and quantile points used in the construction of these two charts are provided for the bivariate non-normal distributions. The effect of improper use of constants and quantile points in the construction of the [GRAPHICS] and the [GRAPHICS] charts are studied in terms of the associated false alarm rates. The performances of the proposed limits of the given charts are evaluated in terms of average run length for the various bivariate distributions and compared. The performances of these control charts are also compared with their respective 3 sigma limits.