Bivariate semiparametric control charts for simultaneous monitoring of process mean and variance

In the present article, two semiparametric bivariate control charts are presented, which use order statistics and are effective in jointly monitoring of possible shifts in the process mean and/or variance. To achieve that both the median location (or more generally the location of a specific order statistic) and the number of specific observations of the test sample lying between the control limits are taken into account. The false alarm rate and the in-control average run length are not affected by the marginal distributions, while the effect of the dependence structure on them is negligible; therefore, they can be used as fully nonparametric charts. A performance-comparison study is carried out, and an illustrative example is provided using a real-world data set.