A multivariate sign chart for monitoring dependence among mixed-type data

Statistical process control (SPC) has been widely utilised for quality improvement and surveillance in industrial engineering. Modern industrial applications have witnessed more and more mixed-type quality characteristics such as those consisting of ordinal categorical and continuous ones. However, traditional charting techniques consider the dependence in either categorical or continuous data and hardly combine the two in quality control. Under the assumption that the ordinal attribute levels of a factor are determined by a latent continuous variable, there exists an order among categorical observations of this factor, which is similar to that among continuous observations. Then mixed-type observations can be transformed into a unified framework of standardized ranks, based on directions of which with respect to their centre parameter, the spatial-sign covariance matrix can be calculated for statistical surveillance of cross-dependence among mixed-type factors. The affine invariant property of consequent charting statistic helps improve the efficiency of detecting dependence shifts in mixed-type data. Simulation results demonstrate the superiority of proposed control chart and an additive manufacturing (3D printing) example shows that it can perform excellently well in practice.