Nonparametric Multivariate Control Charts Based On Quantile Data Depth

Control chart was first developed by Shewhart in the year 1931 to monitor and control a manufacturing process. It is an important method in statistic process control. Control charts for manufacturing processes are often univariate and parametric. In real world, however, multivariate quality characteristics rather than univariate are the one people often encounter. Meanwhile, the assumption of normality especially the multivariate normality is not always valid. When the non-normality is at presence, the performances of these parametric control charts are significantly affected. Thus a nonparametric multivariate control chart is very desirable.While some nonparametric multivariate charts have been constructed based on simplicial data depth introduced by Liu in 1990, this data depth is for some symmetric distributions and the amount of computation involved in is huge. This thesis proposes the quantile data depth that can be applied to some asymmetric distributions. From this new data depth some statistics that follow some certain distributions are derived. It is then reduced to construct common Shewhart chart, CUSUM chart and EWMA chart with these statistics. Thus some nonparametric multivariate charts are then given.In this thesis we prove the consistency of quantile data depth, put forward a bivariate asymmetric distribution--skewed uniform-normal distrubution, and compare the performances of quantile-depth-based charts with some other charts when the underlying distributions are bivariate normal, bivariatet of three degrees of freedom and bivariate skewed uniform-normal. Simulation results show that the robustness and efficiency of quantile-depth-based charts are satisfactory.