Spc for Quality and Risk: Monitoring Processes with Cross-sectional and Serial Interdependence, and Higher Moments

This study attempts to improve the statistical process control (SPC) methods and introduce SPC methods into risk control. Several contributions were made in this study. A correct bias correction coefficient with unequal sample sizes for Shewhart chart was given. The concordance of Shewhart mean and variability pair charts was suggested. Box-Ramerez Cuscore chart was extended to monitor coefficients of ARMA residuals. Vector autoregressive (VAR) chart was studied in details. Vector moving average (VMA) chart with EWMA on processes was proposed. Numerical analysis with integral equation for average run length of multivariate EWMA (M-EWMA) chart was computed. Vector valued state-space model was also applied for general processes. Finally, Lamda chart for monitoring higher moments was discussed. Monitoring higher moments was justified to be useful in Value-at-Risk implementation. Augmented Hull-White (AHW) model was suggested to capture the higher moments of risk factors. The goodness-of-fit chart was proposed as an SPC scheme to monitor the higher moments. Based on AHW model, the relationship between the stock market return and its conditional variation was tested.