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 for quality control and improvement and introduce SPC methods into risk control. With systematic viewpoints, the quality and risk control in business organizations is an issue of the control of cross-sectional and serial interdependent processes. Quality and risk are also determined by not only the first and second moments but also the higher moments of the probabilistic process. 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. Cumulative variation schemes were discussed. Various multivariate EWMA and cumulative schemes were studied based on Box quadratic form. 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. In both VMA and M-EWMA, small exponential weight is preferred to obtain sensitive charts for special causes. Vector valued state-space model was also applied for general processes. Finally, Lamda chart for monitoring higher moments of process was discussed. Monitoring higher moments was justified to be useful in Value-at-Risk implementation. Augmented Hall-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 through AHW model. To justify the validity of using AHW model, the relationship between the expected returns and the conditional variance for equity markets was tested, and the validity was confirmed.