Eighty Years of Control Charts: Some New Developments
J.M. Juran described in his memoirs the beginning of statistical process control (SPC). We can find the remarkable sentence that "Shewhart invented the control chart on May 16, 1924". More than eighty years passed and in the meantime control charts have become one of the main important tools of SPC. In this talk some important new developments will be discussed. Starting with Alwan and Roberts (1989) the extension of control charts to time series has been the subject of many papers. In order to monitor the parameters of a time series it is necessary to determine the control design by taking into account the probability structure of the underlying stochastic process. Explicit formulas of the average run lengths (ARL) are unknown for time series. Inequalities for the ARL of a Shewhart type chart for time series were proposed by Schmid (1995). Moreover, a time series has further characteristic quantities. Control charts for the simultaneous control of the mean and the autocovariances of a stationary Gaussian process were introduced by Rosolowski and Schmid (2003). A very challenging topic is the control of the parameters of a high-dimensional process. Up to now there are only a few papers dealing with the surveillance of the parameters of a multivariate time series (e.g., Theodossiu (1993), Kramer and Schmid (1997)). Several new control charts for the mean are proposed in Bodnar and Schmid (2005). There are many important applications of SPC in finance. This development started with the papers of Yashchin, Stein and Philips (1997) and Lam and Yam (1997). An interesting problem is to make statements about the optimal time points for the adjustment of a portfolio. In this situation we have a high-dimensional series and we have to monitor the optimal portfolio weights. Recently several control charts for this problem were introduced by Golosnoy and Schmid (2005).
