Wolfgang Schmid: Monitoring time dependent processes

In many applications an analyst is interested to detect a change in the course of a time dependent process. Change points provide an important information about the underlying process as they show that something important has happened. Of course it is desirable to detect such changes as soon as possible after its occurrence. Such questions arise in many fields of applications like, e.g., engineering, public health, finance, environmental sciences (see, e.g., Montgomery (2009), Lawson and Kleinman (2005), Frisen (2008)).

In this talk control charts for monitoring time series are considered. In that case it turns out to be very difficult to give an explicit formula for the performance criteria of a chart like, e.g., the average run length or the average delay. In most cases these quantities are estimated within simulation studies. In order to give a mathematical characterization of these schemes stochastic inequalities can be used.
These results provide an important insight into the behavior of these schemes since statements about the probability of a false signal can be obtained (e.g., Schmid and Schöne (1997), Schöne at al. (1999), Okhrin and Schmid (2003, 2015)). Here control charts for various types of time series are discussed and stochastic inequalities for EWMA charts are presented.

Keywords: control charts; statistical process control; change-point detection; time series; stochastic inequalities; EWMA charts