A Bayesian EWMA method to detect jumps at the start-up phase of a process

The start-up phase data of a process are the spine of traditional SPC charting and testing methods and are usually assumed to be i.i.d. observations from the in-control distribution. In this work a new method is proposed to model normally distributed start-up phase data where we allow for serial dependence and randomly occurring unidirectional level shifts of the underlying parameter of interest. The theoretic development is based on a Bayesian sequentially updated EWMA model with normal mixture errors. The new approach makes use of available prior information and provides a framework for drawing decisions and making prediction on line, even with a single observation.