Control Chart Monitoring of Non-Normally Distributed Time Series Data

Statistical process control (SPC) is for monitoring sequential processes to make sure that they work stably and satisfactorily. To do this, one of the main tools used in SPC are Control Charts. In this master thesis, we focus on CUSUM charts which are control charts involving the calculation of a cumulative sum of the process observations. We use the CUSUM chart to test if the mean evolution of our observations starts to deviate significantly from its control value. In the literature a lot of theoretical results can be found under the assumption that the data are normally distributed with a homogeneous variance over time. The central goal of this master thesis is to say more about the use of CUSUM charts in cases where the data used are non-normal and/or dependent. To do this, extensive simulation studies were performed for non-normally distributed data at first, and for dependent data after that. When independent data are drawn from a symmetric distribution, simulations showed that very slightly suboptimal results are obtained and that the CUSUM chart provides acceptable performances. For independent data generated from an asymmetric distribution, simulations results depend on the mean shift direction and on the skewness coefficient of the distribution. After that, two different methods that adapt the CUSUM chart to dependent data were compared. The first method fits an ARMA model to the autocorrelated observations and then apply the CUSUM chart to the fitted residuals while the second method uses block-bootstrap. It was shown that the sign of the autocorrelation dictates which of the two methods provides the best results.