Paper 1 is aimed at practicians to help them test the assumption that the observations in a sample are independent and identically distributed. An assumption that is essential when using classical Shewhart charts. The test can easily be performed in the control chart setup using the samples gathered here and standard statistical software. In Paper 2 a new method for process monitoring is introduced. The method uses a statistical model of the quality characteristic and a sliding window of observations to estimate the probability that the next item will not respect the specications. If the estimated probability exceeds a pre-determined threshold the process will be stopped. The method is exible, allowing a complexity in modeling that remains invisible to the end user. Furthermore, the method allows to build diagnostic plots based on the parameters estimates that can provide valuable insight into the process. The method is explored numerically and a case study is provided. In Paper 3 the method is explored in a bivariate setting. Paper 4 is a case study on a problem regarding missing values in an industrial process. The impact of the missing values on the quality measures of the process is assessed. Furthermore, guidelines along with software is provided to handle similar problems.