Abstract
More and more nonparametric control charts are proposed recently, with a common thought of not assuming the underlying distribution of the process. However, without the information about the distribution, it would be difficult to evaluate and analyze the performance of these control charts. Some authors suggest to use a reference sample to avoid this problem, by using its empirical distribution function. In this thesis, we investigate a nonparametric control chart, namely V-Box control chart proposed by Rafajlowicz, Pawlak and Steland (2004), with a reference sample. This V-Box chart has a intuitive design on whether there are enough points inside a control V-Box over a moving window of time. We derive the general form of average run lengths (ARLs) and compare the V-Box chart with the CUSUM and EWMA control charts. With the ARLs available, we also discuss how to design an optimal V-Box chart. V-Box chart has an efficient performance in detecting outliers (out-of-control points). Furthermore, under a distribution with heavy tails and a short range, e.g. Uniform(0,1), the V-Box chart significantly outperforms the CUSUM and EWMA charts