Phase I Distribution-Free Analysis of Univariate Data

Abstract

In Phase I analysis, data are used retrospectively for checking process stability and defining the in-control state. Most Phase I control charts are based on the assumption of normally distributed observations. However, distribution-free methods appear to be ideal candidates for Phase I applications. Indeed, because little information is available, it is difficult to validate a distributional assumption in Phase I or at least at its beginning stage. In addition, as has been noted in the literature, this assumption cannot be checked before process stability is established. In this article, we propose a new distribution-free Phase I procedure for univariate observations. The suggested method, based on recursive segmentation and permutation, detects single or multiple mean and/or scale shifts. A simulation study shows that our method compares favorably with parametric control charts when the process is normally distributed and performs better than other nonparametric control charts when the process distribution is skewed or heavy tailed. An R package can be found in the supplemental materials.