A nonparametric on-line quality control procedure for vectorial observations

Abstract

We consider an on-line nonparametric quality control procedure for multivariate observations. The goal of the procedure is to rapidly detect an out-of-control situation, that is, to detect a change in sampling distribution after a change point. Each successive observation creates a Voronoi cell indexed by the observation number. Suppose observation n+1 falls into the Voronoi cell with index i, where i is from 1 to n. Then observation n+1 has associated rank i. In the on-target situation these ranks are uniformly distributed but in the off-target situation these ranks tend to be large corresponding to the fact that the later off-target observations tend to clump together because later observations fall according to the off-target distribution. We use these ranks in a Cusum procedure. We found that we can approximately predict the on-target average run length (ARL) of our procedure and get reasonable off-target run lengths for any kind of structural break like a change of mean or a change of dispersion.