Title: A novel approach to the change-point methodology in nonparametric control charts
Authors: Claudio Giovanni Borroni - University of Milano - Bicocca (Italy) [presenting]
Manuela Cazzaro - University of Milano-Bicocca (Italy)
Paola Maddalena Chiodini - University of Milano-Bicocca (Italy)
Abstract: When a stream of single measurements is available, the change-point paradigm is often applied to monitor for possible shifts in location, scale, or other characteristics of the underlying distribution. Any test statistics useful for the two-sample problem can be adapted to this task, by computing it on every split of the stream into two parts and by looking at its maximum value on the set of all possible splits. Especially when no prior assumptions on the distribution are made, that is when a nonparametric chart is built; however, some problems arise due to the sample sizes, which are occasionally imposed on the two-sample test statistic. More specifically, some splits necessarily produce two largely unbalanced samples, of which one has a size too limited to generate a sensible comparison. We propose to revise the change-point paradigm to avoid such inconveniences and, specifically, to work just with tests based on two balanced samples. Our methodology can be applied both to a phase-I control chart, both to a self-starting chart, which we believe to be its more useful application. We show that the determination of critical values to guarantee the desired ARL in the in-control state is made easier, and we explore conditions under which the chart can lead to competitive values of the ARL in the out-of-control state.