A class of new nonparametric circular‐grid charts for signal classification

Abstract

Abstract In this paper, some efficient monitoring and post‐signal follow‐up approaches are studied and compared for joint surveillance of location and scale of a process using the notions of circular‐grid (CG) schemes. Precisely, three variants of CG Cucconi schemes are introduced and compared with three variants of percentile modified Lepage (PML) schemes. One of the PML schemes is equivalent to the traditional CG Lepage scheme, while another may be viewed as the Lepage type statistic using Gastwrith score, which is also a powerful tool for process surveillance. Overall, one of the proposed CG Cucconi schemes is most effective in identifying a class of signals, whether it is a location shift or scale shift or a shift in both parameters. It also indicates the direction of the shifts in either or both the parameters. Detecting a downward scale shift is the most challenging task in joint monitoring, and to this end, a new bias‐corrected CG Lepage scheme is introduced. We compare the competing schemes in terms of correct signal classification probabilities. We illustrate the use of the proposed schemes in monitoring the trip‐duration data in cab services. Some concluding remarks and future research problems are offered.

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