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We propose a numerical method to evaluate the performance of the emergingGeneralized Shiryaev--Roberts (GSR) change-point detection procedure in a"minimax-ish" multi-cyclic setup where the procedure of choice is appliedrepetitively (cyclically) and the change is assumed to take place at an unknowntime moment in a distant-future stationary regime. Specifically, the proposedmethod is based on the integral-equations approach and uses the collocationtechnique with the basis functions chosen so as to exploit a certainchange-of-measure identity and the GSR detection statistic's unique martingaleproperty. As a result, the method's accuracy and robustness improve, as doesits efficiency since using the change-of-measure ploy the Average Run Length(ARL) to false alarm and the Stationary Average Detection Delay (STADD) arecomputed simultaneously. We show that the method's rate of convergence isquadratic and supply a tight upperbound on its error. We conclude with a casestudy and confirm experimentally that the proposed method's accuracy and rateof convergence are robust with respect to three factors: (a) partition fineness(coarse vs. fine), (b) change magnitude (faint vs. contrast), and (c) the levelof the ARL to false alarm (low vs. high). Since the method is designed notrestricted to a particular data distribution or to a specific value of the GSRdetection statistic's headstart, this work may help gain greater insight intothe characteristics of the GSR procedure and aid a practitioner to design theGSR procedure as needed while fully utilizing its potential.

Efficient Performance Evaluation of the Generalized Shiryaev--Roberts Detection Procedure in a Multi-Cyclic Setup