  We propose a numerical method to evaluate the performance of the emerging
Generalized Shiryaev--Roberts (GSR) change-point detection procedure in a
"minimax-ish" multi-cyclic setup where the procedure of choice is applied
repetitively (cyclically) and the change is assumed to take place at an unknown
time moment in a distant-future stationary regime. Specifically, the proposed
method is based on the integral-equations approach and uses the collocation
technique with the basis functions chosen so as to exploit a certain
change-of-measure identity and the GSR detection statistic's unique martingale
property. As a result, the method's accuracy and robustness improve, as does
its efficiency since using the change-of-measure ploy the Average Run Length
(ARL) to false alarm and the Stationary Average Detection Delay (STADD) are
computed simultaneously. We show that the method's rate of convergence is
quadratic and supply a tight upperbound on its error. We conclude with a case
study and confirm experimentally that the proposed method's accuracy and rate
of convergence are robust with respect to three factors: (a) partition fineness
(coarse vs. fine), (b) change magnitude (faint vs. contrast), and (c) the level
of the ARL to false alarm (low vs. high). Since the method is designed not
restricted to a particular data distribution or to a specific value of the GSR
detection statistic's headstart, this work may help gain greater insight into
the characteristics of the GSR procedure and aid a practitioner to design the
GSR procedure as needed while fully utilizing its potential.
