  In the quickest change detection problem in which both nuisance and critical
changes may occur, the objective is to detect the critical change as quickly as
possible without raising an alarm when either there is no change or a nuisance
change has occurred. A window-limited sequential change detection procedure
based on the generalized likelihood ratio test statistic is proposed. A
recursive update scheme for the proposed test statistic is developed and is
shown to be asymptotically optimal under mild technical conditions. In the
scenario where the post-change distribution belongs to a parametrized family, a
generalized stopping time and a lower bound on its average run length are
derived. The proposed stopping rule is compared with the FMA stopping time and
the naive 2-stage procedure that detects the nuisance or critical change using
separate CuSum stopping procedures for the nuisance and critical changes.
Simulations demonstrate that the proposed rule outperforms the FMA stopping
time and the 2-stage procedure, and experiments on a real dataset on bearing
failure verify the performance of the proposed stopping time.
