  In the problem of quickest change detection (QCD), a change occurs at some
unknown time in the distribution of a sequence of independent observations.
This work studies a QCD problem where the change is either a bad change, which
we aim to detect, or a confusing change, which is not of our interest. Our
objective is to detect a bad change as quickly as possible while avoiding
raising a false alarm for pre-change or a confusing change. We identify a
specific set of pre-change, bad change, and confusing change distributions that
pose challenges beyond the capabilities of standard Cumulative Sum (CuSum)
procedures. Proposing novel CuSum-based detection procedures, S-CuSum and
J-CuSum, leveraging two CuSum statistics, we offer solutions applicable across
all kinds of pre-change, bad change, and confusing change distributions. For
both S-CuSum and J-CuSum, we provide analytical performance guarantees and
validate them by numerical results. Furthermore, both procedures are
computationally efficient as they only require simple recursive updates.
