  We study a Wiener disorder problem of detecting the minimum of $N$
change-points in $N$ observation channels coupled by correlated noises. It is
assumed that the observations in each dimension can have different strengths
and that the change-points may differ from channel to channel. The objective is
the quickest detection of the minimum of the $N$ change-points. We adopt a
min-max approach and consider an extended Lorden's criterion, which is
minimized subject to a constraint on the mean time to the first false alarm. It
is seen that, under partial information of the post-change drifts and a general
nonsingular stochastic correlation structure in the noises, the minimum of $N$
cumulative sums (CUSUM) stopping rules is asymptotically optimal as the mean
time to the first false alarm increases without bound. We further discuss
applications of this result with emphasis on its implications to the efficiency
of the decentralized versus the centralized systems of observations which arise
in engineering.
