  We develop a mixture procedure for multi-sensor systems to monitor data
streams for a change-point that causes a gradual degradation to a subset of the
streams. Observations are assumed to be initially normal random variables with
known constant means and variances. After the change-point, observations in the
subset will have increasing or decreasing means. The subset and the
rate-of-changes are unknown. Our procedure uses a mixture statistics, which
assumes that each sensor is affected by the change-point with probability
$p_0$. Analytic expressions are obtained for the average run length (ARL) and
the expected detection delay (EDD) of the mixture procedure, which are
demonstrated to be quite accurate numerically. We establish the asymptotic
optimality of the mixture procedure. Numerical examples demonstrate the good
performance of the proposed procedure. We also discuss an adaptive mixture
procedure using empirical Bayes. This paper extends our earlier work on
detecting an abrupt change-point that causes a mean-shift, by tackling the
challenges posed by the non-stationarity of the slope-change problem.
