Multi-Sensor Slope Change Detection
This work addresses incremental improvements in statistical process control for monitoring systems with multiple sensors, such as in industrial or environmental applications.
The paper tackles the problem of detecting gradual slope changes in multi-sensor data streams, where a subset of sensors experiences unknown increasing or decreasing means after a change-point, and it develops a mixture procedure that achieves asymptotic optimality with accurate analytic expressions for average run length and expected detection delay.
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.