Multi-sensor gradual change detection

We develop a mixture procedure to monitor parallel streams of data for a change-point that causes gradual change of a subset of data streams. We model the gradual change as a change in the trends of the affected data streams. Observations are assumed initially to be independent standard normal random variables with zero mean. After a change-point the observations in a subset of the streams of data have mean values that increase or decrease with time. The rate of change for the affected sensors may be different for the affected sensors. The subset and the post-change means are unknown but we assume the number of affected sensors is small. Our procedure uses a mixture statistics which hypothesizes an assumed fraction p₀ of affected data streams. An analytic expression is obtained for the average run length (ARL) when there is no change and is shown by simulations to be very accurate. Similarly, an approximation for the expected detection delay (EDD) after a change-point is also obtained. Numerical examples based on real-data demonstrate the good performance of the proposed procedure on real data.