Design of change detection algorithms based on the Generalized Likelihood Ratio Test

A design procedure for detecting additive changes in a state-space model is proposed. Since the mean of the observations after the change is unknown, detection algorithms based on the generalized likelihood ratio test, GLR, and on window-limited type GLR, are considered. As Lai (1995) pointed out, it is very difficult to find a satisfactory choice of both window size and threshold for these change detection algorithms. The basic idea of this article is to estimate, through the stochastic approximation of Robbins and Monro, the threshold value which satisfies a constraint on the mean between false alarms, for a specified window size. A convenient stopping rule. based on the first passage time of an F-statistic below a fixed boundary, is used to terminate the iterative approximation, Then, the window size which produces the most desirable out-of-control ARL, for a fixed value of the in-control ARL, can be selected. These change detection algorithms are applied to detect biases on the measurements of ozone, recorded from one monitoring site of Bologna (Italy). Comparisons of the ARL profiles reveal that the full-GLR scheme provides much more protection than the window-limited GLR schemes against small shifts in the process, but the modified window-limited GLR provides more protection against large shifts.