Minimax robust quickest change detection with exponential delay penalties

Quickly detecting changes in the statistical behavior of measurements is important in many applications of control engineering involving fault detection and process monitoring. In this letter, we pose and solve minimax robust Lorden and Bayesian quickest change detection problems for situations where the cost of detection delays compounds exponentially. We show that the detection rules that solve our robust quickest change detection problems are also the rules that solve the standard (non-robust) problems specified by least favorable distributions from uncertainty classes of possible distributions that satisfy a stochastic boundedness condition. In contrast to previous robust quickest change detection results with nonlinear detection delay penalties, our results with exponential delay penalties are exact (i.e., they hold for any false alarm constraint and not only in the asymptotic regime of few false alarms). We illustrate our results through simulations.