Multiple optimality properties of the Shewhart test

Abstract

For the problem of sequential detection of changes, we adopt the probability maximizing approach in place of the classical minimization of the average detection delay, and propose modified versions of the Shiryaev, Lorden and Pollak performance measures. For these alternative formulations, we demonstrate that the optimum sequential detection scheme is the simple Shewhart rule. Interestingly, we can also solve problems which under the classical setup have been open for many years, as optimum change detection with time varying observations or with multiple post-change probability measures. For the last case, we also offer the exact solution for Lorden's original setup when the average false alarm period is within certain limits.