Sequential change detection revisited

In sequential change detection, existing performance measures differ significantly in the way they treat the time of change. By modeling this quantity as a random time, we introduce a general framework capable of capturing and better understanding most well-known criteria and also propose new ones. For a specific new criterion that constitutes an extension to Lorden's performance measure, we offer the optimum structure for detecting a change in the constant drift of a Brownian motion and a formula for the corresponding optimum performance.Comment: Published in at http://dx.doi.org/10.1214/009053607000000938 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Multiple optimality properties of the Shewhart test

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.Comment: 31 page