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For the problem of sequential detection of changes, we adopt the probabilitymaximizing approach in place of the classical minimization of the averagedetection delay, and propose modified versions of the Shiryaev, Lorden andPollak performance measures. For these alternative formulations, we demonstratethat the optimum sequential detection scheme is the simple Shewhart rule.Interestingly, we can also solve problems which under the classical setup havebeen open for many years, as optimum change detection with time varyingobservations or with multiple post-change probability measures. For the lastcase, we also offer the exact solution for Lorden's original setup when theaverage false alarm period is within certain limits.

Multiple optimality properties of the Shewhart test