On Optimum Methods in Quickest Detection Problems

In this paper optimum methods are developed for observing a process (1), in which the moment when a “disorder” θ appears is not known. The basic quantity characterizing the quality of this observation method is the mean time delay τ for detection of a disorder. After making assumption (4) it is shown that for a given false alarm probability ω or for a given N — mathematical expectation of false alarm numbers occurring up to the moment the disorder appears — the observation method minimizing τ = τ (ω) or τ = τ ( N) is based on an observation of a posteriors probability (23). In § 3 a case is considered, wherein, the disorder appears on the background of steadystate conditions arising when the disorder is absent. A method is found for minimizing τ = τ ( T) for a set T — mathematical expectation of the time between two false alarms. The dependence τ = τ ( T) is given by formula (36).