1963/01/01 by Albert N. Shiryaev, A. N. Shiryaev · 6 citations
Decision Sciences · Engineering · Mathematics · #Advanced Statistical Process Monitoring #Fault Detection and Control Systems #Statistical Methods and Inference
paper · doi:10.1137/1108002
crossref issued 1963/01/01 · crossref published 1963/01/01 · crossref published-print 1963/01/01 · openalex publication_date 1963/01/01 · crossref created 2005/03/07 · crossref deposited 2017/01/29 · openalex created_date 2025/10/10 · crossref indexed 2026/07/31 · openalex updated_date 2026/08/01
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 \boldsymbol 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 \bf N — mathematical expectation of false alarm numbers occurring up to the moment the disorder appears — the observation method minimizing \boldsymbol τ = \boldsymbol τ (ω) or \boldsymbol τ = \boldsymbol τ (\boldsymbol 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 \boldsymbol τ = \boldsymbol τ (\bf T) for a set \bf T — mathematical expectation of the time between two false alarms. The dependence \boldsymbol τ = \boldsymbol τ (\bf T) is given by formula (36).