Monitoring a Poisson process subject to gradual changes in the arrival rates where the arrival rates are unknown. Issue 3 (3rd July 2021)

• Record Type: Journal Article
• Authors: Brown, Marlo
• Is Part Of: Sequential analysis. Volume 40:Issue 3(2021)
• Page Start: 427
• Page End: 440
• Publication Date: 2021-07-03
• Subjects: Bayesian stopping rules -- change-point detection -- dynamic programming -- gradual changes -- Poisson processes -- unknown arrival rates; 62L15 -- 60G40; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2021.1940504
• Languages: English
• ISSNs: 0747-4946

Abstract

Abstract: We look at a Poisson process where the arrival rates change from λ 1 to λ 2 . We will assume that the arrival rates both before and after the change are unknown. We also assume that this change does not happen abruptly but gradually over a period of time η where η is known. We calculate the probability that the change has started and completed. We also look at optimal stopping rules assuming that there is a cost for a false alarm and a cost per time unit to stop early.