Steady-state average run length(s)
Methodology, formulas, and numerics
Publication date
2021-09-07
Document type
Forschungsartikel
Author
Organisational unit
Scopus ID
Publisher
Taylor & Francis
Series or journal
Sequential Analysis
ISSN
Periodical volume
40
Periodical issue
3
First page
405
Last page
426
Part of the university bibliography
✅
Language
English
Keyword
Quasistationary distribution
Quasistationary distribution
Abstract
The average run length (ARL), with its various phenotypes, is the prevailing performance measure for evaluating control charts, or change-point detection schemes. Essentially, the ARL counts the number of observations until the corresponding procedure flags a change. To enable a fair comparison between competing designs, one frequently deploys the steady-state ARL. Differing from the older concept of the zero-state ARL (which assumes that the to-be-detected change occurs immediately at startup or never), the former measure postulates this change’s appearance after reaching some steady state. Considering different notions (primarily conditional and cyclical ones) of the measure, we recapitulate its historical development; provide a critical discussion of its often-careless exploitation, including a few misconceptions; and derive some new mathematical characterizations that permit its easy calculation.
Version
Published version
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