Steady-state average run length(s): Methodology, formulas, and numerics

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 betw...

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Published inSequential analysis Vol. 40; no. 3; pp. 405 - 426
Main Author Knoth, Sven
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 03.07.2021
Taylor & Francis Ltd
Subjects
ARL measures
change point
Control charts
integral equation
Markov chain
quasistationary distribution
Steady state
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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.
AbstractList 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.
Author Knoth, Sven
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Snippet The average run length (ARL), with its various phenotypes, is the prevailing performance measure for evaluating control charts, or change-point detection...
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SubjectTerms ARL measures
change point
Control charts
integral equation
Markov chain
quasistationary distribution
Steady state
Title Steady-state average run length(s): Methodology, formulas, and numerics
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