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

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Sequential Analysis-Design Methods and Applications Pub Date : 2021-07-03 DOI:10.1080/07474946.2021.1940501

S. Knoth

引用次数: 19

Abstract

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.

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稳态平均运行长度:方法、公式和数值

平均运行长度(ARL)具有各种表型，是评估控制图或变化点检测方案的主要性能指标。实际上，在相应的过程标记更改之前，ARL会计算观察值的数量。为了在竞争设计之间进行公平的比较，人们经常部署稳态ARL。与旧的零状态ARL概念(假设待检测的变化在启动时立即发生或从不发生)不同，前一种测量假设这种变化在达到某种稳定状态后出现。考虑到该措施的不同概念(主要是有条件的和周期性的)，我们概述了其历史发展;提供对其经常粗心的开发的批判性讨论，包括一些误解;并推导出一些新的数学表征，使其易于计算。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Sequential Analysis-Design Methods and Applications STATISTICS & PROBABILITY-

CiteScore

1.40

自引率

12.50%

发文量

期刊介绍： The purpose of Sequential Analysis is to contribute to theoretical and applied aspects of sequential methodologies in all areas of statistical science. Published papers highlight the development of new and important sequential approaches. Interdisciplinary articles that emphasize the methodology of practical value to applied researchers and statistical consultants are highly encouraged. Papers that cover contemporary areas of applications including animal abundance, bioequivalence, communication science, computer simulations, data mining, directional data, disease mapping, environmental sampling, genome, imaging, microarrays, networking, parallel processing, pest management, sonar detection, spatial statistics, tracking, and engineering are deemed especially important. Of particular value are expository review articles that critically synthesize broad-based statistical issues. Papers on case-studies are also considered. All papers are refereed.