An ARL-unbiased modified chart for monitoring autoregressive counts with geometric marginal distributions

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
Manuel Cabral Morais, P. Wittenberg, S. Knoth
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引用次数: 0

Abstract

Abstract Geometrically distributed counts arise in the industry. Ideally, they should be monitored using a control chart whose average run length (ARL) function achieves a maximum when the process is in control; that is, the chart is ARL-unbiased. Moreover, its in-control ARL should coincide with a reasonably large and prespecified value. Because dependence among successive geometric counts is occasionally a more sensible assumption than independence, we assess the impact of using an ARL-unbiased chart specifically designed for monitoring independent geometric counts when, in fact, these counts are autocorrelated. We derive an ARL-unbiased modified chart for monitoring geometric first-order integer-valued autoregressive or GINAR(1) counts. We provide compelling illustrations of this chart and discuss its use to monitor other autoregressive counts with a geometric marginal distribution.
一种用于监测具有几何边缘分布的自回归计数的arl无偏修正图
摘要行业中出现了几何分布计数。理想情况下,应使用控制图对其进行监控,当过程处于控制状态时,控制图的平均运行长度(ARL)函数达到最大值;也就是说,图表是ARL无偏的。此外,它的控制ARL应该与一个相当大的预先指定的值一致。由于连续几何计数之间的相关性有时比独立性更明智,因此我们评估了使用专门为监测独立几何计数而设计的ARL无偏图的影响,而事实上,这些计数是自相关的。我们导出了一个ARL无偏修正图,用于监测几何一阶整数值自回归或GINAR(1)计数。我们提供了这张图表的令人信服的插图,并讨论了它在监测其他具有几何边际分布的自回归计数中的用途。
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来源期刊
CiteScore
1.40
自引率
12.50%
发文量
20
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.
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