A binary control chart to detect small jumps
A binary control chart to detect small jumps
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DOI：
10.1080/02331880802379405
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发表时间：
2009-05
期刊：
影响因子：
1.9
通讯作者：
E. Rafajłowicz;A. Steland
中科院分区：
文献类型：
--
作者：
E. Rafajłowicz;A. Steland
The classic N p-chart gives a signal if the number of successes in a sequence of independent binary variables exceeds a control limit. Motivated by engineering applications in industrial image processing and, to some extent, financial statistics, we study a simple modification of this chart, which uses only the most recent observations. Our aim is to construct a control chart for detecting a shift of an unknown size, allowing for an unknown distribution of the error terms. Simulation studies indicate that the proposed chart is superior in terms of out-of-control average run length, when one is interested in the detection of very small shifts. We provide a (functional) central limit theorem under a change-point model with local alternatives, which explains that unexpected and interesting behaviour. Since real observations are often not independent, the question arises whether these results still hold true for the dependent case. Indeed, our asymptotic results work under the fairly general condition that the observations form a martingale difference array. This enlarges the applicability of our results considerably, first, to a large class of time series models, and, second, to locally dependent image data, as we demonstrate by an example.
