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Choosing parameter values for a geometric CUSUM chart for detecting an upward shift in a proportion

机译:为几何CUSUM图选择参数值以检测比例的向上移动

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This article considers the task of providing practical advice to quality engineers and practitioners on the choice of values for the two parameters of a geometric CUSUM control chart. This CUSUM chart was developed to enable the detection of sudden shifts from an acceptable level for a proportion (p) such as fraction nonconforming. In the first part of the article, tables are presented listing recommended parameter-choices for each of 18 in-control levels for p in the range (0.04 to 0.001) for detection of each of five sizes of upward shift. In the second part of the article, some empirical relationships among the parameter values are identified. These relationships are used with interpolation to design geometric CUSUM schemes for any in-control level (p(a)) of p within the range covered by the tables, and with extrapolation for levels of p(a) as low as 0.0001. Because of the equivalence between a geometric CUSUM and a Bernoulli CUSUM, the tables and the proposed methods of interpolation and extrapolation also provide assistance in the design of a Bernoulli CUSUM chart.
机译:本文考虑的任务是为质量工程师和从业人员在选择几何CUSUM控制图的两个参数的值时提供实用建议。开发此CUSUM图表的目的是能够检测出可接受的比例(p)的突然变化,例如分数不合格。在本文的第一部分中,列出了表格,列出了18种控制水平中p的推荐参数选择,范围在(0.04到0.001)之间,用于检测五个上移大小。在本文的第二部分中,确定了参数值之间的一些经验关系。这些关系与插值一起用于为表所覆盖范围内的p的任何控制内水平(p(a))设计几何CUSUM方案,并为p(a)的水平低至0.0001进行外推。由于几何CUSUM和伯努利CUSUM之间的等价关系,因此表格和拟议的内插和外推方法也有助于设计伯努利CUSUM图表。

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