The conventional CUSUM chart is usually designed for a known shift size against which the protection is required. In practice, the shift sizes are rarely known, but they may vary within a given interval. Given a range of the shift size, the weighted adaptive CUSUM (WAC) chart provides better protection than the CUSUM chart. In this paper, we propose two types of the WAC chart for monitoring different kinds of shifts in the variance of a normal process, named WAC-I and WAC-II charts, based on the CUSUM and Crosier CUSUM charts, respectively. Monte Carlo simulations are used to compute the run length characteristics of the proposed one-sided and two-sided charts. The proposed charts are compared with existing adaptive and non-adaptive charts in terms of the average run length. It is found that the proposed charts perform uniformly and substantially better than the existing charts. A real dataset is considered to support the theory.

中文翻译：

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新的加权自适应 CUSUM 离散图

传统的 CUSUM 图通常设计用于需要保护的已知移位大小。在实践中，班次大小鲜为人知，但它们可能在给定的时间间隔内变化。给定一个移位大小范围，加权自适应 CUSUM (WAC) 图提供比 CUSUM 图更好的保护。在本文中，我们分别基于 CUSUM 和 Crosier CUSUM 图提出了两种类型的 WAC 图，用于监测正常过程方差的不同类型的变化，分别称为 WAC-I 和 WAC-II 图。蒙特卡罗模拟用于计算所提出的单面和双面图表的运行长度特性。建议的图表在平均运行长度方面与现有的自适应和非自适应图表进行比较。结果发现，所提出的图表比现有图表表现得一致且显着好于现有图表。一个真实的数据集被认为是支持该理论的。