During the design phase of a control chart, the determination of its exact run length properties plays a vital role for its optimal operation. Markov chain or integral equation methods have been extensively applied in the design phase of conventional control charts. However, for distribution‐free schemes, due to the discrete nature of the statistics being used (such as the sign or the Wilcoxon signed rank statistics, for instance), it is impossible to accurately compute their run length properties. In this work, a modified distribution‐free phase II exponentially weighted moving average (EWMA)‐type chart based on the Wilcoxon signed rank statistic is considered and its exact run length properties are discussed. A continuous transformation of the Wilcoxon signed rank statistic, combined with the classical Markov chain method, is used for the determination of the average run length in the in‐ and out‐of control cases. Moreover, its exact performance is derived without any knowledge of the distribution of sample observations. Finally, an illustrative example is provided showing the practical implementation of our proposed chart.

中文翻译：

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EWMA签名的等级控制图具有可靠的游程性能

在控制图的设计阶段，确定其精确的行程长度特性对于其最佳操作起着至关重要的作用。马尔可夫链或积分方程方法已广泛应用于常规控制图的设计阶段。但是，对于无分配方案，由于使用的统计信息具有离散性（例如，符号或Wilcoxon签名秩统计信息），因此无法准确计算其游程长度属性。在这项工作中，经修饰的自由分布相II指数加权移动平均（EWMA）型图表基于Wilcoxon符号秩统计被认为是和它的确切游程长度属性进行了讨论。Wilcoxon符号秩统计量的连续变换与经典的马尔可夫链方法相结合，用于确定控制内和控制外情况下的平均游程长度。此外，它的精确性能是在不了解样本观测值分布的情况下得出的。最后，提供了一个示例性示例，显示了我们建议的图表的实际实现。