Most control charts have been developed based on the actual distribution of the quality characteristic of interest. However, in many applications, there is a lack of knowledge about the process distribution. Therefore, in recent years, nonparametric (or distribution‐free) control charts have been introduced for monitoring the process location or scale parameter. In this article, a nonparametric double generally weighted moving average control chart based on the signed‐rank statistic (referred as DGWMA‐SR chart) is proposed for monitoring the location parameter. We provide the exact approach to compute the run‐length distribution, and through an extensive simulation study, we compare the performance of the proposed chart with existing nonparametric charts, such as the exponentially weighted moving average signed‐rank (EWMA‐SR), the generally weighted moving average signed‐rank (GWMA‐SR), the double exponentially weighted moving average signed‐rank (DEWMA‐SR), and the double generally weighted moving average sign (DGWMA‐SN) charts, as well as the parametric DGWMA‐ $\overline{X}$ chart for subgroup averages. The simulation results show that the DGWMA‐SR chart (with suitable parameters) is more sensitive than the other competing charts for small shifts in the location parameter and performs as well as the other nonparametric charts for larger shifts. Finally, two examples are given to illustrate the application of the proposed chart.

中文翻译：

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用于监视过程位置的非参数双一般加权移动平均带符号秩控制图

大多数控制图是根据感兴趣的质量特征的实际分布而开发的。但是，在许多应用程序中，缺乏有关过程分配的知识。因此，近年来，引入了非参数（或无分布）控制图来监视过程位置或比例参数。在本文中，提出了一种基于带符号秩统计的非参数双重一般加权移动平均控制图（称为DGWMA-SR图）来监视位置参数。我们提供了计算游程长度分布的精确方法，并且通过广泛的仿真研究，我们将建议的图表的性能与现有的非参数图表进行了比较，例如指数加权移动平均正负号（EWMA-SR），$\overline{X}$分组平均值的图表。仿真结果表明，对于位置参数的微小变化，DGWMA-SR图表（具有合适的参数）比其他竞争图表更敏感，并且对于较大的偏移，其性能与其他非参数图表一样好。最后，给出两个例子来说明所提出的图表的应用。