基于Mann-Whitney统计量的非参数控制图
A nonparametric control chart based on the Mann-Whitney statistic
摘要：
在统计过程控制问题中，当对基础过程分布的了解有限或缺乏时，非参数或无分布图可能很有用。在本文中，第二阶段的休哈特型图表被认为是位置，从第一阶段的分析和著名的曼-惠特尼统计的参考数据的基础上。使用Lugannani-Rice鞍点法、Edgeworth法和其他近似法以及蒙特卡罗估计法计算控制限。推导考虑了估计和使用参考样本的依赖性。给出了一个数值例子。所提出的图表的控制性能被证明是远远优于经典的休哈特$\bar{X}$图。进一步比较失控条件游程分布和无条件失控ARL分布的结果表明，对于正态分布，该图与Shewhart $\bar{X}$图几乎一样好，但对于Laplace等重尾分布或Gamma等偏态分布，该图更有效。可在网站上查阅互动软件，以便全面实施该图表。
英文摘要：
Nonparametric or distribution-free charts can be useful in statistical process control problems when there is limited or lack of knowledge about the underlying process distribution. In this paper, a phase II Shewhart-type chart is considered for location, based on reference data from phase I analysis and the well-known Mann-Whitney statistic. Control limits are computed using Lugannani-Rice-saddlepoint, Edgeworth, and other approximations along with Monte Carlo estimation. The derivations take account of estimation and the dependence from the use of a reference sample. An illustrative numerical example is presented. The in-control performance of the proposed chart is shown to be much superior to the classical Shewhart $\bar{X}$ chart. Further comparisons on the basis of some percentiles of the out-of-control conditional run length distribution and the unconditional out-of-control ARL show that the proposed chart is almost as good as the Shewhart $\bar{X}$ chart for the normal distribution, but is more powerful for a heavy-tailed distribution such as the Laplace, or for a skewed distribution such as the Gamma. Interactive software, enabling a complete implementation of the chart, is made available on a website.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
