使用最大 copula 熵的相关性控制图
Dependence control chart using maximum copula entropy
AI总结：
针对多变量制造过程中非正态分布及变量相关性建模问题，本文结合 copula 与最大熵构造联合分布和椭圆形控制限，并通过平均运行长度及实际数据验证其优于传统 Fisher 分布方法。
摘要：
统计质量控制方法对于在制造过程中生产标准产品具有重要意义。在这方面，有许多经典方法可用于控制过程。其中许多方法对过程数据的分布具有全局性假设，即假定数据服从正态分布，但显然这并不总是适用于所有过程。此类控制图会作出一些错误决策，从而浪费资金。因此，在处理多变量数据集时，主要问题是如何找到该数据集的多变量分布，同时保留变量之间原有的相关性。据我们所知，copula 函数能够保证结果函数中的相关性。但当缺少关于统计总体的其他基础信息、而我们只有一个数据集时，这还不够。因此，我们应用最大熵概念来处理这种情况。本文首先获取来自制造过程的数据集的联合分布，该过程在生产运行期间需要处于受控状态。随后，我们通过最大 copula 熵得到椭圆形控制限。最后，我们使用该方法给出一个实际示例。为展示最大 copula 熵的能力，针对若干均值和偏移计算了平均运行长度。最后，给出两个实际数据示例，并将本文方法的结果与基于 Fisher 分布的传统方法进行比较。
英文摘要：
Statistical quality control methods are noteworthy to producing standard production in manufacturing processes. In this regard, there are many classical manners to control the process. Many of them have a global assumption around the distributions of the process data. They are supposed to be Normal, but it is clear that it is not always valid for all processes. Such control charts made some wrong decisions that waste funds. So, the main question while working with multivariate data set is how to find the multivariate distribution of the data set, which saves the original dependency between variables. To our knowledge, a copula function guarantees dependence on the result function. It is not enough when there is no other fundamental information about the statistical society, and we have just a data set. Therefore, we apply the maximum entropy concept to deal with this situation. In this paper, first of all, we get the joint distribution of a data set from a manufacturing process that needs to be in-control while running the production process. Then, we get an elliptical control limit via the maximum copula entropy. Finally, we represent a practical example using the method. Average run lengths are calculated for some means and shifts to show the ability of the maximum copula entropy. In the end, two practical data examples are presented, and the results of our method are compared with the traditional way based on Fisher distribution.
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。
