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.

翻译：统计质量控制方法对于确保制造过程的生产标准化至关重要。为此，存在多种经典过程控制方法，其中许多方法对过程数据的分布做出全局假设，即假定其服从正态分布。但显然，这一假设并非对所有过程均成立。此类控制图可能做出错误决策，造成资源浪费。因此，处理多变量数据集的核心问题在于：如何找到既能保存变量间原始依赖关系的数据集多元分布？据我们所知，Copula函数可保证结果函数的依赖结构，但当缺乏关于统计总体的其他基础信息且仅拥有数据集时，这仍不足够。为此，我们引入最大熵概念应对这一情境。本文首先获取制造过程中需保持受控状态的数据集的联合分布；继而通过最大Copula熵构建椭圆控制限；最后展示该方法的实际应用案例。通过计算不同均值偏移下的平均运行长度来评估最大Copula熵的性能。最终给出两个实际数据案例，并将本方法结果与传统基于Fisher分布的方法进行对比分析。