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制造过程中生产标准化产品具有重要意义。在此方面，存在多种经典的过程控制方法，其中许多方法对过程数据的分布做出了全局性假设—通常假定其服从正态分布，但显然这一假设并非对所有过程都始终成立。此类控制图可能做出错误决策，造成资金浪费。因此，处理多元数据集时的核心问题在于：如何找到既能保留变量间原始依赖关系，又能适用于该数据集的多元分布。据我们所知，Copula函数能够确保结果函数中的依赖关系，但在缺乏统计总体其他基本特征信息且仅掌握数据集的情况下仍显不足。为此，我们引入最大熵概念应对这一困境。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，最后通过实际案例展示该方法的应用。通过计算均值漂移情况下的平均运行长度来验证最大Copula熵的效能，并最终通过两个实际数据案例，将本方法结果与基于Fisher分布的传统方法进行对比分析。