New statistical control limits using maximum copula entropy

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.