  Statistical quality control methods are noteworthy to produced 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
distributions of the process data. They are supposed to be normal, which is
clear that it is not always valid for all processes. Such control charts made
some false 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. Up to our
knowledge, a copula function guarantees the dependence on the result function.
But it is not enough when there is no other functional 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 find out the joint distribution of a data set, which is from a
manufacturing process that needs to be control while running the production
process. Then, we get an elliptical control limit via the maximum copula
entropy. In the final step, we represent a practical example using the stated
method. Average run lengths are calculated for some means and shifts to show
the ability of the maximum copula entropy. In the end, two real data examples
are presented.
