Dependence control chart using maximum copula entropy

Abstract

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 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 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.