Dependence control chart using maximum copula entropy

TL;DR

This paper introduces a novel dependence control chart method using maximum copula entropy to accurately model multivariate dependencies in manufacturing data, especially when distributional assumptions like normality are invalid.

Contribution

It proposes a new approach combining maximum entropy and copula functions to derive joint distributions and control limits without assuming specific data distributions.

Findings

Effective in modeling dependencies in non-normal data

Improves control chart accuracy over traditional methods

Demonstrated with practical manufacturing data examples

Abstract

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.