A bivariate control chart based on copula function

If it would be possible to generate the joint distribution of two attribute quality characteristics, then a bivaraite attribute control chart can be developed based on statistical types I and II errors. Copula function can be a solution to the matter. In this paper we achieve the joint distribution of two correlated zero inflated Poisson (ZIP) distributions using the copula function approach. Then, applying this joint distribution, we develop a bivaraite control chart which can be used for monitoring correlated events. This copula based bivariate ZIP control chart is compared with the simultaneous use of two separate univariate ZIP control charts. Applying the average run length (ARL), as the most common performance measure, it is shown that the developed control chart is much better than the simultaneous use of two separate univariate charts.