Monitoring bivariate zero-inflated Poisson processes: an alternative to copula-based bivariate attribute control chart

Occurrences of two (or more) types of defects are not uncommon in high quality (or zero-inflated) processes. Bivariate (or multivariate) attribute control charts are required to be developed for monitoring such processes. Fatahi et al. (2012) introduced the idea of applying copula function to derive joint distribution of two correlated zero-inflated Poisson distributions, which can be used to develop bivariate attribute control chart (BACC) for monitoring bivariate zero-inflated Poisson (BZIP) processes. However, the copula-based model often fails to represent bivariate zero-inflated data, which we come across in real-life situations. Li et al. (1999) model for BZIP distribution is quite flexible. Thus, it can overcome the limitations of Fatahi et al. (2012) model. In this paper, BACC is developed based on Li et al. (1999) model. The performances of the proposed BACC, in terms of in-control and out-of-control average run lengths, are evaluated extensively using simulations. The results show that the proposed BACC are well capable of detecting shifts in the parameters of a BZIP process. Further, two case studies on BZIP process data obtained by past researchers reveal that the BACC developed based on Li et al. (1999) model is more effective than the BACC developed based on copula-based model.