A Comparison of Shiryaev–Roberts and Cumulative Sum Procedures for Bivariate ZIP Process Monitoring

Abstract

The Zero-inflated Poisson (ZIP) model has been widely adopted in quality control for near-zero-defect processes with sporadic nonconformities, while prior research predominantly focused on univariate ZIP processes for single defect types, modern high-precision manufacturing environments often involve two or more correlated defect categories. This paper proposes a Shiryaev–Roberts (SR) control chart for detecting parameter shifts in bivariate ZIP processes and compares its performance with the existing cumulative sum (CUSUM) chart under both zero-state and steady-state scenarios. Through Monte Carlo simulations, we establish the upper control limits (h) for both schemes while maintaining an identical in-control average run length (ARL) to ensure fair comparisons. Numerical simulations demonstrate that the SR chart exhibits superior out-of-control ARL performance compared to the CUSUM chart under steady-state conditions for detecting small to moderate shifts. The proposed methodology is further validated through a case study in LED packaging, highlighting its practicality in advanced manufacturing quality assurance.