This article develops Time Between Events (TBE) control charts to monitor processes with multiple dependent production lines. To this end, a Shewhart-type and an EWMA-type TBE chart have been proposed. The copula approach is used to describe the dependence between production lines and the homogeneous Poisson process is considered to model the number of defectives. The performance of the proposed methods is evaluated using the average time to signal metric. The numerical study showed that the EWMA-TBE chart uniformly performs better than the Shewhart-type chart. Eventually, the EWMA-TBE chart is applied to monitor two real-world processes with two and four production lines.