  Control charts for zero-inflated processes have attracted the interest of the
researchers in the recent years. In this work we investigate the performance of
Shewhart-type charts for zero-inflated Poisson and zero-inflated Binomial
processes, in the case of estimated parameters. This is a case that usually
occurs in practice, especially prior to starting the process monitoring. Using
Monte Carlo simulation we evaluate charts' performance under an unconditional
perspective and provide guidelines for their use in practice. We examine both
the in-control and the out-of-control performance.
