Statistical process control (SPC) and monitoring techniques are useful in practice in a variety of applications. Recent advancements in the literature have shown the need for distinguishing between Phase I (retrospective) and Phase II (prospective) process monitoring and the importance of taking proper account of the effects of parameter estimation. This work considers the retrospective and prospective process monitoring for the balanced random effects (variance components) model with Phases I and II Shewhart charts and Phase II EWMA chart with estimated parameters. In Phase I, Shewhart-type charts are recommended in this phase because of their broader shift detection ability. The proposed methodology takes proper account of the effects of parameter estimation and uses the false alarm probability (FAP) metric to design the chart. The proposed Phase I chart is shown to be easily adaptable to more general models, with more variance components and nested factors, and can accommodate various estimators of variance. Thus, it enables a broader Phase I process monitoring strategy, under normality, which can be applied within the ANOVA framework applicable for many DOE models. In Phase II, multiple control charts are dominating including the Shewhart-type charts and its generalization, the EWMA charts which is famous of detecting smaller shift. In order to not inflate the false alarm rate, the effect of parameter estimation is considered and the proposed Phase II charts are measured by the average run length (ARL). Two types of corrected limits are provided, following the recent literature, one based on the unconditional perspective and the other on the conditional perspective and the exceedance probability criterion (EPC). In the sequel, the corrected (adjusted) charting constants are calculated and tabulated. The tabulations can be found, on demand, from accompanying R packages. Simulation studies for the robustness and the out-of-control performance are conducted. Illustrations are shown using real-world data. R packages are provided to help deployment of the new methodology in practice.