This work presents a comprehensive framework for determining the optimal number of replications in Completely Randomized Designs (CRD) using both classical and modern computational approaches. Traditional methods based on statistical power, such as those developed by Harris, Hurvitz, and Mood (HHM), and Tukey’s method for confidence interval control, are revisited and automated through Monte Carlo simulations in R. The methodology emphasizes the use of the non-central F-distribution and random effects modeling to estimate the empirical power of the test and the required replication size for different design configurations. Additionally, operating characteristic (OC) curves are implemented to visualize the relationship between statistical power and variance ratios under fixed and random effects models. The study also incorporates a budget-constrained optimization approach to allocate replications efficiently across treatments with different costs and variances, using a Lagrangian minimization framework. Overall, this integrated approach enhances experimental design efficiency by combining theoretical rigor with computational simulation, providing practical tools for determining replication numbers under diverse experimental and resource conditions.