What are the advantages and disadvantages of using replication in experimental design?

🔁 Repetition and Replication are two different techniques that can be combined to reduce costs and variation. Repetition is about making multiple response measurements on the same experimental run (same sample without any resetting between measurements), while replication is about making multiple independent randomized experimental runs (multiple samples with resetting between each runs) for each treatment combination. 📏 Repetitions only reduce the variation from the measurement system (by using the average of the repeated measurements). ⚙️ Replications reduce the total experimental variation (process + measurements) in order to provide an estimate for pure error and reduce the prediction error (with more accurate parameters estimates).

Replication in DoE offers several key advantages: 📉 Replication reduces the total variability of the system (process and measurements), enhancing the signal-to-noise ratio, lowering the standard error of estimates and prediction variance across the experimental space, and improves the probability of detecting active effects. ❌ Replication enables to estimate pure error, the variability of the observations within each treatment. 📈 Replication enables to do a lack-of-fit test on the model found, assessing how well the model fits the actual data, helping to identify potential discrepancies, to refine the model and ensuring its accuracy. 🎯 Replication ensures that results are reliable, robust and reproducible.

Replication in experimental design increases the reliability and validity of results by reducing random errors and providing a more accurate estimate of variability. However, it can be resource-intensive, requiring more time, cost, and effort to replicate experiments consistently.

Replication can be both time-consuming and expensive. 🔎 Instead of dedicating runs solely for replication, one might consider using them to estimate additional effects in the model, such as interactions. This alternative approach has the potential to reduce correlations between effects and prevent aliases (confoundings). ⚖️ In modern designs (like Optimal designs), Replicate Runs offer an efficient alternative to full replication. This strategic choice enables researchers to concentrate their efforts and resources on the most crucial runs, essential for precisely estimating specific effects, minimizing correlations, avoiding aliases, and reducing prediction variance where it is most pronounced.

💡 Choosing a replication strategy depends on study objectives, time, and resources. Repetitions may be helpful only if measurement variation constitutes a significant portion of the total variability. Different replication strategies are possible : ✳️ Replicated Centre Points: Useful for precise pure error estimation and effective lack-of-fit test, aiding in detecting response curvature. However, it doesn't improve estimates of model effects, identify nonlinear effects, or assess variability in the experimental space. 🧪 Replicated Runs: Enhance estimates precision, increase signal-to-noise ratio, and improve the probability of detecting active effects. Enable comprehensive assessment of variability across the entire experimental space.