Question

Explain with an example the process for determining the replicates number for Design of Experiments.

Answer 1

Replicates are multiple experimental runs with the same factor settings (levels). Replicates are subject to the same sources of variability, independently of each other. You can replicate combinations of factor levels, groups of factor level combinations, or entire designs.

For example, if you have three factors with two levels each and you test all combinations of factor levels (full factorial design), one replicate of the entire design would have 8 runs (23). You can choose to do the design one time or have multiple replicates.

The design of an experiment includes a step to determine the number of replicates that you should run. Considerations for replicates:

Screening designs to reduce a large set of factors usually don't use multiple replicates.

If you are trying to create a prediction model, multiple replicates can increase the precision of your model.

If you have more data, you might be able to detect smaller effects or have greater power to detect an effect of fixed size.

Your resources can dictate the number of replicates you can run. For example, if your experiment is extremely costly, you might be able to run it only one time

A manufacturing company has a production line with a number of settings that can be modified by operators. Quality engineers design experiments, with replicates, to evaluate the effect of the settings on quality

The experiment uses replicates. The operators set the factors at predetermined levels, run production, and take one quality measurement. They reset the equipment, run production, and take one quality measurement. In random order, the operators run each combination of factor settings five times, taking one measurement at each run

In each experiment, five measurements are taken at each combination of factor settings. In the experiment, the five measurements are taken in different runs. The variability between measurements taken at the same factor settings tends to be greater for replicates than for repeats because the machines are reset before each run, adding more variability to the process