Replicates and repeats in designed experiments

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.

Repeat and replicate measurements are both multiple response measurements taken at the same combination of factor settings; but repeat measurements are taken during the same experimental run or consecutive runs, while replicate measurements are taken during identical but different experimental runs, which are often randomized.

It is important to understand the differences between repeat and replicate response measurements. These differences affect the structure of the worksheet and the columns in which you enter the response data, which in turn affects how Minitab interprets the data. You enter repeats across rows of multiple columns, while you enter replicates down a single column.

Whether you use repeats or replicates depends on the sources of variability you want to explore and your resource constraints. Because replicates are from different experimental runs, usually spread along a longer period of time, they can include sources of variability that are not included in repeat measurements. For example, replicates can include variability from changing equipment settings between runs or variability from other environmental factors that may change over time. Replicate measurements can be more expensive and time-consuming to collect. You can create a design with both repeats and replicates, which enables you to examine multiple sources of variability.

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

• The first experiment uses repeats. The operators set the factors at predetermined levels, run production, and measure the quality of five products. They reset the equipment to new levels, run production, and measure the quality of five products. They continue until production is run one time at each combination of factor settings and five quality measurements are taken at each run.
• The second 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 first experiment, the five measurements are taken during the same run; in the second 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.