What Are Center Points in a Designed Experiment?

Center points are experimental runs made with every factor set midway between its low and high levels — the exact middle of the design. They are the cheapest insurance in experimental work: a handful of extra runs that tell a two-level experiment whether the straight-line world it assumes actually holds.

How it works

A two-level factorial can only fit straight lines, because two points define a line and nothing more. Center points test that assumption. If the process really is linear across the region, the average response at the center should land close to the average of the corner runs. When it lands well above or below, the response is curved — there is a bump or a dip between the levels — and the experiment has detected it for the price of a few runs. That signal is the standard trigger for moving on to a response surface design that can model the curvature properly.

Replicated center points earn their keep twice more. Because they are genuine repeats of one condition, their spread provides a pure estimate of process noise even in an otherwise unreplicated design. And because they are usually spaced through the run order, a trend in their values exposes an unstable process mid-experiment, while there is still time to act.

A worked example

A plating line runs a two-factor factorial on bath temperature and current density — four corners plus four center points. The corner runs average a coating thickness near target; the center points come in distinctly higher than the corner average predicts. The relationship is curved: somewhere inside the studied region sits a peak the corner runs straddled without touching. A small central composite design follows, maps the curvature, and locates settings better than any corner of the original experiment. The four cheap middle runs are what made anyone look; without them, the team would have standardized on the best corner and called it optimal.

Practical pointers

• Add three to five center points to a two-level design as a default, not an afterthought
• Spread them through the run order — first, middle, and last — so they double as a drift detector
• Compare the center average with the corner average before trusting any straight-line conclusion
• Remember that purely categorical factors have no middle — curvature checks need genuine mid-levels

Center points are the experiment’s way of asking whether the truth lives between the settings you chose.

Center points, curvature checks, and the step up to response surface designs are covered in our Black Belt program — $499, roughly 60 hours, closing with a 150-question proctored exam backed by a 70% pass mark and one free retake. It is the level where experiments stop confirming hunches and start drawing maps.