What is tolerance stack-up?

It is what happens when the tolerances of individual parts accumulate across an assembly. Four parts each held to ±0.1 mm can, in the worst case, combine to ±0.4 mm at the end of the chain. Every part passes its own inspection and the assembly still fails, because nobody toleranced the thing that actually matters — the final gap.

What is the difference between worst-case and statistical stack-up?

Worst-case adds every tolerance arithmetically and assumes all parts are at their extreme in the same direction. It guarantees fit and is expensive. Statistical (root-sum-square) assumes the deviations are random and partly cancel, giving a much smaller predicted range for most assemblies but accepting a small failure rate. Use worst-case for safety-critical fits and for low volumes; statistical becomes defensible at volume with a stable, measured process.

Why do untoleranced dimensions cause rejected production runs?

An untoleranced dimension falls under the drawing's general tolerance block, which is usually loose. Nobody argues about it at the drawing stage, which is exactly why it is dangerous: the factory is entitled to produce anywhere within that loose band, and the assembly may only work at one end of it. The dimension that fails is almost never the one people fought over.

How do you reduce tolerance stack-up without tightening every part?

Shorten the chain. Every joint in a dimension chain adds a tolerance, so combining two parts into one, or datuming both critical features from the same face on the same part in the same setup, removes a contributor entirely. Reducing the number of contributors is nearly always cheaper than tightening the ones you have.

Tolerance Stack-Up: All Parts Pass, Nothing Fits

Every part passed inspection. Nothing fits.

This is the argument that cannot be won by looking at the parts, because the parts are not wrong. Each one is inside its own tolerance. What is wrong is the chain nobody drew — and by the time it shows up, there is a container of components that are individually perfect and collectively useless.

The short version

Four parts at ±0.1 mm each can combine to ±0.4 mm worst case. Every part passes; the assembly fails.
Worst-case or statistical is your decision, not the factory's — and not deciding is the actual mistake.
The cheapest fix is not a tighter tolerance. It is a shorter chain.

How four good parts make one bad assembly

Both numbers are correct. Which one applies depends on your volume, your process capability and how bad a failure is — and that decision belongs to you, not to the factory that was handed the drawing.

Worst case or statistical

Worst case

Add every tolerance arithmetically. Assumes all parts sit at their extreme in the same direction on the same day. Guarantees fit. Expensive.

Safety-critical fits
Low volumes where one failure matters
New supplier, unknown capability

Statistical (RSS)

Root-sum-square. Assumes deviations are random and partly cancel. Much smaller predicted range. Accepts a small failure rate.

High volume
Process capability actually measured, not assumed
A failure means rework, not a recall

The mistake is not choosing wrongly. It is not choosing at all.

A drawing with individually reasonable tolerances and no statement of what the assembly needs discovers its own answer at first article.

The cheapest fix is not a tighter tolerance

When a stack-up does not close, the instinct is to tighten the parts. That is the expensive answer — and often the slowest, because tightening a tolerance can change the machine class, the fixturing and the inspection method. The cost step is not linear →

Shorten the chain instead. Every joint contributes a tolerance, so removing a contributor is worth more than tightening one:

Combine two parts into one. One fewer interface, one fewer tolerance, one fewer supplier.

Datum both critical features from the same face, in the same setup. Two features machined without re-fixturing do not stack against each other.

Move the adjustment somewhere cheap. A slot instead of a hole, or one shimmed joint, absorbs the whole chain for almost nothing.

Tolerance the gap, not the parts. State what the assembly must achieve and let the supplier tell you which parts they can hold — they know their own capability better than you do.

The dimension nobody argued about

In practice, the feature that rejects a production run is almost never the one that got attention in design review. It is the one that fell under the drawing's general tolerance block — because if a dimension has no callout, the factory is entitled to produce anywhere in that loose band, and your assembly may only work at one end of it.

A sealing face with no tolerance. A whole production run rejected. Both sides were right — the parts met the drawing, and the drawing did not describe the product.

The habit worth building: before releasing a drawing, list every dimension in the chain that produces your critical gap — including the ones with no callout — and check whether the general block is good enough for each. It takes twenty minutes. It is the single highest-return twenty minutes in the whole process.

Measured, not assumed

Statistical stack-up only works if the process capability is real. That means measurement — six CMMs verifying to ≤0.0005 mm, six vision measuring systems, and inspection defined by a sample plan rather than by whoever is on shift.

Dial indicator measurement on a granite surface plate — Granite plate and dial indicator — still the fastest honest answer

CMM measuring a machined part — CMM to ≤0.0005 mm — where capability data comes from

Dimensional inspection at the QC bench — The check that decides release or hold