Tolerance Stack-Up in Assemblies
How individual part tolerances add up across an assembly, with a worked worst-case and statistical example
An assembly of five parts each within tolerance can still fail to fit if their tolerances stack in the same direction, which is the most common design review finding CutLinq sees on multi-part welded or bolted assemblies. Tolerance stack-up is the analysis that predicts the combined variation across a chain of dimensions so a gap, clearance or interference is checked before parts are cut.
This page explains the two common stack-up methods, worst-case and statistical (root-sum-square), with a worked numeric example so you can check your own assembly tolerance before sending files for quoting.
Worst-case versus statistical stack-up
Worst-case stack-up simply adds every part tolerance in the chain: total tolerance = sum of individual tolerances. It guarantees the assembly fits under any combination of part variation but is overly conservative for chains of four or more parts, often forcing tolerances tighter and more expensive than necessary.
Statistical stack-up (root-sum-square, RSS) assumes part variation is random and normally distributed, and combines tolerances as the square root of the sum of squares: total tolerance = sqrt(t1² + t2² + t3² + ...). This is realistic for laser-cut and CNC parts made under normal process control and gives a smaller, more economical total tolerance, but assumes no single process is biased and out of statistical control.
| Method | Formula | Best for | Result vs actual risk |
|---|---|---|---|
| Worst-case | T_total = Σ ti | Safety-critical, low part count (2-3) | Conservative, may over-specify |
| Statistical (RSS) | T_total = √(Σ ti²) | 4+ parts, normal process control | Realistic, requires process capability |
Worked example: a 4-part welded frame
A welded frame assembly has four laser-cut and bent parts stacking in one direction, each with an individual length tolerance of ±0.3 mm (typical for a bent flange dimension in the 100-300 mm range). Worst-case: total tolerance = ±0.3 x 4 = ±1.2 mm. If the mating clearance in the design is only ±0.8 mm, the assembly fails under worst-case analysis even though every part is individually within tolerance.
Statistical (RSS): total tolerance = sqrt(0.3² + 0.3² + 0.3² + 0.3²) = sqrt(0.36) = 0.6 mm. Under RSS, the ±0.8 mm clearance is sufficient with margin, because it is statistically unlikely all four parts hit their tolerance limit in the same direction simultaneously. This is why CutLinq recommends RSS analysis for chains of four or more laser-cut parts rather than defaulting to worst-case.
Where tolerance stack-up commonly causes problems
Bolt hole patterns across multiple welded or bolted parts are the most common failure: each plate's hole position tolerance (typically ±0.2-0.3 mm from laser cutting) combines with the mating part's tolerance, and if the design assumed zero stack-up the bolts will not align. Slotting holes in one of the mating parts (±2-3 mm of adjustment) is the standard fix rather than tightening every individual tolerance.
Welded assemblies add distortion on top of cutting tolerance: a frame with four welded corners can pick up an additional 0.5-1.5 mm of dimensional variation from weld shrinkage alone, which should be included as a separate term in the stack-up rather than assumed to be zero.
Design tips
- Use RSS (statistical) stack-up for chains of 4 or more parts under normal process control; reserve worst-case for 2-3 part safety-critical chains.
- Add weld distortion as its own tolerance term (0.5-1.5 mm typical) in any welded assembly stack-up, not just cutting tolerance.
- Use slotted holes (±2-3 mm adjustment) on at least one mating part in a bolted chain rather than tightening every individual hole tolerance.
- State the tolerance stack-up method assumed (worst-case or RSS) on the assembly drawing so a supplier's parts are checked against the right standard.
- Identify the critical dimension chain on the drawing explicitly; not every dimension in an assembly needs the same scrutiny.
- For a chain with a mix of laser-cut and CNC machined parts, use the tighter machined tolerance only where it directly affects the critical stack, not throughout.
- Request a first-article check on a new multi-part assembly to confirm the stack-up assumption before a full production run.
Applications
| Industry | Example assembly | Stack-up concern |
|---|---|---|
| Machinery and OEM | Multi-plate welded frames | Bolt hole alignment across parts |
| Sheet metal enclosures | Multi-panel chassis | Panel gap and cover fit |
| Structural steelwork | Bolted splice connections | Hole pattern alignment |
| HVAC ductwork | Multi-piece duct runs | Flange alignment over length |
| Signage and facade | Multi-panel cladding systems | Visible joint line consistency |
Pricing and lead time
Tolerance analysis itself adds no direct cost, but the outcome affects price: specifying worst-case tolerance on every part in a long chain increases machining or inspection cost, while RSS-based tolerancing on the same chain often allows standard laser and bend tolerances to be used, keeping cost down. Standard laser-cut and bent parts remain in the usual 2-5 working day range across Egypt, the UAE and Saudi Arabia; a first-article check on a new multi-part assembly typically adds 1-2 working days before full production.
Frequently asked questions
Only for short chains (2-3 parts) or safety-critical dimensions. For 4 or more parts under normal process control, worst-case usually over-specifies tolerance and increases cost without a proportional reduction in risk; RSS is more realistic.
Upload your DXF or STEP file with the assembly tolerance chain noted, and receive a binding quote within 12 hours.