When every part is in tolerance but the product still does not fit, the problem is the stack-up. Worst-case versus statistical analysis, how to find the few dimensions that matter, and how to tolerance for both function and cost.
Every dimension on every part was inside its tolerance. The inspection reports were clean. And yet roughly one lid in twelve would not close flush on the base, leaving a step that customers could feel with a fingernail. The quality team blamed the moulder, the moulder blamed the design, and the design team pointed at the drawings, which were, technically, all being met.
That is the signature of a tolerance stack-up problem: parts that are individually right and collectively wrong.
What a stack-up is
Any gap, flushness, alignment or clearance in an assembly is created by a chain of dimensions across several parts. The variation in each of those dimensions adds up. A stack-up analysis traces that chain, from one surface of interest to the other, and calculates how much the final gap can vary.
A typical lid-to-base flushness chain might include the base wall height, the position of the lid's locating rib, the hinge pin position on both parts, the pin diameter and the hole diameter. Five or six dimensions, each with a sensible tolerance of ±0.1 mm, can easily add up to more variation than the product can tolerate.
Worst case versus statistical
There are two main ways to add tolerances, and choosing between them is a business decision as much as an engineering one.
- Worst case (arithmetic): add every tolerance at its limit. If six dimensions are each ±0.1 mm, the gap varies by ±0.6 mm. Safe, simple and conservative, but it often forces tolerances tighter, and more expensive, than they need to be.
- Statistical (root sum square, RSS): assumes variations are random and independent, so they rarely all hit their limits at once. The combined variation is the square root of the sum of the squares: for six dimensions at ±0.1 mm, about ±0.24 mm. Realistic for well-controlled, high-volume processes, but only if the processes really are centred and capable.
Many teams use worst case for safety-critical or low-volume assemblies, and statistical analysis, sometimes with an inflation factor, for high-volume consumer products.
Finding the dimensions that matter
The real value of a stack-up is not the final number. It is seeing which dimensions dominate it. In most chains, two or three contributors account for most of the variation. Typical culprits are:
- Dimensions that cross a parting line or depend on mould shrinkage.
- Long dimensions on large plastic parts, where shrinkage variation scales with length.
- Locating features that rely on clearance fits, such as pins in holes.
- Assembly variation that nobody thought to include, such as how far a screw pulls parts together.
Ways to fix a stack-up
- Shorten the chain. Locate parts directly to each other rather than through intermediate parts.
- Change the datum scheme so that the critical features are located from the same reference.
- Tighten only the dominant contributors, and loosen the rest to standard process-capable tolerances.
- Add a deliberate adjustment or compliant feature, such as a crush rib or flexible locating finger, where variation is unavoidable.
- For moulded parts, control shrinkage at the source with gate location, process windows and post-mould conditioning.
Tolerancing for cost
Every tolerance has a price. Tight tolerances mean more precise tools, slower processes, more inspection and more scrap. A practical approach:
- Identify functional requirements first: what gaps, fits and alignments actually matter to the customer.
- Use stack-ups to derive the tolerances those requirements need.
- Apply standard, process-capable tolerances everywhere else.
- Confirm with process capability data once parts exist.
A habit worth building
Run a stack-up for every gap, flush condition and fit that a customer can see or feel, before drawings are released. It typically takes a few hours. It is one of the cheapest items in a Design for Manufacture review, and one of the few that prevents problems nobody can fix later by inspection. We worked through a real example of exactly this in the lid misalignment case study.
