KEVOS® MAKEOS · Quality
Tolerance Stack Design (Worst Case, RSS and Predicted Rejects)
Will this assembly gap stay within its limits by worst case, by root-sum-square, and what share of assemblies will fall outside at my process capability?
One-dimensional tolerance stack of up to six dimensions with symmetric tolerances: nominal gap, worst-case limits, root-sum-square (RSS) limits with an inflation factor (as the RSS tolerance stack tool), the statistical spread from each dimension’s process capability index Cp, the predicted share of assemblies outside the required gap assuming normal distributions centred on nominal, and the dimension contributing most.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Dimension 1 | choice | Whether dimension 1 adds to or subtracts from the gap (or is unused), going round the loop. |
| Dimension 1 nominal | mm | Nominal size of dimension 1. |
| Dimension 1 tolerance (±) | mm | Plus-or-minus tolerance of dimension 1. |
| Dimension 2 | choice | Whether dimension 2 adds to or subtracts from the gap (or is unused), going round the loop. |
| Dimension 2 nominal | mm | Nominal size of dimension 2. |
| Dimension 2 tolerance (±) | mm | Plus-or-minus tolerance of dimension 2. |
| Dimension 3 | choice | Whether dimension 3 adds to or subtracts from the gap (or is unused), going round the loop. |
| Dimension 3 nominal | mm | Nominal size of dimension 3. |
| Dimension 3 tolerance (±) | mm | Plus-or-minus tolerance of dimension 3. |
| Dimension 4 | choice | Whether dimension 4 adds to or subtracts from the gap (or is unused), going round the loop. |
| Dimension 4 nominal | mm | Nominal size of dimension 4. |
| Dimension 4 tolerance (±) | mm | Plus-or-minus tolerance of dimension 4. |
| Dimension 5 | choice | Whether dimension 5 adds to or subtracts from the gap (or is unused), going round the loop. |
| Dimension 5 nominal | mm | Nominal size of dimension 5. |
| Dimension 5 tolerance (±) | mm | Plus-or-minus tolerance of dimension 5. |
| Dimension 6 | choice | Whether dimension 6 adds to or subtracts from the gap (or is unused), going round the loop. |
| Dimension 6 nominal | mm | Nominal size of dimension 6. |
| Dimension 6 tolerance (±) | mm | Plus-or-minus tolerance of dimension 6. |
| Requirement | ||
| Smallest gap allowed | mm | Smallest gap the function allows. |
| Largest gap allowed | mm | Largest gap the function allows. |
| RSS inflation factor | × | Factor on the RSS result to allow for non-normal or off-centre processes (often 1.0–1.5). |
| Process capability index of each dimension | Capability of the processes making the parts: tolerance = 3 × Cp × standard deviation. | |
| Largest reject share accepted | % | Largest share of assemblies outside the gap you accept. |
Method and formulas
- Gap = Σ (sign × nominal); worst-case half-range = Σ tolerance; RSS half-range = inflation × √Σ tolerance² (as the RSS tolerance stack tool).
- Each dimension σ = tolerance ÷ (3 Cp); gap σ = √Σσ².
- Predicted reject share = Φ((min − gap) ÷ σ) + 1 − Φ((max − gap) ÷ σ), with Φ the normal distribution.
- Example: the gap is 0.5 mm, worst case ±0.28 mm, RSS ±0.14629 mm; predicted rejects 0%.
Limitations
- Linear one-dimensional stack with symmetric tolerances; geometric tolerances and non-linear stacks need more.
- Assumes centred normal processes; real processes drift.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check an assembly gap before releasing a drawing
- Decide whether worst-case or statistical tolerancing is justified
- Find the dimension to tighten first
Who it is for
- Design engineers
- Quality engineers
- Drafters
What you get
- Nominal gap, worst-case and RSS limits
- Statistical spread and predicted reject share
- Largest contributor
Interpreting the result
- Tighten the largest contributor first: it gives the biggest RSS reduction for the cost.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 628–634, 128–130. Topic reference; no source tables or recommended settings are reproduced.
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