KEVOS® MAKEOS · Quality
Statistical (RSS) Tolerance Stack
Will this gap stay within its limits, worst case and statistically?
Worst-case and root-sum-square (RSS) results for a linear stack of up to five dimensions, checked against the required gap limits.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Dimension 1 | ||
| Direction | choice | Whether dimension 1 increases or decreases the gap. |
| Nominal | mm | Nominal size from the drawing. |
| Tolerance ± | mm | Symmetrical ± tolerance; convert unequal tolerances to a mean nominal with equal ±. |
| Dimension 2 | ||
| Direction | choice | Direction of dimension 2. |
| Nominal | mm | Nominal of dimension 2. |
| Tolerance ± | mm | Tolerance of dimension 2. |
| Dimension 3 | ||
| Direction | choice | Direction of dimension 3. |
| Nominal | mm | Nominal of dimension 3. |
| Tolerance ± | mm | Tolerance of dimension 3. |
| Dimension 4 | ||
| Direction | choice | Direction of dimension 4. |
| Nominal | mm | Nominal of dimension 4. |
| Tolerance ± | mm | Tolerance of dimension 4. |
| Dimension 5 | ||
| Direction | choice | Direction of dimension 5, or not used. |
| Nominal | mm | Nominal of dimension 5. |
| Tolerance ± | mm | Tolerance of dimension 5. |
| Requirement and statistics | ||
| Minimum allowed gap | mm | Smallest gap the function allows, from the design requirement. |
| Maximum allowed gap | mm | Largest gap the function allows. |
| RSS inflation factor | × | 1.0 for plain RSS; a larger factor (your organisation’s rule, e.g. Bender’s 1.5) allows for shifted or non-normal processes. |
Method and formulas
- Nominal gap = Σ(+ nominals) − Σ(− nominals).
- Worst case = nominal ± Σ tolerances.
- RSS = nominal ± k√(Σ tolerance²), with k the inflation factor.
- Each dimension’s share of variance = tolerance² ÷ Σ tolerance².
- Example: the default stack has a nominal gap of 0.5 mm, worst case ±0.28 mm and RSS ±0.14629 mm.
Limitations
- RSS assumes independent, centred, roughly normal dimensions with tolerances at the same number of standard deviations.
- Linear one-dimensional stack only; angular and geometric tolerances need their own analysis.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check an assembly gap or clearance
- Decide whether statistical tolerancing is justified
- Find the dimension that drives the variation
Who it is for
- Design engineers
- Quality engineers
What you get
- Nominal gap
- Worst-case limits
- RSS limits
- Largest contributor
Interpreting the result
- If only the RSS result fits, the design depends on process control: confirm capability of the main contributors.
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.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
