Manufacturing & engineering
Statistical tolerance analysis
Definition
Statistical tolerance analysis estimates the distribution of an assembly result from distributions assigned to its contributing dimensions and geometric controls. Unlike worst-case stack-up, it predicts a probability of meeting a requirement and depends on valid assumptions about process spread, centring, correlation, and assembly behaviour.
Also known as: statistical tolerance stack-up, statistical stack-up
Updated
RSS and Monte Carlo methods#
Root-sum-of-squares analysis combines input standard deviations for a linear result. NIST Technical Note 1297 calls RSS the usual method for combining standard uncertainty components and says covariance must be included when appropriate.
Monte Carlo analysis samples input distributions repeatedly and calculates the resulting output distribution. It is useful when the relationship is nonlinear or when contributors use different distributions. The SOLIDWORKS partner page for 3DCS lists Monte Carlo and high-low-mean sensitivity among the product's analysis outputs.
A drawing limit is not a standard deviation#
A plus-or-minus drawing tolerance states an allowed limit. It does not establish that production is centred, normally distributed, independent of other contributors, or contained within a chosen number of standard deviations.
Statistical analysis therefore needs manufacturing or inspection evidence for its distributions and correlations. Converting every drawing limit to three sigma without capability data can produce a precise probability from invented inputs.
Limits of the prediction#
The output is conditional on the assembly model. Metrologic DCS's 2026 tolerance-analysis guidance notes that locating strategy, assembly constraints, and flexible-part behaviour can change the predicted dimensional result.
A statistical pass is not a guarantee that every conforming set of parts will assemble. Keep the assumptions, model revision, process data, and acceptance threshold with the released study, then compare the prediction with measured assemblies.
Sources
Related terms
Tolerance stack-up
A tolerance stack-up is an analysis of how permitted dimensional and geometric variation combines to affect a functional assembly result, such as a gap, fit, alignment, or preload. It follows the dimensions and locating relationships that control the result rather than adding every tolerance on the drawing.
Tolerance
A tolerance is the allowed variation from a nominal dimension, such as 10.00 ± 0.05 mm. Tolerances drive fit, cost, and inspection, and they have to be specified deliberately because a CAD model on its own stores only nominal sizes.
GD&T
GD&T is a symbolic language for specifying the allowed variation in a part's form, orientation, location, and runout relative to datum features. In the US it is defined by ASME Y14.5, and it tells the manufacturer and inspector which geometry actually matters for fit and function.
Clearance
Clearance is the positive space between components, often measured in CAD as their minimum nominal separation. Required clearance must account for function and manufacturing variation; the absence of geometric interference does not by itself provide enough clearance.