Tolerance analysis

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Tolerance analysis is the general term for activities related to the study of accumulated variation in mechanical parts and assemblies. Its methods may be used on other types of systems subject to accumulated variation, such as mechanical and electrical systems. Engineers analyze tolerances for the purpose of evaluating geometric dimensioning and tolerancing (GD&T). Methods include 2D tolerance stacks, 3D Monte Carlo simulations, and datum conversions.

Tolerance stackups or tolerance stacks are terms used to describe the problem-solving process in mechanical engineering of calculating the effects of the accumulated variation that is allowed by specified dimensions and tolerances. Typically these dimensions and tolerances are specified on an engineering drawing. Arithmetic tolerance stackups use the worst-case maximum or minimum values of dimensions and tolerances to calculate the maximum and minimum distance (clearance or interference) between two features or parts. Statistical tolerance stackups evaluate the maximum and minimum values based on the absolute arithmetic calculation combined with some method for establishing likelihood of obtaining the maximum and minimum values, such as Root Sum Square (RSS) or Monte-Carlo methods.


In performing a tolerance analysis, there are two fundamentally different analysis tools for predicting stackup variation: worst-case analysis and statistical analysis.


Worst-case tolerance analysis is the traditional type of tolerance stackup calculation. The individual variables are placed at their tolerance limits in order to make the measurement as large or as small as possible. The worst-case model does not consider the distribution of the individual variables, but rather that those variables do not exceed their respective specified limits. This model predicts the maximum expected variation of the measurement. Designing to worst-case tolerance requirements guarantees 100 percent of the parts will assemble and function properly, regardless of the actual component variation. The major drawback is that the worst-case model often requires very tight individual component tolerances. The obvious result is expensive manufacturing and inspection processes and/or high scrap rates. Worst-case tolerancing is often required by the customer for critical mechanical interfaces and spare part replacement interfaces. When worst-case tolerancing is not a contract requirement, properly applied statistical tolerancing can ensure acceptable assembly yields with increased component tolerances and lower fabrication costs.

Statistical variation[edit]

The statistical variation analysis model takes advantage of the principles of statistics to relax the component tolerances without sacrificing quality. Each component’s variation is modeled as a statistical distribution and these distributions are summed to predict the distribution of the assembly measurement. Thus, statistical variation analysis predicts a distribution that describes the assembly variation, not the extreme values of that variation. This analysis model provides increased design flexibility by allowing the designer to design to any quality level, not just 100 percent.

While no official engineering standard covers the process or format of tolerance analysis and stackups, these are essential components of good product design. Tolerance stackups should be used as part of the mechanical design process, both as a predictive and a problem-solving tool. The methods used to conduct a tolerance stackup depend somewhat upon the engineering dimensioning and tolerancing standards that are referenced in the engineering documentation, such as American Society of Mechanical Engineers (ASME) Y14.5, ASME Y14.41, or the relevant ISO dimensioning and tolerancing standards. Understanding the tolerances, concepts and boundaries created by these standards is vital to performing accurate calculations.

Tolerance stackups serve engineers by:

  • helping them study dimensional relationships within an assembly.
  • giving designers a means of calculating part tolerances.
  • helping engineers compare design proposals.
  • helping designers produce complete drawings.

Concerns with tolerance stackups[edit]

A safety factor is often included in designs because of concerns about:

  • Operational temperature and pressure of the parts or assembly.
  • Wear.
  • Deflection of components after assembly.
  • The possibility or probability that the parts are slightly out of specification (but passed inspection).
  • The sensitivity or importance of the stack (what happens if the design conditions are not met).

See also[edit]


  • "Automation of Linear Tolerance Charts and Extension to Statistical Tolerance Analysis". Journal of Computing and Information Science in Engineering 3 (1): 95–99. March 2003. 
  • ASME publication Y14.41-2003, Digital Product Definition Data Practices
  • Alex Krulikowski (1994), Tolerance Stacks using GD&T, ISBN 0-924520-05-1
  • Bryan R. Fischer (2011), Mechanical Tolerance Stackup and Analysis, ISBN 1439815720
  • Jason Tynes (2012), Make It Fit: Introduction to Tolerance Analysis for Mechanical Engineers, ISBN 1482350254