# What are the statistical calculation methods: RSS, Monte Carlo and their differences with the worst case method?

Enventive Concept offers three different calculation methods: Statistical analysis based on RSS, Worst Case and Monte Carlo.

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Enventive Concept does Root Sum of Squares (RSS) analysis, which means that it is calculating the sigma value for the derived/analyzed dimension according to the following formula:

That is, for each individual contributor, multiply its sigma value by its sensitivity value, and then square that number to get the variance value for that contributor.

The Solver is the heart of Enventive Concept, and is what differentiates Enventive Concept from other types of mechanical engineering software.

Behind the scenes, the Enventive Concept Solver is creating a mathematical equation that describes a path between any two objects. (We call this the dependency graph.) Every contributor on the path (dimensions, constraints, forces/moments, and variables) has a nominal value and a sigma value, and the Solver computes the first partial differential of the mathematical equation to determine sensitivity and percent of contribution values for each contributor:

Note that Enventive identifies itself the list of contributors. The user doesn’t have to build the stack-up.

The results of the RSS analysis are given in terms of Fail Rate (ppm), % in Torlance and Cpk (add a link to the page discussing those topics)

## Worst Case

In worst case analysis, the system analyzes the behavior of the model and predicts an outcome based on contributor values being at maximum and minimum tolerance limits.

A Linear Worst Case is performed every time you run a Tolerance Analysis. The system uses sensitivity values to provide a linear estimate of the outcome based on contributor values being at maximum and minimum tolerance limits. When designing for worst case, the worst case values listed on the report for Upr Tol and Lwr Tol should be less than the Upr Tol and Lwr Tol values set for your design limits.

The system estimates the minimum and maximum amount of variation in the analyzed dimension. Compare these values to the design limits to determine if the dimension will be in tolerance during a worst case scenario.

If you are designing for worst case and the worst case tolerance values are larger than the values stated in the design limits, you will need to improve your design by reallocating constraints or dimensions, or by tightening tolerances on sensitive contributors.

In addition, when designing for worst case, the worst case and ±3 Sigma tolerance values should be less than the tolerance range set in the design limits.

## Monte Carlo

Monte Carlo uses statistical random sampling to calculate values for an analyzed dimension, including mean, sigma, accuracy, largest/smallest value, and percent in tolerance.

Enventive Concept’s standard tolerance analysis uses a Root Sum of Squares (RSS) calculation,
which is appropriate for most needs, but Monte Carlo analysis may be preferable in cases such
as:

• Nonlinear sensitivity values
• Changing contact locations (different contributor list)
• Non-Gaussian contributors
• Transition fit for pin-in-hole assembly

In the case of Non-Gaussian contributors, the following distribution types are available for use with Monte Carlo simulation:

• Custom Gaussian
• Uniform
• Triangular
• Weibull
• 2D Gaussian (for concentric circles and position constraints only)
• 2D Circular Uniform (for concentric circles and position constraints only)
• 2D Circular Gaussian (for concentric circles and position constraints only)
• 2D Pin in Hole (for pin-in-hole constraints only)
• Truncated Gaussian
• Trapezoidal

Monte Carlo Simulation results include “goodness of fit,” which tests how well the analyzed data fits the selected distribution type.

Sample moments and Pearson distribution analysis is performed to determine whether output data may be considered Normal/Gaussian or whether a different Pearson distribution type provides a better fit. Depending on the determined distribution type, appropriate distribution parameters are displayed; i.e., Mean, Sigma, and Cpk or Mean, Variance, Skew, and Kurtosis.

## The tolerance analysis software you’ve been looking for

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“The combination of graphical layouts, robust equation solvers, and Excel interface makes Enventive Concept an indispensable tool that should be a part of every mechanical design engineer’s toolbox!”
Matthew LOEW
DAXCON Engineering

Our conceptual design abilities combined with Enventive Concept’s tolerance analysis and design optimization tools make Enventive Concept a superior tool for mechanical engineering design. One Enventive customer tells us that using Enventive Concept is 10 times faster than using their CAD system for his mechanical engineering design projects:

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