Statistical Tolerance Calculation

Statistical tolerance calculation offers a more accurate understanding of production variability compared to traditional tolerance limits, allowing for realistic early-stage assessments of customer specifications and identifying critical variables.

This course covers the key principles, including assumptions about input variable distributions derived from production or Cpk data, and models linking input variables to target values based on design, DoE, or process insights.

Participants will learn how to use Cornerstone software to replace Gaussian error propagation with distribution simulations, including handling special cases like truncated and mixed distributions. The course also demonstrates how integrating DoE with these simulations leads to more robust and cost-effective process designs.

Course outline: 

1. Statistical basics
2. Steps in statistical tolerance calculation
3. Designing trial plans

Overview

Course Content

Statistical Basics

• Important distribution types for statistical tolerance calculation (square, triangle, normal, Weibull)
• Simulation of distributions for tolerance calculation (incl. distributions, cut-out and correlated distribution)
• Basic understanding of confidence intervals and probability networks
  
  

Steps in Statistical Tolerance Calculation

• Functional approach for process behavior
• Statistical models for measuring errors, noise variables, and unknown factors
• Presenting a trial area
  
  

Designing Trial Plans

• Process model for tolerance calculation (presenting the process as a mathematical model)
• Determining the type of distribution and parameter of the tolerance values (e.g. production data of the facilities used)
• Tolerance calculation: simulation of the process by using a process model on a large virtual sample and determination of the distribution of response variables
• Optional addition of a process capability prognosis.
  
  

Learning Objective

Target Groups & Requirements

Training Methods

The focus is on understanding the methods, not mathematics, the integration of this method into linked processes requiring process validation suitability (trial planning, process capability) is closely examined, the steps in the process are explained as we discuss application examples or simulations, trust in the processes is developed, and from a practical point of view, a clear strategy for using statistical tolerance calculation is given.

This course is designed for:

Engineers in construction and development who would like to assess the process capability and industrial feasibility of future projects ahead of time.

Requirements:

• Mathematical thinking
• Interest in modelling error propagation in the running of a process
  
  

The course includes lectures, simulations of specific scenarios, discussions of real-world application examples, and hands-on exercises. Simulations and practical exercises can be completed independently on a laptop, providing participants with a flexible and interactive learning experience.