Robust Tolerance Analysis (2 day)

A modern approach to engineering product/process variation.  Part of our Six Sigma program.


Dr. Wayne A. Taylor

Course Description

Design offers the first and best opportunity for reducing variation. This seminar teaches you a practical approach for selecting targets and tolerances for both products and processes in order to improve quality and reduce costs. Many real-world examples are worked in class including the design of a pump and the setting of a process window for a heat seal machine. The course provides practical strategies and tools for dealing with real-world complexities.  It covers the process for setting specifications as described in STAT-11, Statistical Techniques for Setting Specifications, of the book Statistical Procedures for the Medical Device Industry as well as how it fits into the Six Sigma Improvement process and Six Sigma Design process.

As part of the course, the VarTran® software package is used to perform all the required calculations. This allows the course to concentrate on the key concepts, strategies and issues.

This course addresses all the classical tools of tolerance analysis including worst-case tolerancing, statistical tolerancing, simulations, and sensitivity analysis. However, it goes beyond the classical tools to cover new tools for selecting optimal targets that optimize performance and reduce variation. This results in robust designs.

What You Will Learn

You will learn to achieve higher quality products and processes while simultaneously reducing costs by learning:

  • What Six Sigma quality is and how to achieve it up front in design through robust design and tolerance analysis.
  • How to predict the performance of a product or process early in the design process before investing in equipment, tooling, etc.
  • The five critical pieces of information driving DFSS.
  • How to use the five critical pieces of information to set specifications limits.
  • How to perform the two classical approaches to tolerancing, worst-case tolerances and statistical tolerances, along with their pros and cons.
  • A unified approach to tolerancing that combines these two approaches and solves the dilemma of worst-case versus statistical tolerances.
  • How to identify the critical tolerances that must be tightened to improve quality and how to identify tolerances that can be widened to reduce costs.
  • How to design manufacturable products based on machine and supplier capabilities.
  • How to handle tough nonlinear problems and other complications such as component wear, process cycling, and unstable processes.
  • How to avoid having to tighten tolerances by designing the product or process to be robust to variation in the components and conditions by determining the targets optimizing Ppk, Taguchi loss, percent defective, etc.

Intended Audience

This course is intended for all engineers, scientists, and technical managers involved in product or process design. It is also equally applicable to plant engineers involved in process improvement. No special statistical or mathematical background is required.

Course Outline


  • Optimization & Variation Reduction
    • The goal is to optimize product/process performance while at the same time reducing variation.
    • Four types of problems: larger the better, smaller the better, closer to target the better and closer to target function the better.
    • The cause of variation.
  • Variation Reduction and Robustness
    • The three approaches to reducing variation.
    • Finding the cause of the variation.
    • Robustness and its importance
    • Using robustness to improve product reliability
    • Benefits of reducing variation
    • Cost reduction opportunities
  • Variation Transmission Analysis
    • A procedure for designing high-quality low-cost products and processes
    • Case study – Designing a pump
    • Strategy
    • Lessons learned
  • Obtaining and Entering Information
    • Introduction to VarTran software
    • Entering data
    • Viewing the data
  • Performing Analysis
    • The 3-step process
    • Evaluating the initial design
    • Finding the optimal targets
    • Selectively tightening tolerances

DAY 1 – PM

  • Capability Studies (Cp, Cpk, 6σ)
    • Understanding Cp and Cpk
    • Six Sigma quality
  • Understanding the results
    • Effects tables
    • Plots
  • Optimization, Prediction & Simulation
    • Methods of optimization
    • Methods of predicting the variation
    • Monte Carlo simulations
  • Design of Experiments
    • Case study – Heat Sealer
    • Dual response approach to robustness
    • Using VarTran to perform the dual response approach
  • VTA Following an Experiment
    • An alternative approach to robust design using tolerance analysis
    • Advantages of this approach
    • Combining the two approaches

DAY 2 – AM

  • Review of Day 1
  • Three Approaches to Robustness
    • Taguchi’s inner/outer array approach
    • Dual response approach
    • Tolerance analysis approach
    • Comparison
    • Tolerance analysis approach is best-demonstrated practice
  • Tolerances
    • What is the designers intent?
    • The Achilles heel of the design process
  • Worst-Case Tolerances
    • Linear case
    • Nonlinear case
    • Clear intent
    • Overly expensive
  • Statistical Tolerances
    • Linear case
    • Nonlinear case
    • How they lower costs
    • Difficulties interpreting
    • Danger of using

DAY 2 – PM

  • Process Tolerances
    • A new approach where requirements are specified for the process producing the product
    • A unified approach to tolerancing that combines both the previous methods
      Using process tolerances to combine worst-case tolerances and statistical tolerances in the same analysis. No longer are you forced to choose
    • Deciding what type of tolerance to use
    • Accurately describing the behavior of a variable
    • Using process tolerances to ensure product quality while lowering cost
  • Reliability and Special Applications
    • The relationship between reliability and variation
    • Using robustness to achieve high reliability without adding product cost
  • Putting It All Together

Software Used



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