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Dr. Wayne Taylor - Taylor Enterprises, Inc.
Applied Statistics
for Engineers and Quality in the FDA Regulated Industries

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Robust Tolerance Analysis (2 day)

A modern approach to engineering product/process variation


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.

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 tolerancing.
  • 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. This is done by simply clicking a button and asking the software to determine the targets optimizing Ppk, Taguchi loss, percent defective, etc.

Intended Audience

This course is intended for all engineers, scientists, and technical management 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, 6s)

  • 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


  • 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 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 costs

Reliability and Special Applications

  • Relationship between reliability and variation
  • Using robustness to achieve high reliability without adding product cost

Putting It All Together

Software Used




Related Courses

Design of Experiments I - Screening Experiments
Statistical Process Control I - Introduction


Copyright 1997-2017 Taylor Enterprises, Inc.
Last modified: September 08, 2017