Introduction to Statistical Tolerance Stacks 1-Day Workshop     


I.D.# ETY130Printable Description
Duration: 1 Day
  Delivered in
November 16, 2017 (8:30 a.m. - 4:30 p.m. ) - Livonia, Michigan    

Hotel & Travel Information

Providing you have an understanding of tolerance stacks, this course teaches an introduction to statistical tolerance stacks, a crucial skill in today’s competitive workplace. Utilizing the expertise of world-renowned GD&T expert Alex Krulikowski, the course includes a brief overview of several terms used in statistical stacks. It explains four methods for applying statistics to tolerance stacks and covers precautions about when and how to use statistics in stacks. Newly acquired learning is reinforced throughout the class with stacks that allow the student to practice applying statistical methods. Each attendee receives a robust collection of learning resources including:

  • A copy of Introduction to Statistical Tolerance Stacks workbook, by Alex Krulikowski
  • Class handouts
  • ETI’s Digital Design Dictionary software ($79 value)
Thousands of students have learned GD&T through Alex Krulikowski’s textbooks, self-study courses, computer-based training, and online learning center. Students who attend courses like this one walk away with more than knowledge. They gain on-the-job skills because the learning materials are performance-based.

Learning Objectives
By attending this class, you will be able to:

  • Define the terminology used with statistical tolerance stacks
  • Describe common statistical tolerance stacks methods
  • Calculate statistical tolerance stacks using the RSS method
  • Calculate statistical tolerance stacks using the realistic method
  • Apply the RPL method to statistical tolerance stacks
  • Apply the Monte Carlo method to tolerance stacks
  • Describe precautions needed when using statistical tolerance stacks

Who Should Attend
This course is valuable for individuals who create or interpret engineering drawings, product and gage designers; process, product, and manufacturing engineers; supplier quality engineers/professionals; CMM operators; buyers/purchasers; checkers; inspectors; technicians; and sales engineers/professionals.

Please be aware that this is not an introductory course. In order to understand the course content, students should have completed ETI's Tolerance Stacks Using GD&T course or equivalent.

Topical Outline
Importance of statistical stacks

  • The three assumptions that apply to Worst-case tolerance stacks
  • The two laws of probability that apply to statistical stacks
  • Two common probability distribution curves used in statistical stacks
  • The probability of an assembly of six parts with uniform distributions reaching extreme limits
  • The probability of an assembly of six parts with normal distributions reaching extreme limits
Statistical stacks terminology
  • Statistics and data
  • Uniform and normal frequency distributions
  • Range, mean, and deviation
  • Variance and standard deviation
  • Specification limits
  • Standard normal curve and the Empirical Rule
  • A Z score and parts per million rejects
  • Control limits
  • How CP and CPK relate to a normal distribution
  • The difference between dependent and independent variables
Common statistical tolerance stacks methods
  • What a statistical tolerance stack is
  • The Realistic Predicted Limits (RPL) method its assumptions
  • The Root Sum of Squares (RSS) method and its assumptions
  • The Motorola Six Sigma Root Sum of Squares method and its assumptions
  • The Motorola Six Sigma Dynamic Root Sum of Squares (DRSS) method and its assumptions
  • The Monte Carlo Simulation method and its assumptions
  • The formulas for and results of using the different statistical stack methods
  • Three benefits of statistical stacks
  • Two common reasons why statistical stacks are done
The ETI statistical stack form
  • How to complete the ETI statistical stack form
  • The four stack consequences that must be considered when doing statistical stacks
The RPL statistical stack method
  • The formula for calculating the RPL factor
  • A qualified dimension used in the RPL method
  • How to do the RPL method using the ETI statistical stacks form
  • The advantages and disadvantages of the RPL method
  • Calculating a statistical stacks using the RPL method
The Six Sigma DRSS statistical method
  • The derivation of the standard RSS statistical stack formula
  • The seven steps in calculating a RSS statistical stack
  • Calculating a stack using the RSS method with a safety (Bender) factor applied
  • The Motorola Six Sigma RSS formula and its advantages
  • The Dynamic RSS (DRSS) formula and its advantages
  • The eight steps in calculating a DRSS statistical stack
  • How to do a DRSS stack using the ETI statistical stack form
  • How to interpret the stack results shown on the ETI statistical stack form
  • How to adjust a statistical stack to handle dependent variables (bonus & shift)
  • Statistical stack results before and after adjusting for dependent variables
The Monte Carlo statistical simulation method
  • Simulation and Monte Carlo simulation
  • The parameters used in a Monte Carlo simulation
  • List common distributions used in a Monte Carlo simulation stack
  • The minimum number of trials that should be used in a Monte Carlo simulation stack
  • Available software that can perform Monte Carlo simulations
  • How a Monte Carlo simulation works
  • How to do a Monte Carlo simulation using the ETI stack form with RiskAMP plug-in
Statistical tolerance stacks precautions
  • The guidelines for determining when a statistical stack should be done
  • The seven assumptions of RSS statistical tolerance stacks
  • The four precautions to reduce risk of using statistical tolerance stacks
  • Why the ST symbol from Y14.5 should be used on a drawing that specifies statistical tolerances
  • How the ST is used on a drawing to indicated a tolerance is based on statistical methods
  • The benefits of using the ST symbol on product drawings
DRSS and RPL statistical stack calculations
  • Calculating statistical tolerance stacks
  • Making adjustments for bonus and shift
  • Calculating a stack using the DRSS and RPL methods
  • Using CPK values in a statistical stack
Course summary, final learning assessment

All of ETI's instructors are industry professionals with years of experience applying GD&T on the job. ETI trainers have:

  • Expert knowledge of the Y14.5 Standard
  • Current or recent industrial experience using GD&T
  • At least five years of experience using GD&T
  • Experience and skill using ETI teaching materials
Our instructors use identical training materials and lesson plans, so you receive the same class presentation from every trainer.

Fees: $770.00 ; SAE Members: $616.00 - $693.00

.7 CEUs
You must complete all course contact hours and successfully pass the learning assessment to obtain CEUs.

To register, click Register button at the top of this page and submit the online form, or contact SAE Customer Service at 1-877-606-7323 (724/776-4970 outside the U.S. and Canada) or at

For a quote on bringing this course to your company site, fill out a Corporate Learning Solutions Request Form