Each attendee receives a robust collection of learning resources including:

- A copy of Introduction to Statistical Tolerance Stacks workbook, by Alex Krulikowski
- Class handouts
- An official certificate of completion

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.

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.

**Prerequisites**

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.

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