Tolerance Stack-Up Analysis - Methods and Best Practices

Guide to tolerance stack-up analysis: worst-case, RSS, Monte Carlo. How to predict and manage dimensional variation in assembled products.

What Is Tolerance Stack-Up?

Tolerance stack-up analysis determines the cumulative effect of individual part tolerances on an assembly dimension.

Why It Matters

• Prevents assembly failures - parts that do not fit, gaps, interference
• Reduces cost - targeted tolerances are efficient
• Improves quality - predictable variation allows SPC
• Drives design decisions - shows which tolerances are critical

Worst-Case (WC) Analysis

All tolerances at extreme values in worst combination.

• Formula: Total = sum of individual tolerances
• Pros: Guarantees 100% assembly
• Cons: Overly conservative, drives up cost
• Use when: Safety-critical, under 6 parts

RSS (Root Sum Square) Analysis

Assumes tolerances follow normal distribution. Total = sqrt of sum of squared tolerances.

• Pros: More realistic, cost-effective
• Cons: 0.27% reject rate at 3-sigma
• Use when: High volume, process in control

Monte Carlo Simulation

Random sampling from tolerance distributions, thousands of iterations.

• Pros: Flexible, handles non-linear stack-ups
• Cons: Requires software and computation time

Best Practices

• Identify the critical assembly dimension
• Create a tolerance chain diagram
• Use WC for simple, RSS for medium, Monte Carlo for complex
• Apply 10-20% design margin