statistical tolerance analysis basics: worst-case tolerance analysis

worst case tolerance analysis

fair warning: if you’ve never heard the phrase “tolerance analysis”, you’ll likely never have to perform it and should just spend the next 5 minutes elsewhere. Otherwise…

A well-performed tolerance analysis will add years to your life.

No worrying about parts fitting together, no worries about sloppy fits.  A well-done tolerance analysis both proves the design and helps communicate which dimensions are really important to the manufacturer.

It’s a good place to be.

But where to begin?  The easiest place to start is the worst-case method.

the worst-case method

A worst-case tolerance analysis method is simple arithmetic (that’s right… just addition and subtraction), so lets start there.

For example, let’s say we have a block.

Tolerance Analysis Stackup

The block is is 1.000″ thick, and the (honest) guy selling it to you guarantees accuracy within ±0.005″ (5 thousandths of an inch). Thus, you are guaranteed that the part will be between 0.995″ and 1.005″.

Simple enough? Great. You just performed a worst-case tolerance analysis of that part.

Easy right? You bet.

But what happens if you stack, lets say, five blocks?

Tolerance Stack 2

The five 1.000″ blocks add up to, no surprise here, 5.000″. But the tolerances stack up as well, to ±0.025″.

Now things are becoming less precise. When we had one block we knew the thickness within 0.010″ (0.995″ – 1.005″). Now that we have five blocks, our range has ballooned to .050″ (4.975″ – 5.025″).

sidebar: 0.050″ is just under 1/16th of an inch. If that seems negligible to you, just look at the sticky gas pedal problems Toyota has been having lately. This stuff is important, especially when it comes to mechanisms.

If you want to determine a window inside which every last one of your block assemblies will land, you are done.  Just design everything else around the fact that this block assembly will be off by ±0.025″. Either that or go back to the block salesmen and shell out a small fortune for more accurate blocks.

If, on the other hand, you lack the small fortune for precision parts, the ambivalence to accept such a sloppy block assembly, or both, you do have a recourse:

You need to delve into the world of Root Sum Square (RSS) tolerance analysis.

update: My series of posts on worst-case, root sum square, and monte carlo tolerance analysis started off as just a brief introduction to the basics. Since then I have heard from a number of you asking for a clear, concise (everything else out there is so heavy), usable guide to both the math behind tolerance analysis and real-world examples of when to use it. I’m currently working on it, but would love to hear what YOU would like out of it. Let me know in the comments or contact me through the site.

Related posts:

  1. statistical tolerance analysis basics: Root Sum Square (RSS)
  2. statistical tolerance analysis basics: Monte Carlo Simulation
  3. First Cut prototype

Tagged as: example, root sum square, stack up tolerance analysis, tolerance analysis, tolerance analysis fundamentals, worst-case tolerance analysis

Article by chris loughnane

Chris is Design Engineer + Sustainability Advocate at a Boston area design consultancy and has written 127 sweet posts for the Product Development Notebook.

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  • Guilherme Rocha

    Nice article,

    I am diving into Tolerance Analysis now just because we’ve became resellers of CETOL 6Sigma software, we are the biggest PTC VAR here in Brazil, I confess I am not familiar with Tolerance Analysis, I am interested to hear more!
    Nice job.

  • http://www.pdnotebook.com/ loughnane

    Yeah, I’ve seen CETOL 6sigma. It can do some pretty amazing stuff (imagine if you had a gear , a rack, a cam, and a slider in series and wanted to see the effect of tolerance analysis)

    price tag is a bit too much for a lot of people though.

    Do you find a lot of buyers in Brazil?

  • Guilherme Rocha

    Not too much, but we are starting now with this product so let’s see.
    Our first customer is the Army, wich wants to improve the tolerances of the new service rifle they are working on.

  • Ibrahim

    So; the tolerance analysis is somthing for engineers only ? buildings and mechanic related analysis? or even for manufacturer that they want to get the best quality with the lowest cost possible.

    What if I tell you that I am a good distributor, I distribute canned food to the retail outlets; what this analysis can add to my business? any value?

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