Tolerance Stacking
In mechanical engineering there's a notion tolerances. Every measurement has a nominal dimension and then the tolerance to allow for machining differences. Of course you can, as the engineer, make the tolerances as small as you want if you want to trade precision for cost.Most parts work in a system -- parts fit into and around their neighboring parts. Each part in a system interacts with other parts. Each of those parts has a tolerance associated with it.Most times, when thinking about systems, you mainly think of the nominal measurement. Something that's an inch is an inch. The tolerance could be +/- 0.02". For the most parts this might be just fine. Now, let's say it needs to fit into a hole that is speced at one inch, +/- 0.02". Perhaps half the time it'll fit just fine; the rest of the time the part will be bigger than the hole -- maybe a 1.01" pin into a 0.99" hole.Ok. let's be a bit more generous.Let's keep the pin a 1.00 +/- 0.02" and now let's spec the hole at 1.04 +/- 0.02". At worse you'll have a 1.02" pin and a 1.02" hole, right? Nope. How many standard deviations are you going to go out to ensure all parts meet spec exactly? More cost.This, however, is still the easy part.What happens in you have a group or parts? Each with their own tolerance. If that subassembly's parts are all on one end of the scale, maybe that subassembly won't fit where it needs. Sure, a lot of the time the tolerances cancel each other out with one part being a bit small and another a bit big -- averaged out you get pretty much what you want.This concept is called tolerance stacking.
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This isn't just mechanical engineering.Let's take software for instance.The specs you deal with are timelines. Every estimate has, implicitly, a set of tolerances. Many times things work out -- like before some things take longer, some things go quicker. No problem. Most times you ever put in a bit of padding to allow for it.But, what happens if you take the tolerances away? Let's say an estimate is 2-4 weeks for project 1, and 3-4 weeks for project 2, and 1-2 weeks for project 3. You can be safe and say a total of 10 weeks but that's silly and potentially wasteful. Alternately you can say 6 weeks and hope for the best. Now that you've picked the tightest hole, you have no tolerance if anything gets bigger. You've squeezed out all the room for variation -- this isn't error, it's expected variance.Tolerance. It's important to look at it.
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Whenever you're dealing with numbers, especially groups of numbers, it pays to look at the tolerance values for each part to see how things interact. This way you won't get as surprised when a tolerances stack against you.