A tolerance stack-up answers a deceptively simple question: given that every part varies within its tolerance, will the assembly still fit and function? Get it wrong and you find out on the production line, not the drawing board.
Define the loop
Start by drawing the chain of dimensions from one side of the gap you care about to the other, and give each contributor a sign: dimensions that open the gap are positive, those that close it are negative. The sum of the nominals is your nominal gap; the tolerances are what you now have to combine.
Worst-case: guaranteed, but expensive
Worst-case assumes every part is simultaneously at its worst limit, so you simply add all the tolerances. It guarantees the assembly always fits — but that scenario is astronomically unlikely with more than a few parts, so it forces needlessly tight (expensive) individual tolerances.
RSS: what production actually delivers
Root-Sum-Square recognises that parts vary independently and randomly, so extremes rarely
line up. It combines tolerances as √(Σt²), giving a much tighter predicted spread — which means you
can open up the individual part tolerances and still hit the assembly target. Use RSS when you have volume and
the processes are centred and capable (see Cpk); use worst-case for safety-critical or
low-volume work. The Tolerance Stackup tool runs both plus a Monte Carlo simulation.
Monte Carlo: for the hard cases
When contributors aren't normal, aren't centred, or interact, sample each one from its real distribution a few thousand times and look at the resulting histogram. It's the most realistic method and gives you a direct defect rate — the tool does this and reports Cpk against your limits.