Tolerance stack-up
Predict whether a chain of toleranced parts will assemble using both worst-case and statistical (RSS) stacks, and state when each method applies.
Try this first — before any explanation.
A 3-part stack (plate 6.000, spacer 9.000, cap 5.000) drops into a housing pocket of depth 20.200; the retaining-clip gap must stay in 0.10–0.50 mm. With supplier tolerances (plate ±0.10, spacer ±0.12, cap ±0.08, housing ±0.05), will the clip always fit? Compute the worst-case range, then run Monte-Carlo 5000 and notice how much head-room the statistical answer gives. Tighten the cheapest tolerances until guaranteed.
Both stack methods plus a deterministic 5000-draw Monte-Carlo, exactly as the autograder uses. Edit the tolerances to guarantee the fit.
Tolerance stack-up
Both stack methods plus a deterministic 5000-draw Monte-Carlo, exactly as the autograder uses. Edit the tolerances to guarantee the fit.
The idea, built visually.
Three parts — six, nine, five — sum to twenty, leaving a two-tenths gap; the clip fits at nominal. But nothing is at nominal, and each part's little band stacks. The pessimist's method, worst-case: assume every part lands at its worst extreme at once and just add the tolerances — 0.10+0.12+0.08+0.05 = 0.35 mm of swing, which can eat the whole gap. Worst-case is a guarantee: fit here and it fits always.
But all four hitting their worst extreme simultaneously is wildly unlikely — they're independent draws. So the statistical stack combines them as root-sum-of-squares: √(0.10²+0.12²+0.08²+0.05²) = 0.18 — half the worst-case. Both are true. Worst-case never fails but forces tight, costly tolerances; RSS is realistic and cheaper but admits a tiny reject rate.
▣ Stage animation: Worst-case: every band snaps to its extreme, the gap crushes toward zero, tolerances sum linearly to 0.35; then a Monte-Carlo cloud of 5000 rains in forming a narrow RSS bell at 0.18, half as wide, with a few tails poking past.
Build it up, step by step.
- Step A (worked): nominal gap 0.200; worst-case Σ|tol| = 0.350 → [−0.150, 0.550] FAIL; RSS √Σtol² = 0.1825 → [0.018, 0.382], still fails low but far less.
- Step B (fade): compute worst-case sum and RSS for a new supplier set; the Monte-Carlo overlay confirms RSS predicts the cloud width.
- Step C (independent): make the stack worst-case-safe at lowest cost — tightening the largest contributor (the spacer, 0.12) gives the most relief per cost unit — and state one scenario to ship the RSS answer.
How the Bench grades your run.
PASS WHEN Worst-case gap range ⊆ [0.10,0.50] (guaranteed fit), typed worst-case sum and RSS each within ±0.005 mm of reference, the tightening costs ≤1.6× the cheapest worst-case-safe solution, and a correct RSS-vs-worst-case statement, on MC seed 303.
- Worst-case gap is [−0.05, 0.45] — the low end is negative, so in the worst extreme the parts interfere. Tighten until the worst-case low ≥ 0.10 mm.
- You entered 0.35 for RSS, but that's the linear (worst-case) sum. RSS = √(0.10²+0.12²+0.08²+0.05²) = 0.182. Re-enter the RSS value.
- You tightened the cap (0.08), but the spacer (0.12) is the largest contributor — tightening it removes the most worst-case swing per cost unit.
- The assembly is guaranteed, but you tightened every part to ±0.03 — cost 4.1×. You only needed the spacer and plate; loosen the cap back toward ±0.08.
Bring back what you've already mastered.
- From 3.2: if a tool-wear drift shifts one part's mean off-nominal, is the RSS prediction still trustworthy? → no; RSS assumes centered/random, a systematic drift biases the stack.
- From 3.1: roughly how much does halving the spacer's band cost? → ~doubles that part's cost share.
- From M2: which sequencing/setup choice helps hold a tight thickness tolerance? → single-setup machining of the stack faces.
What you must demonstrate to advance.
On a fresh 3-part stack seed with new nominals and gap, compute both worst-case and RSS ranges (±0.005), tighten so the stack is worst-case-guaranteed at ≤1.6× the cheapest such solution, and state when each method applies. Unlocks Module 4.
How this feeds your build.
Feeds the M5 capstone: the worst-case-vs-RSS decision becomes a line-level yield lever; the same √Σtol² logic scales from a 3-part stack to the full assembly tolerance budget the capstone factory must satisfy.