A component can be perfectly within tolerance and still contribute to an assembly that does not work. That is because assemblies do not experience dimensions individually. They experience the cumulative effect of every dimension and tolerance in the stack. A ±0.05 mm variation here and ±0.10 mm somewhere else can quickly become a much larger functional problem once several components come together.
This is the principle behind tolerance stack-up. If Part A, Part B, and Part C each vary within their acceptable limits, the final assembly dimension can shift significantly from nominal. In a worst-case condition, those individually acceptable variations may accumulate in the same direction, reducing clearance, changing alignment, or creating an interference fit.
The problem becomes especially important around functional interfaces. Shafts and bearings, locating features, mating surfaces, fastener patterns, seals, and moving mechanisms often depend on several dimensions interacting correctly. Checking each drawing independently does not guarantee that the complete assembly will function across the full range of manufacturing variation.
Tolerance analysis allows engineers to evaluate that risk before production. Worst-case analysis can identify whether the assembly remains functional at dimensional extremes, while statistical approaches can provide a more realistic picture of expected variation in higher-volume production. The objective is not simply to tighten every tolerance, but to understand which dimensions actually control assembly performance.
Reliable assemblies are designed around variation rather than nominal geometry alone. A CAD model may fit perfectly because every component exists at its ideal dimension. Production never works that way. Designing the tolerance system as carefully as the individual parts is what turns a theoretically correct assembly into a repeatable one.