Both parts measured correctly. They still would not fit together, and the drawing never asked about the thing that was wrong

A shaft is specified at 25 mm. It is machined, measured at 25.00 mm, and passes. The housing bore is specified at 25.05 mm, is measured at 25.05 mm, and passes. On assembly, the shaft will not go in — or it goes in and the machine vibrates itself apart in a month.

Both parts were within specification. Both inspection reports are honest. The failure is real, and the explanation is that a dimension on a drawing is a far weaker statement than most people assume it to be.

Every dimension is a range, and the range is the specification

Nothing has ever been manufactured to an exact size. Cutting tools wear, machines flex under load, materials spring back, temperature moves everything. A part that is "25 mm" is a part that came out somewhere near 25 mm, and the engineering question is only ever how near is near enough.

That permitted band is the tolerance, and the crucial reframing is that the tolerance is not a grudging allowance for sloppiness. It is the actual specification. A drawing that says 25 mm without a tolerance has not specified anything manufacturable.

The reason tolerances are not simply made very tight everywhere is cost, and the relationship is brutally non-linear. Loosening or tightening by a factor of two does not change cost by a factor of two. Each step tighter can mean a different process — turning, then grinding, then lapping — slower feeds, more frequent tool changes, better machines, a more skilled operator, more inspection, and more scrap. A tolerance that is ten times tighter than the function requires is not caution. It is money spent for nothing, and in a competitive shop it is the difference between winning a job and losing it.

The corresponding failure is the opposite one: tolerancing by habit, copying the title-block default onto every dimension, so the features that matter and the features that do not are held to the same standard. Good tolerancing is an act of deciding what the part is actually for.

Small errors add up, but not the way you expect

Assemblies stack. Ten plates, each 10 mm thick with a tolerance of ±0.1 mm, are bolted into a column. What is the tolerance on the total height?

The worst-case answer is ±1.0 mm — every plate at its maximum, or every plate at its minimum. Designing to worst case guarantees the assembly always works, and it is often absurdly conservative, because it assumes an outcome that in practice essentially never occurs.

The statistical answer is different. If the plate thicknesses vary independently around their nominal values, the variations partly cancel, and the combined variation grows with the square root of the number of parts rather than in proportion to it — around ±0.32 mm for the same ten plates. That is a third of the worst-case figure, and designing to it allows much looser and cheaper part tolerances.

The catch is the assumption. Statistical stacking is valid when the errors are genuinely independent and roughly centred. If all ten plates came from one machine on one shift with a worn tool, they are not independent — every one is oversized in the same direction, and the errors add rather than cancel. This is precisely how a design validated statistically fails in production when a supplier consolidates a batch, and it is one of the more common ways good analysis produces bad outcomes.

Size is not shape, and it is not position

Here is the failure the opening example was actually about.

A hole can be exactly the right diameter everywhere and be in the wrong place. A shaft can measure 25.00 mm across every diameter you check and be bent, so no single measurement reveals it. A bore can be the right size and oval — measure across one axis and it is 25.05, across the perpendicular axis it is 24.98, and a two-point measurement taken in one orientation reports a pass. A machined face can be the right distance away and not be flat, or be flat and not perpendicular to the face it must seal against.

Size does not capture form, orientation or location. This is why geometric dimensioning and tolerancing exists — a formal language for specifying flatness, straightness, circularity, cylindricity, perpendicularity, parallelism, position, concentricity and runout, separately from size. When people say a part "passed inspection but didn't fit", the usual explanation is that the drawing controlled size and the failure was in something size cannot see.

Attached to this is datums, which are quietly the most important idea in the whole subject. A measurement is meaningless without stating what it is measured from. If a drawing does not establish a reference frame, then the designer measures from one face, the machinist sets up from another, and the inspector places the part on a third — and all three get different, defensible numbers for the same feature. A large share of supplier disputes are not disagreements about the part. They are disagreements about the origin.

A tolerance is a decision about what the part must do. A drawing that does not say what to measure from has not made that decision, and every party downstream will make it differently.

The measurement is not the truth

Inspection has its own variation, and it is easy to forget that a measured value is an estimate.

If a tolerance band is 0.02 mm wide and the measuring instrument, the fixture and the operator together produce readings that vary by 0.01 mm on the same part, then a large fraction of what the inspection is reporting is the measurement system talking to itself. Good parts get rejected, bad parts get accepted, and the scrap rate becomes a property of the gauge rather than the process. The usual working rule is that the measurement system's variation should consume no more than about a tenth of the tolerance band, and the formal way of checking this is a gauge repeatability and reproducibility study.

Temperature deserves a paragraph of its own, because it is routinely ignored and it is not small. Dimensional metrology is defined at a reference temperature of 20 °C. Steel expands by roughly 11 to 12 micrometres per metre per degree. A one-metre steel component measured on a shop floor at 35 °C is about 0.18 mm longer than the same component at 20 °C — a difference that dwarfs many tolerances it is being checked against. On an uncooled Indian shop floor in summer, a part machined in the afternoon and inspected in the morning has genuinely changed size between the two events. Precision work either happens in a temperature-controlled room or it happens with a correction applied, and a workshop that does neither is measuring the weather.

Capability, and why interchangeability was the point

Two more ideas complete the picture.

Process capability compares the tolerance band with the actual spread of the process producing the parts. If the process spread is wider than the tolerance, no amount of inspection fixes the situation — you are sorting, not manufacturing, and the good parts are an accident. The capability indices used in industry exist to make that comparison explicit before production begins rather than after the rejections arrive.

Interchangeability is the reason all of this matters commercially. The historical shift from craft to manufacture was the shift from fitting each part to its mating part by hand, to making parts that any example of A fits any example of B. That is what makes spares possible, assembly lines possible, and multiple suppliers possible. Every time a workshop says "we'll file it to fit", it is quietly stepping back across that line — the assembly works, and the part is no longer a part, it is a one-off, and the machine can no longer be repaired with a component bought from anyone else.

Why it matters for students and researchers

Tolerancing is where design meets economics, and it is chronically under-taught relative to its importance — a graduate can typically calculate stresses in a beam and has often never had to decide whether a hole needs positional control.

The research questions are practical and, for India especially, consequential. Tolerance allocation is a genuine optimisation problem: given a functional requirement on an assembly, how should the allowable variation be distributed across parts to minimise total manufacturing cost, and it becomes harder and more interesting with real supplier constraints. In-process and on-machine measurement, which closes the loop rather than inspecting after the fact, is advancing quickly. Additive manufacturing has its own tolerance and surface behaviour that the existing standards were not written for. And metrology in uncontrolled environments — how to get trustworthy measurements in a workshop that will never have a climate-controlled room — is exactly the kind of problem that matters enormously in practice and attracts little publication.

That applied, immediately usable emphasis is what the International Journal of Machine Systems and Manufacturing Technology (ISSN 3108-1266) sets out to publish — a peer-reviewed hybrid open-access journal launched in 2023, explicitly favouring work focused on application across machine systems and manufacturing technology. For mechanical and production engineering students, tolerancing is worth more attention than it usually gets: it is the part of a drawing that decides what the part costs, whether it can be inspected honestly, and whether it will fit something made in a different factory next year.

Frequently asked questions

What is a manufacturing tolerance?

The permitted range of variation for a dimension. Since no part can be made to an exact size, the tolerance is the real specification, and a dimension quoted without one has not specified anything manufacturable.

Why not just make all tolerances very tight?

Because cost rises steeply and non-linearly as tolerances tighten — often requiring different processes, slower machining, better equipment, more inspection and more scrap. Tolerances should be set by what the part functionally needs, not by habit.

What is tolerance stack-up?

The accumulation of individual part tolerances across an assembly. Worst-case stacking adds them directly and is very conservative; statistical stacking assumes independent variation and grows with the square root of the number of parts, but is invalid if the parts share a common source of error.

How can a part be the right size and still be wrong?

Because size does not describe form, orientation or location. A hole can be the correct diameter but in the wrong position; a shaft can measure correctly at every point and still be bent; a bore can be oval and pass a single two-point measurement. Geometric tolerancing exists to control these separately.

Why do drawings specify datums?

Because a measurement has no meaning without a stated reference. Without datums, the designer, machinist and inspector each measure from different faces and obtain different but defensible results for the same feature.

Does temperature really affect measurement?

Yes. Metrology is defined at 20 °C, and steel changes by roughly 11 to 12 micrometres per metre per degree. A one-metre part measured at 35 °C reads about 0.18 mm longer than at 20 °C, which exceeds many tolerances being checked.