A 1400 mm office desk was built from two drawings, and both of them said the cable port sat 250 mm from the rear edge. They were 20 mm apart. The desk was assembled from both, and nobody ever measured the two together.

Two drawings, one number, and a desk that came out wrong

A European office fit-out company ordered 360 executive desks from a factory in Foshan. The desk was a 1400 by 700 mm desktop on a powder-coated steel frame, with a 60 mm cable port in the top, a cover plate over the port and a brush seal inside the cover. The unit price was $175 and the order was $63,000. Thirty per cent, $18,900, was paid on order. Seventy per cent, $44,100, was due against a pre-shipment inspection report.

The buyer had approved the desktop as a finish sample and the frame as a metal-finish sample. They were approved in different rooms, on different days, by different people, and they were never assembled together before the panels were cut.

The cable port was the fault, and it was twenty millimetres out on every desk in the lot. The interesting part is not that it was out. It is that every party who touched the order did their job correctly, and the desk was still wrong.

Where the twenty millimetres came from

Two drawings described the same hole. The factory's product drawing went to the panel shop, which cut the desktops. The frame was bought in as a sub-assembly from a frame maker, and the frame maker's drawing showed the cable exit hole and the cover bracket already positioned.

Both drawings put the cable port centre 250 mm from the rear edge. That was the whole of it, and it was enough to be wrong, because on this desk there are two rear edges and they are 20 mm apart.

The desktop overhangs the frame at the back. The steel frame's rear rail face sits 20 mm forward of the desktop's rear edge, because the desktop is carried on two mounting brackets set behind the rail. A frame hole dimensioned 250 mm from the rail face therefore lands 270 mm from the desktop's rear edge, while a desktop hole dimensioned 250 mm from the desktop's rear edge lands 250 mm from it. Both drawings were correct. Both factories built to their own drawing. The two holes were 20 mm apart.

This is the thing nobody writes down. The interface between two parts is not a number on either part's drawing. It only exists once the parts are in the same object, and by then the panels are cut.

Eight millimetres of overlap, and what twenty millimetres does to it

The cover plate is not decoration. It carries the brush seal that grips the cables, and it covers the cut edge of the desktop cut-out so that a cable dragged across the desk does not meet a raw board edge. The drawing therefore required the plate to overlap the 60 mm cut-out by at least 8 mm all round.

A 76 mm plate over a 60 mm cut-out gives exactly 8 mm of overlap on each side when the two are concentric. Twenty millimetres of offset takes 8 mm of that away on one side and adds 20 mm on the other.

So the measured result was 12 mm of open cut-out on the rear side of the port and 28 mm of overlap on the front side. Nobody would see that by looking at a cover plate. A plate that overlaps by 28 mm looks exactly like one that overlaps by 8 mm, because in both cases the plate covers the hole. It has to be measured.

What the gap did to a cable

The exposed strip is not a clean edge. It is the cut edge of a 25 mm melamine-faced particle board panel, cut in a saw kerf and left as it came out of the router. It is the one surface on the desk that is not finished.

That strip sits exactly where a cable changes direction. A cable comes down through the 60 mm port, turns, and drops into the frame's exit hole to reach the floor box. On a correct desk the turn happens inside the brush and the cut edge sits behind the seal. On this desk the cut edge was on the outside of the seal, on the side the cable rubs against.

The inspector's check was a cable, not a gauge. A 6.4 mm three-core mains lead was pushed through the port of an assembled desk. On a correct build the cable goes straight down and the brush closes on it. Here it had to be pushed sideways 20 mm to find the frame's exit hole, and it had to pass over the raw edge to get there.

On two of three attempts the outer jacket of the lead came out with a visible scuff. On the desk that had been opened and closed the most, the jacket carried a 4 mm scratch along the line where it had been dragged across the cut edge. A desk specified to take a power lead through the top without damaging it was a desk that damaged the lead.

None of this shows in a photograph of a closed cover plate, and none of it shows in a report that records the cable port as present.

Why the bench check of each part passed

The panel shop had cut a correct desktop. Every hole was on the drawing dimension, within the tool's own tolerance. The frame maker had built a correct frame. The cover bracket was where the frame drawing said, and the exit hole was punched to the same dimension from the same rear face.

The factory ran its own assembly check on every desk: the cover clips onto the bracket, the brush sits in it, the desk ships. That check passed on all 360. A cover that is 20 mm out still clips on, because the clip engages the bracket and the bracket is where it is. The clip does not care whether the plate overlaps the hole.

So the factory had a check that passed on every unit, a buyer who had approved two part samples separately, and a drawing set with no dimension that joined them. The defect lived only in the assembly, and no check in the chain was pointed at the assembly.

This is worth saying plainly, because the usual explanation after the fact is that the inspection was not thorough enough. That is not what happened here. The factory checked the assembly. It checked the wrong property of the assembly.

The measurement that found it, and the twelve that explained it

The inspector measured across the interface, on an assembled desk, from one physical edge: the rear edge of the desktop. The centre of the cut-out was at 250.0 mm. The centre of the cover plate, on the same desk and measured from the same edge, was at 270.0 mm. The difference was 20.0 mm.

Both numbers were correct against their own drawings. Neither was correct against the other, and only one of them was a number the buyer had ever been given.

Then twelve desks were measured. The offsets came out at 19.6, 19.9, 20.1, 20.0, 19.8, 20.2, 20.0, 19.9, 20.1, 19.7, 20.0 and 19.9 mm. The spread across twelve desks was 0.6 mm, against an error of 20 mm.

What the sampling plan could and could not have told you

The lot was 360 desks. Under ISO 2859-1 that falls in code letter H, and general inspection level II gives a sample of 50. At AQL 2.5 the accept number is 3 and the reject number is 4.

Those are the right numbers for a random defect. If the 20 mm error had turned up on 8 of the 360 desks instead of all of them, a 50-unit sample would have found it with probability 70.2%, and a single defective desk in the lot would have been missed with probability 86.1%.

Neither figure applies here, and that is the point worth taking away. The defect was on 100% of the lot. One desk would have found it, a hundred would have found it, and no sample size at all would have found it if the inspector had been counting defects instead of measuring one.

Sampling tells you how many are bad. It does not tell you whether the drawing is right. Those are different questions and they need different instruments: a sample answers the first, and a measurement taken across an interface answers the second.

Twelve desks were worth measuring, not because twelve finds more than one does, but because twelve tells you whether the fault is systematic. One desk proves there is a fault. Twelve prove whether there is one fault or three hundred and sixty.

What the report had to say

A report that said the cable port was 20 mm off position and the lot was rejected would have been true and would have told the buyer almost nothing. The buyer still had to decide whether to scrap the desktops, rework the frames or sort the lot, and the report had to make that decision possible.

So the report carried five things.

• The datum for every measurement, stated on the page: the rear edge of the desktop, on the assembled desk, standing on its frame. A number without its reference is not a finding.
• Both drawings, by number and by the line that conflicts, so the buyer could see that the fault was in the specification and not in the factory's workmanship.
• The twelve offsets, with the mean and the spread, because the difference between a systematic fault and a random fault decides whether 12 desks or 360 are affected.
• The consequence in use, not the deviation: 12 mm of exposed cut edge, a 4 mm scuff in a cable jacket, and the fact that the cover plate still clipped on and would have passed a factory check.
• What was not verified: the cable management inside the frame beyond the exit hole, and whether the frame maker's incoming inspection had checked the bracket against the frame drawing. A report that lists only what it checked reads as a clean bill of health for everything it did not check.

The bill, and which part had to change

The factory could change the desktop or the frame. The desktop was a finished melamine face. Re-cutting a new hole in it would have left the old one, and filling the old one in melamine over particle board leaves a plug you can see under a desk lamp. Replacing 360 desktops at $46 each would have cost $16,560.

The frame had 20 mm of plain steel in the right place. Moving the cover bracket and re-punching the 60 mm exit hole 20 mm rearward on every frame was $11 of labour and $5 of bracket and fixings each, so $16 a frame and $5,760 for the lot.

The factory reworked the frames. It also drew the lesson the buyer cared about more: this was a specification error, so the fix belonged in the drawing. Correcting it on the shop floor without changing the product drawing would have produced the same twenty millimetres on the next order cut from the same files.

The inspection that found it cost $398, two man-days at $199, which is 0.6% of the order value. The rework it prevented came to $5,760, which is 9.1%. The buyer withheld the $44,100 balance and released it after the frames were reworked and re-checked.

The specification lines that would have caught this

None of this needed a better instrument. It needed six lines in the purchase order and one on the drawing.

• Name the datum, and mark it on the part. 250 mm from the rear edge of the desktop, plus a physical reference point on every frame and every top so that both are dimensioned from the same place. A dimension that names an edge nobody can find is not a dimension.
• Write the requirement as an interface condition, not a part dimension: the cover plate overlaps the 60 mm cut-out by at least 8 mm all round on the assembled desk, with no exposed panel edge. That sentence can be checked by measuring across the assembly, which is where the fault lived.
• Use a position tolerance across the interface instead of two independent ones: cut-out position to the frame datum, diameter 0.8, rather than a 250 mm dimension on the top and a 250 mm dimension on the frame.
• State that the drawing applies to the assembled desk. If a buyer can approve a panel and a frame separately, and both approvals are honest, the purchase order has to say that approval covers the assembly.
• Require one assembled first article, built from a production frame and a production top, before any panel is cut. The defect was visible in one unit in about four minutes with a tape measure.
• Put the cable in the check: a 6.4 mm lead must pass through the port on the assembled desk and the brush must grip it. A functional test catches a misaligned cover that a dimensional check on the cover alone never will.

Three questions to ask before the panels are cut

Does every position dimension on the drawing name an edge that exists on the part being cut, and is that edge marked on the part itself.

Which two parts have to line up, and is that relationship written as a measurable condition on the assembled desk rather than as a dimension on each part.

Is the first article an assembled desk, or a set of parts that have each been approved on their own.

None of those needs a gauge, a factory visit or a sample size. They are three questions to send to the factory before a single panel is cut, and three lines to add to the furniture QC Foshan brief that goes out with the purchase order.