[my_username_is_]

>Reputable factories will test 100% of every product shipped.

Frankly, this just isn't true. It depends on your expected defect rate, how your defect rate drifts over time, the cost of doing 100% inspection, and effects of product failures. If you're making safety-critical gear, yes you will probably inspect 100%. If you're making injection molded clamshells for connected consumer products, you're probably only doing inspection in batches.

[kev009]

I guess it depends on the industry but it is somewhat common for electronic components. There are a lot of failure modes in parts, picking, soldering, and assembly. The economics widely favor doing testing at manufacturing time (versus something like at a distributor or dealing with customer RMA which may come with other externalities like brand damage) because boards can be reworked in the factory and you avoid other waste like packaging, shipping, and tariffs.

Back in the day extremely elaborate and massive bed of nails in circuit test rigs would poke the leads of a through hole circuit board to do continuity testing and basic functions checks. Now a lot of that can be done with JTAG circuitry, a serial bus many ASICs implement and chain together to provide less invasive way to similar tests. Xray, thermal, optical scanners are often used in various parts of the assembly. And of course plenty of humans. Test rig design is a big part of any manufacturing process and may be used to verify overall system function like button presses and connector fidelity.

As a separate but related thought, in VLSI: verification design, for both manufacturing and BIST, can easily eclipse the rest of the design in some ASICs in terms of cost/effort/complexity.

Software engineering is kind of the odd duck in that it is frequently a shoot first ask questions later pursuit in most organizations (funnily, even commonly in places like semiconductor companies that invent and progress new formal methods). There are plenty of decent tools like Lamport's TLA+ that aren't widely used in addition to more familiar aspects of code test.