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DFT should not add more than 1~10 % of the product cost depending on volume.
It should detection >99% of most common faults, which are related to manufacturing and design flaws. Advanced test design will also location >99% of faults.
There is a wide array of tools from BITE, (built-in Test equip), Analog, Digital, ATE low level and functional testers ($K xxx) POST, Auto-cal.
The most important aspect is for an experienced Test Engineer to be part of the design team from the start and ensure the design spec is detailed enough to use a starting point for Test verification.
Much of Design , in DFT is electro-mechanical as layout, chip, PCB and system interconnects are critical for access to test points. But there is also a lot of parametric tests and statistics involved with monitoring Quality with test results.
Xbar, 3 sigma and Design Margin Analysis and testing (Cpk) during DVT with all environmental stress tests incl HALT, that determine which subset of tests will be kept for production. HASS is another method for accelerating test margin to predict failures.