Quantifying Structural Netlist Coverage Limitations Using Standard IEEE Boundary Scan Protocols
Boundary scan netlist coverage is bounded by physical TAP access, requiring explicit fault universe math to quantify unverified structural escape risks.
Williams and Brown Formula
Coverage Calculation
Mathematical models predicting the escape rate of defective boards based on the fault coverage of the test program assist in quality planning. Production engineers use the williams and brown formula to estimate the defect levels in shipped products after testing. This calculation relates the defect rate of the shipped boards to the defect rate before testing and the test fault coverage.
This provides a clear metric for deciding whether further test development is required to meet quality targets.
Mathematical Model
High-yield goals on the assembly line require a balance between the cost of test vector generation and the reduction of shipped defects. The calculation uses the function where the output defect level is the initial defect level raised to the power of one minus the fault coverage. This exponential relationship shows that even a small increase in fault coverage can yield a massive reduction in the number of defective boards that escape to the customer.
When test coverage is low, the escape rate rises rapidly even if the initial assembly quality is high.
Quality Management
Applying this equation allows manufacturers to justify the time spent developing comprehensive boundary-scan tests and x-ray inspection routines. If the estimated escape rate is above the contract threshold, engineers must add additional test points or automated optical inspection steps. This mathematical guidance transforms test development from a guessing game into a predictable quality assurance process.