Statistical Model
Dimensional tolerance analysis models radial positioning errors that result from independent normal distributions on orthogonal axes. The Rayleigh distribution provides the continuous probability distribution governing vector magnitude offsets in two-dimensional positional alignment. Printed circuit board fab labs apply this model to evaluate drill true position performance.
Position Variation
Radial deviation of a drilled hole from its theoretical center represents a vector composite of X and Y axis positional errors. Applying the Rayleigh distribution models this radial distance, assuming X and Y error components are normally distributed, uncorrelated, and possess equal variance. The resulting probability density function describes the likelihood of radial drill drift exceeding designated annular ring safety limits.
Process capability indices derived from radial distributions yield accurate yield predictions for microvia landing pads. Asymmetric axis movement or spindle runout distorts the distribution, signaling mechanical drill wear or table alignment failures. Statistical quality software fits empirical coordinate data against this theoretical curve to establish process control thresholds.
Capability Calculation
Advanced statistical process control tools utilize radial error models to set machine acceptance limits. Evaluating drilling results with a Rayleigh distribution ensures that radial alignment tolerances reflect real-world two-dimensional variance. Process engineers calculate required capture pad diameters based on predicted distribution percentiles.
Yield modeling accuracy improves when radial vector models replace simple linear axis metrics.
