 NIST and SEMATECH e-Handbook of Statistical Methods

Publisher: National Institute of Standards and Technology.

Section 1.3.6.6.11, Gamma Distribution: www.itl.nist.gov/div898/handbook/eda/section3/eda366b.htm gives density, shape/scale conventions and the gamma-function integral. Section 1.3.6.6.9, Lognormal Distribution: www.itl.nist.gov/div898/handbook/eda/section3/eda3669.htm defines the logarithmic-normal parameterization and gives mean, standard deviation and coefficient of variation. These conventions support the original inverse-moment derivations in the thickness-model article.

Section 7.2.4.1, Confidence intervals: www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm . The subsections One-sided confidence intervals and Exact Intervals for Small Numbers of Failures explain one-sided limits and binomial-tail inversion. Inverting the extreme probabilities gives an upper event-probability bound one minus alpha raised to the power one over n for zero events, and a lower detection-probability bound beta raised to the power one over m for all-success calibration. The joint-coverage and rare-event examples are original derivations, not NIST experimental data.

Section 7.4.7.3, Bonferroni’s method, www.itl.nist.gov/div898/handbook/prc/section4/prc473.htm : simultaneously valid statements are obtained by dividing the allowed error probability among comparisons. This supplies the finite-candidate coverage principle used in the confidence-allocation article; the uniform-location counterexample there is an original construction.