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edfas.org ELECTRONIC DEV ICE FA I LURE ANALYSIS | VOLUME 24 NO . 3 10 in curve a, the lme cannot estimate the lot component and, similar to the prior t-test results, without being able to properly account for that lot variance component, the effective α increases. Curve b, with 5 lots, is able to allow for the lot variance component to bring the effective α back down to the 0.05 level but as we saw earlier within W2W, the power is greatly reduced. To approach our desired targets of α = 0.05 and power = 0.8, we would need to sample something on the order of 16 lots from our L2L MC (curve d, Fig. 11). CONCLUSION The inherent nature of sites embed- ded within wafers embedded within lots induces a hierarchical variance component structure that will impact statistical sampling properties. The operational characteristics of acceptance sampling will be sensitive to the relative difference between cumulative components at/above versus within the level at which sampling occurs. The operational char- acteristics of statistical hypothesis testingwill be sensitive to the relative proportions of variance components across all levels. To achieve a desired α and power in hypothesis testing, lots and wafers need to be declared as nested random effects and a suitable sample size established across all levels based on their relative contributions to the overall variance. [6] REFERENCES 1. NIST/SEMATECH e-Handbook of Statistical Methods, Chapter 1.3.6.6.18. Binomial Distribution, https://www.itl.nist.gov/div898/ handbook/eda/section3/eda366i.htm, 2013. 2. NIST/SEMATECHe-Handbook of Statistical Methods, Chapter 1.3.5.3. Two-Sample t-Test for Equal Means, https://www.itl.nist.gov/div898/ handbook/eda/section3/eda353.htm, 2013. 3. NIST/SEMATECHe-Handbook of Statistical Methods, Chapter 7.2.2.2. Sample sizes required, https://www.itl.nist.gov/div898/handbook / prc/section2/prc222.htm, 2013. Fig. 11 L2L: lme OC curves under sequential sampling of lots. 4. R Core Team (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, https://www.R-project.org/. 5. J. Pinheiro, D. Bates, S. DebRoy, D. Sarkar, and R Core Team: nlme: Linear andNonlinear Mixed Effects Models. R package version 3.1-148, https://CRAN.R-project.org/package =nlme, 2020. 6. A. Brendler, P. McCutcheon, and P. Moffat: “Effective Sample Size in the Presence of Batch Effects,” ISMI Symposium, 2008. ABOUT THE AUTHOR David Potts received his B.S. in electrical engineering from Lehigh University, Bethlehem, Pa., and M.S. in statistics from the University of Southern Maine, Portland, Maine. Throughout his career in semicon- ductor manufacturing, he has held positions within failure analysis, quality control, product characterization, statistical SPICE circuit modeling, and yield engineering. Current interests include enhancing data architecture and analyt- ics efficiency in support of rapid optimization of process performance and yield. Advertise in Electronic Device Failure Analysis magazine! For information about advertising in Electronic Device Failure Analysis: Kelly Johanns, Business Development Manager 440.318.4702, kelly.johanns@asminternational.org Current rate card may be viewed online at asminternational.org/mediakit.