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An integrated and compact model for probability of failure in carbon nanotube field-effect transistors (CNFETs) that includes 1) void CNFETs, 2) carbon nanotube (CNT) density variation, and 3) metallic CNTs is presented based on binomial probability distribution. Comparison with experimental data shows that the compact model successfully predicts the failure probability in CNFET devices. The model is used in a new design space to explore tradeoffs, key limitations, and opportunities for today's gigascale CNFET integrated systems. To achieve 1-part-per-billion failure rate in a gigascale system, it is shown that an asymmetrically correlated stack of 25 CNFETs, each containing 18 CNTs in the channel can be used when the probability of metallic CNT occurrence is reduced to 3%. However, if the density of metallic CNTs approaches zero, then a similar failure rate can be achieved with a single CNFET that contains 15 CNTs in the channel.