Equation 15 · When the Substrate Became the Product
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the dies with individual probabilities. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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subscript
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
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What the article says around this equation
Multiplication is brutal at scale. Eight components at 99 percent each land near 92 percent together before assembly loss is counted; the same eight at 95 percent land near 66 percent. And the loss is not proportional to the failing part — scrapping a package destroys every good die in it plus the assembly work. This is precisely why known-good-die testing dominates the discussion: the whole point is to move the terms as close to unity as possible before dies are committed to an assembly that cannot be undone.
Sources cited in the article section
- [2] Chiplet Actuary: A Quantitative Cost Model and Multi-Chiplet Architecture Exploration ↗
- [9] Opportunities and Challenges for 3D Systems and Their Design ↗
- [11] Heterogeneous Integration Roadmap ↗
These citations give research context. Read each source to check which claims it supports.