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Equation 14 · Part 4 · When the Substrate Became the Product

Symbol N

Ypkg=Yassy∏i=1NYi.Y_{\mathrm{pkg}} = Y_{\mathrm{assy}} \prod_{i=1}^{N} Y_i .
NN

What this part means

N appears in the bound of this product. The bound states where the repeated operation starts, ends, or which values it includes.

Its job in the formula

N appears in the bound of this product. The bound states where the repeated operation starts, ends, or which values it includes.

The passage around this formula

A multi-die package inherits a property that a single die does not have: its yield is a product, not a term. If a package contains dies with individual probabilities YiY_i of being good, and the assembly itself succeeds with probability YassyY_{\mathrm{assy}} , then Ypkg=Yassy∏i=1NYiY_{\mathrm{pkg}} = Y_{\mathrm{assy}} \prod_{i=1}^{N} Y_i . 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 YiY_i…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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