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Equation 5 · Part 10 · From Origins to Frontier: A History of Chiplets and Advanced Packaging

Ending index or upper bound: N

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

What this part means

This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.

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

…the product of every component’s yield together with the yield of the assembly step that joins them. Write the package yield YpkgY_{\text{pkg}} as a function of the assembly yield YassyY_{\text{assy}} and the yield YiY_i of each of N individual die placed into the package: Ypkg=Yassy∏i=1NYiY_{\text{pkg}} = Y_{\text{assy}} \prod_{i=1}^{N} Y_i . Multiplication is unforgiving at scale. Every die added to a package is another factor less than one, so a package holding several die each individually manufactured at a very respectable yield can still fail at an uncomfortable rate…

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Learn the underlying idea

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

Open the illustrated sums and products: repeat an operation over an index guide →

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.