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Published equation contexts

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

Why this formula appears here

The arithmetic behind that reputation is straightforward and still governs every multi-die package built today. A packaged part’s yield is not the yield of its worst component; it is 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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YpkgY_{\text{pkg}}

Symbol Y_pkg

YpY_pkg is part of the quantity the equation computes from the expression on the right.

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YassyY_{\text{assy}}

Symbol Y_assy

YaY_assy is an input to the expression that computes the quantity on the left.

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ii

Symbol i

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

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NN

Symbol N

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

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i=1i=1

Starting index or lower bound: i=1

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

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NN

Ending index or upper bound: N

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

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Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

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

Equation 5 · AI Hardware & Semiconductors

From Origins to Frontier: A History of Chiplets and Advanced Packaging

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

The arithmetic behind that reputation is straightforward and still governs every multi-die package built today. A packaged part’s yield is not the yield of its worst component; it is 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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