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Equation 14 · Part 2 · When the Substrate Became the Product

Symbol Y_assy

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

What this part means

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

Its job in the formula

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

The passage around this formula

…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…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

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Sources cited in the article section

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