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Equation 3 · Part 9 · Chiplets and Advanced Packaging in Practice: An Advanced Technical Guide

Starting index or lower bound: i=1

Ypackage≈∏i=1nyiY_{\text{package}} \approx \prod_{i=1}^{n} y_i
i=1i=1

What this part means

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.

Its job in the formula

i=1 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 arithmetic behind that claim is a plain probability composition, and it is worth writing down because it is the one piece of real math in advanced packaging that most design reviews skip past. If each of n chiplets bonded into one package has an independent per-die yield yiy_i , the assembly’s final yield is approximately Ypackage≈∏i=1nyiY_{\text{package}} \approx \prod_{i=1}^{n} y_i. which is a first-order model — it assumes bonding introduces no additional defects and that die yields are independent, both of which are simplifications addressed separately below. Even under this optimistic assumption, four chiplets each yielding 95% compose to roughly 81% assembly yield, and a twenty-die stack at the same per-die yield falls to…

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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.

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Sources cited in the surrounding passage

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