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Equation 12 · Part 11 · How Advanced Semiconductor Fabrication Actually Works

Denominator: 3σ

Cpk=min⁡(USL−μ3σ, μ−LSL3σ),C_{pk} = \min\left(\frac{\mathrm{USL} - \mu}{3\sigma},\ \frac{\mu - \mathrm{LSL}}{3\sigma}\right),
3σ3\sigma

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

3σ occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

The oldest tool for doing this is the control chart, and it works by testing a sequence of measurements against known patterns rather than against a single pass/fail threshold. The classic Western Electric decision rules flag a process as suspect if, for example, a single point lands more than three standard deviations from the target, or two of three consecutive points land beyond two standard deviations, or a long run of consecutive points falls on the same side of the target line — patterns that are each individually unlikely under normal random variation and therefore signal that something about the process, not the sample, has changed [ 10 ] . Alongside the chart sits a single summary…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

Open the illustrated fractions: division written vertically guide →

Sources cited in the surrounding passage

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