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Equation 12 · Part 3 · How Advanced Semiconductor Fabrication Actually Works

Symbol σ

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

What this part means

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

Its job in the formula

σ 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 variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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