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Equation 12 · Part 10 · How Advanced Semiconductor Fabrication Actually Works

Numerator: mu - LSL

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

What this part means

The complete quantity above the fraction bar.

Its job in the formula

mu - LSL occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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.