What does this equation mean?

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 number, the process capability index, $C_{pk} = \min\left(\frac{\mathrm{USL} - \mu}{3\sigma},\ \frac{\mu - \mathrm{LSL}}{3\sigma}\right)$. comparing the distance from the process mean $\mu$ to its nearer specification limit against three standard deviations of the process’s own spread. A $C_{pk}$ at or above about 1.33 is generally treated as acceptable capability, 1.67 or above as excellent, and below 1.0 as a process that cannot reliably meet its own specification even when perfectly centered [ 10 ] . The index does one specific job: it converts “how tight is this distribution” and “how close is it to the edge of what’s allowed” into one comparable number across hundreds of different measured parameters in the same fab.