Cpk, Explained

Cpk is the actual capability index. Where Cp asks whether a process could fit its specification if perfectly centered, Cpk measures how well it fits right now, wherever its average happens to sit. It takes the distance from the process average to the nearest specification limit, divides by three standard deviations, and reports the worse side.

How it works

Cpk can never exceed Cp; centering can only be imperfect. The gap between the two indices is therefore a diagnosis. When Cpk roughly equals Cp, the process is well centered, and improving capability means reducing variation — usually the hard, expensive road. When Cpk sits well below Cp, the process is off center, and the cheapest improvement available is simply moving the average. Cpk also works with one-sided specifications, where only an upper or a lower limit exists.

As with every capability index, Cpk assumes a stable process and a trustworthy measurement system. Without both, the number is decoration.

One habit separates careful practitioners: they ask what the index will be used for before quoting it. A Cpk destined for a customer report needs the long-term honesty of Ppk beside it; a Cpk guiding this week’s machine adjustment can lean on recent data alone. The arithmetic is identical either way — the obligation the number carries is not.

A worked mini-example

Return to the illustrative bottling line from the Cp entry: limits at 490 and 510 millilitres, standard deviation 2.5, so three standard deviations is 7.5. Suppose the average has drifted to 503. The upper side gives 510 minus 503 over 7.5, or 0.93; the lower side gives 503 minus 490 over 7.5, or 1.73. Cpk is the worse of the two: 0.93 — inadequate, despite the healthy Cp of 1.33. The diagnosis is written in the gap between the indices: the spread is fine, the centering is not, and re-centering the fill volume is the fix.

• Always read Cpk next to Cp; the gap tells you whether to re-center or reduce variation
• A Cpk that looks fine over a short sample can hide long-term drift — compare with Ppk
• Confirm stability and measurement quality first; the index inherits their flaws
• Do not chase Cpk by trimming data or widening specs; the customer notices eventually
• Benchmarks such as 1.33 are starting points, not laws — the right target depends on risk

Cp measures the width of the garage. Cpk asks how well you parked.

Cpk is taught alongside Cp in the capability portion of our Green Belt program — $299, about 35 hours, ending in a 100-question proctored exam. Black Belt carries the topic further, into non-normal capability and tolerance analysis.