How this instrument works
Process capability indices answer a manufacturing question: given how tightly your specification limits are set and how much your process naturally varies, is the process actually capable of staying inside those limits? Cp compares the width of the tolerance band (USL minus LSL) to six standard deviations of the process — six because nearly all of a normally distributed process's output falls within plus-or-minus three sigma of its mean. A Cp of 1.0 means the spec width exactly equals that six-sigma spread, with no room to spare.
Cp has one blind spot: it only looks at spread, not where the process is actually centered. A process could have excellent Cp and still produce defects if its mean has drifted toward one spec limit. Cpk fixes this by taking the smaller of two ratios — the distance from the mean up to the upper limit, and the distance from the mean down to the lower limit — each divided by three sigma. Cpk can never exceed Cp; the two are equal only when the process is perfectly centered between USL and LSL.
In practice, quality engineers treat Cpk as the headline number precisely because it penalizes off-center processes that Cp alone would miss. A commonly cited rule of thumb treats Cpk of 1.33 or higher as capable and 1.67 or higher as excellent for many industries, though the right threshold depends on the process and the cost of a defect — this calculator reports the raw indices so you can apply whatever standard your process calls for.
- Enter the upper specification limit into USL — the highest acceptable value for the process output.
- Enter the lower specification limit into LSL — the lowest acceptable value.
- Enter the process mean — the average of your measured process output.
- Enter the process standard deviation (sigma) — how much individual measurements typically vary from that mean.
- Read Cp (spread only) and Cpk (spread and centering) — Cpk is the number most quality standards actually use to judge capability.
Worked example — an off-center process shifts Cpk down
A process has spec limits USL = 63 and LSL = 57, with sigma = 1. Enter those into the calculator along with a process mean of 61 — deliberately shifted 1 unit above the spec midpoint of 60. Cp = (63−57)/(6×1) = 6/6 = 1.0 exactly — spec width equals six sigma, the same result as if the process were perfectly centered.
Cpk tells a different story: Cpk = min[(63−61)/3, (61−57)/3] = min(0.6667, 1.3333) = 0.6667. The upper limit is now much closer to the process mean than the lower limit is, so the smaller ratio — the one facing the nearer limit — drags Cpk well below Cp. This is exactly why Cpk, not Cp, is the number most quality standards check first: it catches an off-center process that Cp alone would report as perfectly fine.
Questions
What's the difference between Cp and Cpk?
Cp measures only how wide the process spread is relative to the tolerance band — it assumes the process is perfectly centered between the spec limits, even when it isn't. Cpk corrects for that by using whichever spec limit the process mean is actually closer to, so a process that drifts toward one limit gets a lower Cpk even though its Cp stays unchanged. Cpk is always less than or equal to Cp, and the two are equal only when the process is perfectly centered.
What counts as a 'good' Cpk value?
There's no single universal cutoff, but common quality-engineering guidance treats Cpk below 1.0 as not capable (some output will fall outside spec even under normal variation), 1.0-1.33 as marginally capable, 1.33-1.67 as capable, and above 1.67 as excellent. Automotive and aerospace suppliers often require Cpk of 1.33 or higher as a contractual minimum. Always check what standard applies to your specific industry and process before treating any threshold as a hard rule.
Can Cpk be negative?
Yes — if the process mean has drifted past one of the spec limits entirely, the distance from the mean to that limit becomes negative, and Cpk goes negative too. A negative Cpk means the process's central tendency is already outside the tolerance band, not just too variable — a more serious problem than a low but positive Cpk, which just means the spread is too wide relative to the tolerance.
Why does this calculator assume the process is normally distributed?
The 6-sigma and 3-sigma constants in the Cp and Cpk formulas come directly from the normal distribution's property that about 99.73% of values fall within plus-or-minus three standard deviations of the mean. If your process data is heavily skewed or otherwise non-normal, Cp and Cpk can be misleading, and quality engineers typically switch to a distribution-specific capability method or transform the data first.
How is Cpk different from Ppk?
Cpk uses the process's short-term, within-subgroup standard deviation, capturing the process's inherent capability under controlled conditions. Ppk (process performance index) uses the overall standard deviation calculated across all the data, including shifts and drifts between subgroups over time, and is usually equal to or lower than Cpk because it captures more sources of variation. This calculator computes the Cpk-style formula using whatever sigma value you supply.