A capability index is a ratio:
Cpk = min(USL - mean, mean - LSL) / (3 * sigma) Everything in that formula is unambiguous except sigma. Two different sigmas are in common use — the within-subgroup (short-term) one and the overall (long-term) one — and they can differ by 50% on the same data. Swapping them is the single most common reason a capability study reports a comfortable number for a process that is visibly struggling.
The two sigmas
Within-subgroup sigma is estimated from the spread inside each rational subgroup:
sigma_within = Rbar / d2 (for subgroup size n, look d2 up in a table) It deliberately ignores drift between subgroups. It answers: if the process stayed exactly where it is right now, how much would individual parts scatter?
Overall sigma is just the sample standard deviation of every measurement pooled together, s. It includes the drift between subgroups. It answers: what did the process actually produce over this period?
The first number feeds Cp/Cpk (and Cpk is sometimes called a "short-term" index). The second feeds Pp/Ppk ("long-term" or "process performance"). ISO 22514 and AIAG's SPC manual both keep the distinction; a lot of homegrown spreadsheets do not.
A worked example
25 subgroups of 5 parts, specification 90–110, observed mean 101:
| Quantity | Value |
|---|---|
| sigma within (Rbar/d2) | 1.2 |
| sigma overall (s) | 1.8 |
Cpk = min(110-101, 101-90) / (3 * 1.2) = 9 / 3.6 = 2.50 Ppk = min(110-101, 101-90) / (3 * 1.8) = 9 / 5.4 = 1.67 Same parts, same specification, two numbers that look like two different factories. The gap is the drift: the process mean wandered between subgroups, so the long-term spread is larger. Cpk 2.50 says "capable when centred and stable"; Ppk 1.67 says "but it is not staying centred and stable".
Which number do you show a customer? Both — side by side. The gap itself is the diagnosis. If Cpk >> Ppk, you have a stability problem, not a capability problem, and no amount of process tweaking will fix it until the drift is found.
Three checks before you quote either number
1. Is the process in control? Capability indices assume a stable process. Run the control chart first. A Cpk computed on an out-of-control process is describing an average of several different processes, which is not a thing.
2. Is it roughly normal? Cpk is a ratio of distances measured in standard deviations, so it inherits the assumption behind that denominator. For clearly non-normal data (cycle times, flatness, anything one-sided and bounded at zero) either transform the data or use a percentile-based capability measure such as Ppk on Box-Cox transformed values — or report the fraction out of spec directly and skip the index.
3. How many parts? A confidence interval on Cpk with 20 measurements is enormous — roughly ±0.4 at Cpk ≈ 1.3. If the decision is "ship or not", the interval matters more than the point estimate. AIAG suggests at least 25 subgroups of 4–5 for a study you can defend in an audit.
The trap in the spreadsheet
Most capability templates compute s from the whole column and call it Cpk. That produces a Ppk with a Cpk label — which is why so many supplier reports claim 1.67 while the receiving inspection finds defects. If your template has a single STDEV() over all the data, it is not computing Cpk.
Check the row count, then check which sigma the formula actually uses. You can reproduce both numbers in a browser here if you want to compare against your own template — Cp/Cpk process capability calculator, no signup, and the data stays in the browser tab.
Disclosure: I maintain 6SQ Tools, a set of free browser-based quality/statistics calculators. The statistics above follow AIAG SPC and ISO 22514 conventions; the tool is what makes the two-sigma comparison a 30-second check instead of a spreadsheet archaeology project.
