Cpk calculator
Paste your measurements, enter the spec limits, and get Cp, Cpk, Pp and Ppk, the parts per million expected out of spec, and a histogram against your limits.
Cpk
- Cp
- spread only
- Cpk
- Pp
- spread only
- Ppk
How it works
Cpk measures how much room a process has inside its tolerance. It is the distance from the process mean to the nearer spec limit, divided by three standard deviations. A Cpk of 1 means the nearer limit sits exactly three sigma from the mean; anything above 1 means more room than that.
The calculator works out two standard deviations from your measurements. Within-subgroup sigma is the short-term variation, estimated the way the AIAG SPC manual teaches: the average subgroup range divided by d2 when you measured parts in groups, or the average moving range between consecutive readings divided by 1.128 when you measured them one at a time. Cp and Cpk use it. Overall sigma is the ordinary sample standard deviation of every reading, so it also catches any drift between subgroups. Pp and Ppk use it, and so does the expected parts per million, which makes that figure the cautious one.
All of it assumes the measurements are roughly normal and the process was stable while you measured. Check the histogram: one hump, no long tail, nothing piled against a limit. If the data is badly skewed or the process was changing, the indices will mislead.
What each value means
| Cpk | Nearer limit | Out of spec, centered |
|---|---|---|
| 0.67 | 2σ from the mean | 45,500 ppm |
| 1.00 | 3σ | 2,700 ppm |
| 1.33 | 4σ | 63 ppm |
| 1.50 | 4.5σ | 6.8 ppm |
| 1.67 | 5σ | 0.57 ppm |
| 2.00 | 6σ | 0.002 ppm |
1.33 is the most common customer minimum for an established process, and 1.67 the usual requirement for a new one in a PPAP initial study. The verdict beside your result uses those two lines, but the real requirement is the one your customer sets.
Questions
What does a Cpk of 1.33 mean?
It means the nearer spec limit is four standard deviations from the process mean, because Cpk is that distance divided by three sigma: 4 ÷ 3 = 1.33. A centered, normal process at 1.33 makes about 63 parts per million outside the limits, about 32 on each side. It is the most common minimum customers ask for on an established process.
What does a Cpk of 1.67 or 2.0 mean?
A Cpk of 1.67 puts the nearer limit five standard deviations from the mean, about 0.6 parts per million out of spec for a centered process. It is the usual target for a new process in a PPAP initial study, where it is asked for as Ppk, and for safety or critical characteristics. A Cpk of 2.0 is six standard deviations, about 0.002 ppm: the process uses only half of the tolerance.
How do you calculate Cpk?
Divide the distance from the mean to each spec limit by three standard deviations: CPU = (USL − mean) ÷ 3σ and CPL = (mean − LSL) ÷ 3σ. Cpk is the smaller of the two. With a mean of 10.02, a sigma of 0.01 and limits of 9.95 and 10.05, CPU is 1.00 and CPL is 2.33, so Cpk is 1.00. With only one limit, Cpk is that side alone.
How many sigma is a Cpk?
Multiply the Cpk by three to get the distance from the mean to the nearer limit in sigmas: 1.00 is 3σ, 1.33 is 4σ, 1.67 is 5σ and 2.00 is 6σ. The Six Sigma figure of 3.4 defects per million is different: it assumes the mean drifts by 1.5σ over time, so a six sigma process is credited with a long-term Cpk of 1.5.
What is a bad Cpk?
Anything under 1.0. The process spread is then wider than the room between the mean and a limit, so out-of-spec parts are expected rather than merely possible. A Cpk of 0.67 puts a limit only two sigma away: about 4.6 percent of a centered process, or 45,500 parts per million, falls outside. A negative Cpk means the mean itself is outside a limit.
What is the difference between Cp and Cpk?
Cp compares the width of the tolerance with the width of the process, six sigma, and ignores where the process sits. Cpk also accounts for centering, because it uses the distance to the nearer limit. The two are equal when the process is centered. A high Cp with a low Cpk means the process is capable but off target, and moving the mean will fix it.
What is the difference between Cpk and Ppk?
They use the same formula with a different standard deviation. Cpk uses within-subgroup sigma, the short-term variation; Ppk uses the overall standard deviation of every reading, so it includes drift between subgroups and is usually lower. A large gap means the process mean moves over time. Minitab’s default pooled standard deviation gives slightly different within figures from the AIAG methods used here.
How do you convert Cpk to ppm?
For a centered normal process, the parts per million beyond each limit is the normal tail past 3 × Cpk sigmas: Cpk 1.00 gives 1,350 on each side, 2,700 in all; 1.33 gives about 32 on each side; 1.67 gives 0.29. A real process is rarely centered, so the calculator works out each side from its own distance and shows the expected ppm below and above separately.
How many parts do you need for a Cpk study?
More than most studies use. A Cpk from 25 parts is uncertain: the example’s 1.25 from 25 readings could be as low as 0.87 at 95 percent confidence. Thirty readings is the usual floor and 100, often 25 subgroups of four or five, is the common standard. The calculator shows the 95 percent lower bound, so you can see whether you have measured enough.