Cpk measures how capable a stable process is, using the short-term variation inside small subgroups. Ppk measures how the process actually performed over the whole run, using the overall variation, so it includes drift between subgroups. Both compare the spread of your data to the tolerance, and both mark a process down for running off center. When Ppk sits well below Cpk, the process is moving over time. Many customers ask for 1.67 or better on an initial study and 1.33 or better in production, but your customer’s own requirement decides.
The short answer
Cp and Cpk answer the question: if this process ran steadily, could it hold the tolerance? Pp and Ppk answer a different one: did this process hold the tolerance over the run we measured? The versions with the “k” also mark you down when the average sits off the center of the tolerance. Plain Cp and Pp ignore centering.
| Index | Variation used | Centering | The question it answers |
|---|---|---|---|
| Cp | Within subgroups | Ignored | Would the spread fit the tolerance if the process were centered? |
| Cpk | Within subgroups | Counted | How capable is the process right now, short term? |
| Pp | Overall | Ignored | Did the overall spread fit the tolerance? |
| Ppk | Overall | Counted | How did the process actually perform over the whole run? |
The formulas, in words
- Cp = (USL minus LSL) divided by (6 times sigma within)
- Cpk = the smaller of (USL minus the mean) and (the mean minus LSL), each divided by (3 times sigma within)
- Pp and Ppk Same as Cp and Cpk, but with overall sigma in place of sigma within
USL and LSL are the upper and lower specification limits. Sigma within is estimated from the ranges inside your subgroups: the average range divided by a constant called d2. For subgroups of 5, d2 is 2.326. Overall sigma is the ordinary sample standard deviation of every reading in the study.
Worked example: a bore diameter
The bore is 25.000 mm plus or minus 0.050, so LSL is 24.950 and USL is 25.050. Five parts were measured each hour for 25 hours, which gives 125 readings. The first three subgroups look like this.
| Subgroup | Readings (mm) | Range |
|---|---|---|
| 1 | 24.979, 24.995, 25.001, 24.986, 24.978 | 0.023 |
| 2 | 24.991, 24.997, 25.003, 24.980, 24.979 | 0.024 |
| 3 | 25.000, 24.997, 25.008, 25.003, 24.992 | 0.016 |
Across all 125 readings the mean is 25.0011, the overall standard deviation is 0.01137 and the average range is 0.02304. That makes sigma within 0.02304 divided by 2.326, or 0.00991.
| Index | Calculation | Result |
|---|---|---|
| Cp | 0.100 divided by (6 times 0.00991) | 1.68 |
| Cpk | (25.050 minus 25.0011) divided by (3 times 0.00991) | 1.65 |
| Pp | 0.100 divided by (6 times 0.01137) | 1.47 |
| Ppk | (25.050 minus 25.0011) divided by (3 times 0.01137) | 1.43 |
Read it like this. Cp and Cpk are nearly the same, so the process is well centered. Pp and Ppk are lower because the hourly averages crept from about 24.988 at the start of the run to about 25.015 at the end. That movement counts in the overall spread but not in the spread inside each subgroup. When Cpk is comfortably above Ppk, the process is not wide, it is walking. Look for tool wear, thermal growth or an offset someone keeps nudging.
What counts as a good value
The guidance usually quoted from the PPAP manual for an initial study is this: above 1.67 is acceptable, 1.33 to 1.67 may be acceptable depending on the customer’s review, and below 1.33 is not acceptable. Many customers also set 1.33 as the minimum for ongoing production and ask for more on special characteristics. Your customer’s written requirement always wins.
By that guidance, the example’s Ppk of 1.43 would sit in the middle band for an initial study and would pass an ongoing minimum of 1.33. It would also be worth finding out why the process drifted before the customer asks.
When the number lies
- An unstable process. Capability only means something when the process is in statistical control. Plot a control chart first. If the chart shows out-of-control points, a Cpk describes one moment, not the process.
- Data that is not bell shaped. The formulas assume roughly normal data. One-sided limits such as flatness and runout, and skewed data, need a different method or a transformation.
- Too few readings. A common guideline for an initial study is at least 100 readings from 25 or more subgroups. Thirty parts from one shift tells you little.
- A weak gauge. Measurement variation is inside your data and inflates sigma. Run a Gage R&R before you trust the study.
- Sorted or selected parts. If someone picked the good ones, the number is fiction.
How to calculate it in Excel
Lay out the data
Put the subgroup number in column A and the five readings in columns B to F, one subgroup per row, rows 2 to 26.
Add the range
In G2 enter
=MAX(B2:F2)-MIN(B2:F2)and fill it down to row 26.Find the mean
In K3 enter
=AVERAGE(B2:F26).Find overall sigma
In K4 enter
=STDEV.S(B2:F26).Find sigma within
In K5 enter
=AVERAGE(G2:G26)/2.326. For other subgroup sizes use d2 of 1.128 for 2, 1.693 for 3, 2.059 for 4 and 2.534 for 6.Enter the limits
Put USL in K1 and LSL in K2.
Calculate the four indices
Cp:
=(K1-K2)/(6*K5). Cpk:=MIN((K1-K3)/(3*K5),(K3-K2)/(3*K5)). Pp:=(K1-K2)/(6*K4). Ppk:=MIN((K1-K3)/(3*K4),(K3-K2)/(3*K4)).
If you would rather not build the sheet, the Process Capability Study workbook does the calculation and the SPC Control Chart workbook handles the stability check. The SPC & Process Capability Bundle has both.
Questions people ask
Which is bigger, Cpk or Ppk?
Usually Cpk. Overall variation includes drift between subgroups, so overall sigma is normally larger than sigma within. If Ppk comes out larger, check the data and the calculation.
When do I use Ppk and when Cpk?
Many customers ask for Ppk on the initial study, because the process has not yet had time to show it is stable, and Cpk once it runs in control. Check your customer’s requirement.
What is a good Cpk?
Commonly quoted: above 1.67 acceptable, 1.33 to 1.67 may be acceptable, below 1.33 not acceptable. Your customer’s requirement decides.
Can a Cpk be below 1?
Yes. Below 1.00 means the process cannot reliably hold the tolerance. A negative value means the average is outside the limits.
Do I need normal data?
The standard formulas assume it. For skewed data or one-sided limits, use a method for non-normal data, or fix the process so the data behaves.