How to use the process capability cpk calculator
- Paste the measurements in the order they were taken, separated by lines, spaces or commas. Use at least 10.
- Enter the lower and upper specification limits. Leave one empty for a one sided limit.
- Enter the subgroup size: 1 for single readings, or 2 to 25 when readings were taken in consecutive groups.
- Read Cpk and Ppk first, then Cp and Pp, and the expected parts per million beyond the limits.
Formula
Cp = (USL - LSL) / (6 sigma)
Cpk = min(USL - mean, mean - LSL) / (3 sigma)
within sigma = average subgroup range / d2 (or average moving range / 1.128 for single readings)
Pp and Ppk use the overall standard deviation with n - 1
Cp compares the width of the limits with the spread of the process. Cpk also penalizes a process that is off center. The within sigma comes from the short term spread, while Pp and Ppk use the long term spread of all readings.
Shaft diameters of 10.00 plus or minus 0.15
Twenty five readings in five subgroups of five have a mean of 10.0068 and an overall standard deviation of 0.02734. The average range gives a within sigma of 0.03182. With limits of 9.85 and 10.15, Cp is 1.572 and Cpk is 1.500, while Pp is 1.829 and Ppk is 1.746. About 4 parts per million are expected beyond the limits using the within sigma.
As a hand check, a process with a mean of 7, a standard deviation of 1 and limits of 4 and 10 has Cp and Cpk of 1.000. The nearest limit is 3 standard deviations away, so about 0.135 percent falls beyond each limit and 2,700 parts per million in all.
Short term and long term
Cp and Cpk use the variation inside each subgroup, so they show what the process can do when it is stable. Pp and Ppk use all of the readings together, so they also include shifts and drift between subgroups. A Ppk far below Cpk is a sign that the process moves around.
The constant d2 is the average range of n readings from a normal curve. The page works it out by numerical integration, so it covers every subgroup size from 2 to 25.
Use it with a control chart
The indexes assume the process is stable and the readings are roughly normal. An unstable process has no single capability, so plot the readings on a control chart first. The Control Chart Limits Calculator gives the limits.
The ppm figure comes from the normal curve with the same mean and sigma. Real parts beyond the limits in a sample are shown separately as a count.
Assumptions and limits
- The process is stable and the readings come from a roughly normal distribution.
- Subgroups are consecutive readings of equal size. A leftover partial subgroup is ignored.
- The within sigma uses the average range, not a pooled standard deviation.
- At least two full subgroups are needed when the subgroup size is 2 or more.
- Up to 5,000 measurements are read.
Frequently asked questions
What is a good Cpk?
There is no universal cutoff. Customers and industries set their own targets. A Cpk of 1.00 puts the nearest limit 3 sigma from the mean, and higher values give more room. Use the target in your own specification.
Why is my Ppk lower than my Cpk?
Ppk includes the shifts between subgroups, and Cpk does not. A large gap suggests the average moves from one subgroup to the next, so look for causes of drift.
What if I only have an upper limit?
Leave the lower limit empty. Cp and Pp then need both limits and show that, while Cpk and Ppk use the single distance to the limit you gave.
Why does the page refuse data that are all the same?
If every reading is identical the spread is zero, and dividing by zero would give no meaningful index. Add real readings or check the instrument resolution.