Worked example
25 readings of a Ø20 H7 bore, specification 20.000 to 20.021 mm, mean 20.01132 and standard deviation s = 0.002231. The tolerance is 0.021, so Pp = 0.021 / (6 × 0.002231) = 1.57. The mean is 0.00968 below the upper limit and 0.01132 above the lower one, so the nearer limit decides: Ppk = 0.00968 / (3 × 0.002231) = 1.45. With the short-term spread from the moving range the same data give Cp = 1.25 and Cpk = 1.15. Paste these 25 values to check the calculator yourself:
20.012 20.008 20.015 20.010 20.011 20.009 20.013 20.012 20.007 20.014 20.011 20.010 20.012 20.016 20.009 20.011 20.013 20.010 20.008 20.012 20.014 20.011 20.010 20.013 20.012
Cpk or Ppk?
- Ppk uses the spread of all the data – what the process actually did in this sample. It is the index customers usually ask for in a first submission, as a preliminary study.
- Cpk uses the spread within a short window and shows what the process could do if it were stable; it belongs to ongoing series production.
- Cp and Pp ignore where the mean sits; Cpk and Ppk punish an off-centre mean.
- Customers often ask for an index of 1.33 in series and 1.67 for preliminary or special characteristics. The requirement in your order or customer manual decides – not this page.
Why 25 values?
An index computed from five parts is a guess dressed up as a number: the spread you measure in so few parts can be far from the real one, and the index inherits that error. The calculator refuses to give an index under 25 values and shows the mean and spread instead. A capability study of a first article needs its own sample from a stable run, not the five parts of the inspection report.
Frequently asked questions
How do I calculate Cpk?
Cpk = min(USL − mean, mean − LSL) / (3σ), where σ is the short-term spread within the data. The index uses the limit nearer to the mean, so an off-centre process scores lower than a centred one with the same spread.
What is the difference between Cpk and Ppk?
Ppk uses the standard deviation of all the values and describes what the process did in the sample; Cpk uses the short-term spread within subgroups or the moving range and describes what a stable process could do.
How many measurements do I need for Cpk?
At least 25 values from a stable run. An index from five parts is a guess: the spread of so few parts can be far from the true one.
What is a good Cpk value?
That is for your customer to say. Customers often ask for 1.33 in series and 1.67 for preliminary studies or special characteristics; check the requirement in the order or the customer manual.
Does this work for one-sided limits?
Yes. Leave the missing limit empty. You then get Cpk and Ppk for the side that exists, but no Cp or Pp.
Is my data stored?
No. The values are sent to our server to be calculated and are not stored; the page sets no cookies.
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