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Cpk vs. Ppk

Q: What is the difference between the Ppk values reported by Statit and the Cpk values? Why are they both reported? Which one is correct?

A: For Pp and Ppk calculations, the standard deviation used in the denominator is based on all of the data evaluated as one sample, without regard to any subgrouping. This is sometimes referred to as the overall standard deviation, total.

For Cp and Cpk calculations, the standard deviation is based on subgroups of the data using subgroups ranges, standard deviations or moving ranges. This "within-subgroup" process variation can be considerably smaller than the overall standard deviation estimate, especially when there are long-term trends in the data.


 

When there are slow fluctuations or trends in the data, the estimate of the process variability based on the subgroups can be smaller than the estimate using all of the process data as one sample. This often occurs when the differences among observations within the subgroup are small, but the range of the entire dataset is significantly larger. Since the within-subgroup variation measures tend to ignore the range of the entire group, they can underestimate the overall process variation.

All of the observations and their variability as a group are what is important when characterizing the capability of a process to stay within the specification limits over time. Underestimating the variability will increase the process capability estimate represented by Cp or Cpk. However, these estimates may not be truly representative of the process.

The following box plot shows data where the within group variability is small, but there are both upward and downward trends in the data. There are a significant number of observations beyond the specification limits.

When the Process Capability procedure in Statit is performed based on this data, there are significant differences between the estimates of Pp and Cp (and, analogously, Ppk and Cpk).

For example, the calculated Cpk, which uses the within-subgroup estimate of the process variability is 1.077. This would typically be considered to represent a marginally capable process - one with only about 0.12% of the output beyond the specifications (12 out of 1000 parts). However, the calculated Ppk value, which uses the variability estimate of the total sample, is only 0.672. This would indicate a process that is not capable and probably produces a high percentage of output beyond the specifications. Note that the actual amount of production beyond the specifications is 5% or roughly 1 out of every 20 parts.

Which of these values are correct? Both are calculated correctly according to their equations, but here the Ppk value is probably the most representative of the ability of the process to produce parts within the specifications.

Note: One way to determine that the variability estimate is not truly representative of the process is to compare the Estimated and Actual values for the Product beyond Specifications in the Statit output. If the estimated percentage of samples beyond specification is significantly different than the actual percentage reported, then more investigation and analysis of the data would be warranted to achieve the best Process Capability estimates possible based on the data.