At Ellistat, we don't calculate Cpk. And that's by design!
If you’ve ever opened a capability report in Ellistat and looked for the Cpk, you didn’t find it. This isn’t an oversight. It’s a deliberate choice, based on a simple conviction: in the vast majority of industrial contexts, the Cpk paints an overly optimistic picture of the process, and this picture can lead you to make poor decisions.
Cpk and Ppk: Same Formula, Very Different Assumptions
Both indicators measure a process’s capability—that is, its ability to produce parts within specified tolerances. They combine two pieces of information: the process’s dispersion and its alignment with the target. The difference lies in how the dispersion is estimated.
The Cpk uses a standard deviation in the short term, estimated based on the internal variation within the subgroups (the ranges or average spans of a conventional sampling plan). This estimate assumes that the process is under statistical control: stable, repeatable, and free of special causes. Under these ideal conditions, it reflects the potential of the process.
The Ppk uses the standard deviation global, calculated directly from the entire data set for the observed period. It therefore incorporates all actual sources of variation: gradual drifts, changes in raw material batches, operator effects, tool wear, and variations between shifts. It reflects the actual performance of the process over a representative period.
The formula for calculating the center of mass is the same in both cases. Only the denominator changes. But that denominator changes everything.
The Problem with Cpk in Actual Production
In theory, Cpk is a useful metric: it isolates the natural variability of the process and helps distinguish between control issues and issues of intrinsic capability. It is a valuable tool during the process development phase or during initial qualification, in a controlled environment.
In mass production, the reality is different. A production line never operates for long under perfectly stable conditions. Changes in material batches alter the input characteristics. The gradual wear of tools introduces a slow drift. The morning and evening shifts do not follow exactly the same procedures. A machine that restarts after a weekend does not behave quite the same way as it does during the week.
These phenomena are not anomalies that need to be corrected: they are the normal conditions of industrial production. A Cpk calculated over a few hours of stable production deliberately ignores this reality. It may show 1.67, while the Ppk measured over a full month drops to 1.12. The part you deliver to your customer is the one produced under these actual conditions, not under ideal short-term conditions.
Using Cpk as a routine indicator means running the risk of validating a process based on its best performance, not its typical performance.
Why PPK Is the Benchmark Metric at Ellistat
At Ellistat, we believe that a capability indicator should answer a specific question: Does my process actually produce conforming parts under actual manufacturing conditions over a representative period of time?
The PPK answers this question. It is calculated using long-term data collected under normal operating conditions: including variations between shifts, changes in production runs, and day-to-day variations. It is the indicator that predicts what the final inspection or the customer will actually experience.
This approach also changes the way results are interpreted. A Ppk of 1.33 over three months of production is solid data. A Cpk of 1.67 measured over two hours on a Tuesday morning is a fragile promise. To manage an industrial process, you need robust indicators, not misleading ones.
What if we need short-term capacity?
Sometimes we want to distinguish between short-term and long-term variability, particularly when diagnosing a problem: Is the process itself inadequate, or is it instability that is degrading performance? In this case, the correct approach is not to rely on Cpk as a routine indicator, but to analyze the Ppk/Cpk ratio as a one-time diagnostic tool, in addition to a control chart.
How This Affects Your Analyses
In practical terms, using the Ppk as your primary metric requires you to collect data over sufficiently long and representative periods. A sample taken over a single hour of stable production is not a valid basis. A week that spans multiple shifts, multiple material batches, and multiple machine startups begins to provide meaningful insights.
This requires a bit more rigor when designing the sampling plan. But it ensures that you get an accurate picture of what your process is actually doing—and that is the only solid basis for deciding whether a process is truly under control or whether it needs improvement.