# Process Stability and Capability Analysis

A customer recently sent us some data (which we've disguised). He was trying to do a capability study on his process and got a surprising result: Cp was significantly greater that Pp. The customer thought it was a problem with the QI Macros, but it was really a problem with their process.

While Cp uses the difference between each sample to estimate the standard deviation, Pp actually uses the standard deviation of the data.

Any time there is a significant difference between Cp and Pp or Cpk and Ppk, there are special causes at work.

### Prerequisites for Capability Analysis

One of the prerequisites for capability analysis is a stable process. The only way to evaluate stability is with a control chart, in this case an XbarR chart. As you can see from the chart below, the process is unstable (i.e., there are special causes of variation at work).

Without knowing much about the process, I assume that the machine drifts in its settings as production moves along. Then, every so often when parts approach the upper specification limit, the operator adjusts the machine back toward the lower specification limit so that the machine can drift for awhile without intervention.

Looking at the data gave me an idea: even though I can only use one sample per batch, I thought it might be interesting to run an XmR Trend chart on one of the drifts. Here's an XmR Trend of the first sample in the first trend:

Oddly enough, this suggests that the drift is stable! The question becomes how to eliminate the drift and produce consistent parts. Then it is possible to conduct a capability study that means something.

### Another Example

A different customer sent us similar kinds of data. The Xbar and R charts are both stable:

Having a stable process, we can now conduct a capability study:

As you can see, Cp (1.1921) and Cpk (1.1787) are greater than 1 as are Pp and Ppk. They aren't quite up to 1.33 (4-sigma), so there is room for improvement as most customers demand at least a Cp and Cpk of 1.33.

### Capability studies are simple using the QI Macros.

1. Analyze the stability of the data using an X chart.
2. Clear up any unstable (i.e., special causes of variation) first using root cause analysis.
3. Use the histogram or frequency histogram to analyze the process capability.
4. If Cp is significantly greater than Pp, or Cpk is significantly greater than Ppk, there may still be special causes at work. Further root cause analysis and countermeasures will be required to ensure capability.
5. If Cp and Cpk are less than 1.33 (i.e., 4-sigma), further root cause analysis and countermeasures will be required to achieve most customer's requirements.