As a subject matter expert in quality control and statistical analysis, I can explain the CPK calculation, which is a measure of process capability. CPK stands for Process Capability Index and is used to determine how well a manufacturing process is able to produce output within specified limits.

The CPK is calculated by comparing the natural tolerance of a process (the observed variation in the process data) with the specification limits (the acceptable range of variation for the product or process). It is a statistical index that measures the potential of a process to produce parts within specification.

Here's how you calculate CPK:

1. Determine the specification limits (USL - Upper Specification Limit and LSL - Lower Specification Limit).
2. Calculate the mean (average) of the process data.
3. Determine the standard deviation of the process data.
4. Calculate the short-term process capability by finding the number of standard deviations between the process mean and the nearest specification limit. This is done separately for both the upper and lower specification limits.
5. The CPK value is the smaller of the two values obtained in step 4.

The formula for CPK is as follows:
```
CPK = min[ (USL - Mean) / (3 * Standard Deviation), (Mean - LSL) / (3 * Standard Deviation) ]
```

A higher CPK value indicates a process that is more capable of producing parts within the specification limits. Generally, a CPK of 1.0 or higher is considered acceptable, with higher values indicating better process capability.

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The equation for Cpk is more complicated: [minimum(mean - LSL, USL - mean)] / (0.5*NT). LSL stands for Lower Specification Limit and USL stands for Upper Specification Limit. Often we describe Cpk as the capability the process is achieving whether or not the mean is centered between the specification limits.read more >>