Process capability index

In process improvement efforts, the process capability index or process capability ratio is a statistical measure of process capability: The ability of a process to produce output within specification limits. The concept of process capability only holds meaning for processes that are in a state of statistical control.

If the upper and lower specifications of the process are USL and LSL, the target process mean is T, the estimated mean of the process is $$\hat{\mu}$$, and the estimated variability of the process is $$\hat{\sigma}$$, then commonly-accepted process capability indices include:

$$\hat{\sigma}$$ is estimated using the sample standard deviation.

Recommended values
Process capability indices are constructed to express more desirable capability with increasingly higher values. Values near or below zero indicate processes operating off target ($$\hat{\mu}$$ far from T) or with high variation. Fixing values for minimum "acceptable" process capability targets is a matter of personal opinion, and what consensus exists varies by industry, facility, and the process under consideration. However, at least one academic expert recommends the following: