A process must be in control before attempting to assess the capability. An out-of-control process is unpredictable and not capable of been characterized by a probability distribution.
Most process capability indices assume a normally distributed quality characteristic. If the distribution is non-normal, it may be possible to transform the data to be normally distributed. The process mean and process sigma define the normal distribution.
Capability indices are either "long-term" or "short-term" depending on the definition of the process sigma:
If the process is stable over time, the estimates of short-term sigma and long-term sigma are very similar. They are both estimates of the same parameter, although statistically speaking the long-term sigma is a slightly more efficient estimator.
However, if there are any changes in the process mean over time, the estimate of long-term sigma is greater than that of short-term sigma. The larger the difference between the values of long-term and short-term indices, the more opportunity there is to improve the process by eliminating drift, shifts and other sources of variation.
From the Statistical Reference Guide for Analyse-it 6.24.0: https://analyse-it.com/docs/user-guide/process-capability
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