Z benchmark describes the sigma capability of a process.
Z benchmark indices are an alternative to Cp and Pp indices. They are the definition of the sigma capability of a Six Sigma process.
All of the indices assume a normally distributed process quality characteristic with the parameters specified by the process mean and sigma. The process sigma is either the short-term or long-term sigma estimate.
Z shift is the difference between the short-term and long-term indices. The larger the Z shift, the more scope there is to improve the process by eliminating shifts and drifts in the process mean. Some industries define the sigma capability of a process as the long-term Z benchmark + a 1.5 Z shift. Meaning a process with a long-term Z benchmark of 4.5 is quoted as a Six Sigma process. It is best to avoid such rules and directly measure the short-term and long-term Z benchmark