Cg/Cgk are Instrument Capability Indexes.

The idea for Cg is the same than for Cp, the "conceptual" formula for Cg is:

Cg = (allowable variation)/(actual variation

The differences are what we take for allowable and actual variation. For Cp, the actual variation is the process variation, and the allowed variation is the specification range.

For Cg, the actual variation is the INSTRUMENT ALONE variation (6 x Sinst No between parts, within part, between operators or along time variation is included. About 50 measurements are made consecutively on a master gauge or "best available" part, and always on the same point of the part, and by the same person, and in a controlled environment (usually the metrology room

The allowable variation is taken as 1/5 of the process variation (6 x Sproc) or 1/5 of the product specification range, depending on whether you want the instrument to control the process or to check conformance of the parts, then:

Cg=(0.2 x 6 x Sproc)/(6 x Sinst)=Sproc/5Sinst

or

Cg=(0.2 x Tol))/(6 x Sinst)=Tol/30Sinst

Cgk, as Cpk, takes into account the position (which would be the bias):

Cgk=(0.5 of the allowable variation - |bias|) / (0.5 of the actual variation)

The idea of Cg/Cgk is to have this information in advance to use it for the decision about if the instrument would be "selectable" for a given measurement.