Capability Ratios for True Position - Computational Details

By taking the radius of a circle as 1/2 of the quantities defined in the numerator and denominator of this equation, Positional Cp can be computed as:

where D is the tolerance diameter.

Positional Cpk is computed as:

Note: in these computations it is assumed that the specification limits in both dimensions are the same (and define a circle around the target), that the two variables X and Y (the two measured dimensions) are uncorrelated, and that the variability in each dimension (for X and Y) is approximately the same. As a practical matter, the larger  of the observed variances in the two dimensions is taken to estimate in these computations (see also Krishnamoorthi, 1990).

Default specification limits for individual X/Y dimensions

If individual specification limits (for X and Y) are not specified on the Capability ratios for True Position dialog - Specification tab, then default LSL/USL limits are computed as:

 True Position +/- Positional Tolerance * sin(45)

where sin(45)  = .70711, and

 Positional Tolerance = (Tolerance diameter)/2

For additional details, see Krishnamoorthi, 1990. See also Capability Ratios for True Position - Introductory Overview.