Calculating Process Capability for Circular True Position Tolerances

Abstract

There are many occasions where using a two dimensional, true position tolerance for a specifying the tolerance of a dimension is preferred to using a standard onedimensional plus/minus tolerance. Unfortunately, it is difficult to demonstrate process capability for such dimensions. The key challenge is determining the standard deviation of the data. For over 30 years, many efforts have been made to determine process capability for positional tolerances. In some cases, the authors do not address calculating the standard deviation and in others they make errors in the process. This paper calculates a onedimensional standard deviation in a non-typical but logical, methodical way, revealing a strategy to be easily determine the two-dimensional standard deviation. First find the center of the data and then the distance from each point to the center of the data. That distance can be used to calculate the standard deviation, but with a slight modification to the customary method. The end result is that the standard deviation for true position radius is the RSS of the standard deviation of the x and y components. That this technique is used in the field of geometric information systems supports its use for quality engineering.