A multivariate statistical analysis of sampling uncertainties in geometric and dimensional errors for circular features

Traditional research on sampling strategies for circular features has focused on reducing the error in estimation of form error for determining the optimal sample size. However, circular features have more than one geometric dimensioning and tolerancing (GD&T) error (form, position, and size) that need to be estimated simultaneously using a single inspection procedure. The inspection method used should, therefore, have a good overall performance in simultaneously assessing all of the GD&T parameters of interest. In this paper, a multivariate statistical model using Exploratory Factor Analysis has been presented for simultaneously analyzing the effect of sampling strategies on the sampling uncertainty of the GD&T errors. Realistic circular profiles have been generated incorporating lobes, eccentricity, and roughness, and a minimum zone fitting algorithm has been used to determine the form error. The error in position and size are computed based on the minimum circumscribed circle of the profile, in accordance with ANSI guidelines. A six-dimensional performance metric vector quantifies the difference between the true value of the errors and the value evaluated using the sample. This vector is used as a basis to recommend a sample size and technique that performs well in simultaneously evaluating the form error, position, and size of a circular profile. The results obtained from the simulated profiles are validated using data collected from manufactured parts.