Capability indices for circular tolerance regions based on a Gaussian copula

Abstract

Positional characteristics can be found in many manufactured products. This type of quality characteristics requires the use of capability indices to measure their performance regarding a circular tolerance region and the center of this region. Different indices have been proposed in the literature. However, the main assumption of these indices is that the positional characteristic follows a bivariate normal distribution. In this sense, two process capability indices are proposed in this paper. These indices are based on the Gaussian copula in the aims of allowing the marginal components to follow any type of probability density function. Thus, these copula-based indices can be applied when the normality assumption cannot be followed. The construction of the indices is based on the Cpm and Cpmk indices, given the interest that the positional characteristics to be close to the center of the tolerance region. A simulation study is carried out to analyze the performance of the proposed indices, and a case study about the position of a pin is also analyzed. It is shown in the results of both studies that the proposed indices can be used to measure the performance of positional characteristics with circular tolerance regions.