Making Inferences with Indirect Measurements

This article considers the characterization of the distribution of part quality for parts produced by a manufacturing process when only indirect quality measurements are available. The proposed method uses the relationship between the indirect and direct measurements, which is not completely deterministic, as well as a key property of the assumed distribution. The proposed method provides tolerance bounds of the part quality distribution. A diagnostic is also proposed to assess the validity of the distribution assumed. The proposed method and diagnostic are demonstrated with an illustrative data set.

Keywords:

• Scale distribution
• Scale equivariance
• Simulation
• Tolerance interval

ACKNOWLEDGMENTS

We thank Dee Won for her encouragement of this work, Cheryll Faust and Patrick Rodriguez for helpful discussions, Vivian Romero for graphics assistance, and Jeroen de Mast for insightful comments and suggestions on an earlier version of this article.