An Empirical Investigation into the Distribution of Flatness Measurements

Abstract

The flatness of individual components can critically influence the fit or lack-of-fit of compact, small assemblies. To ensure high yield, flatness is tightly toleranced and controlled. According to the standard definition of flatness, the underlying distribution of flatness measurements should be asymmetric. In this paper, 20 industrial flatness data sets from four different processes and three different materials are examined. To accommodate measurement round-off and small sample sizes, the Moran log spacing statistic is used to test if the normal distribution provides an adequate fit. The results demonstrate that the symmetric normal distribution provides an adequate fit for all the data sets. Such a result is important in confirming the use of root-mean-square tolerance analysis techniques, as well as selecting process monitoring and summarizing statistics.

Keywords:

• Form tolerance
• Moran goodness-of-fit statistic
• Tolerance analysis

ACKNOWLEDGMENT

The authors express their appreciation to their industrial partners, General Dynamics, Intel, Simula Corporation, and Datum Inspection for their data sets and collaboration in this research. Funding for this research was derived from a National Science Foundation grant, DMII-0226410, for which the authors are grateful. We also acknowledge and appreciate the early data processing assistance of two students, Ms. Kathryn Kennedy and Mr. Gabriel Rodriguez.