Kirsten Marie Carr

Verification of form tolerances part II: Cylindricity and straightness of a median line

Abstract Most inspectors measure form tolerances as the minimum zone solution, which minimizes the maximum error between the datapoints and a reference feature. Current coordinate measuring machines verification algorithms are based on the least-squares solution, which minimizes the sum of the squared errors, resulting in a possible overestimation of the form tolerance. Therefore, although coordinate measuring machines algorithms successfully reject bad parts, they may also reject some good parts. The verification algorithms developed in this set of papers compute the minimum zone solution of a set of datapoints sampled from a part. Computing the minimum zone solution is inherently a nonlinear optimization problem. This paper develops a single verification methodology that can be applied to the cylindricity and straightness of a median line problems. The final implementable formulation solves a sequence of linear programs that converge to a local optimal solution. Given adequate initial conditions, this solution will be the minimum zone solution. This methodology is also applied to the problems of computing the minimum circumscribed cylinder and the maximum inscribed cylinder. Experimental evidence that the formulations are both robust and efficient is provided.

Verification of form tolerances part I: Basic issues, flatness, and straightness

Abstract The ANSI Y14.5 National Standard on Dimensioning and Tolerancing definition for form tolerances requires the form error of a surface to be less than some set limit. However, most inspectors are interested in the minimum form error, known as the minimum zone solution. To compute the minimum zone flatness, an algorithm must determine the minimum distance between two parallel planes so that all datapoints are between the two planes. Therefore, the minimum zone solution minimizes the maximum error between the datapoints and a reference plane. Current coordinate measuring machine verification algorithms are based on the least-squares solution, which minimizes the sum of the squared errors, resulting in a possible overestimation of the form tolerance. Therefore, while coordinate measuring machine algorithms successfully reject bad parts, they may also reject some good parts. The verification algorithms developed in this set of papers compute the minimum zone solution of a set of datapoints sampled from a part. Computing the minimum zone solution is inherently a nonlinear optimization problem. The proposed algorithms solve a sequence of linear programs that converge to the solution of the nonlinear problem. The linear programs result from a novel combination of coordinate and scaling transformations and do not change the original optimization problem. Therefore, given adequate initial conditions, the sequence of linear programs will converge to the minimum zone solution. Implementation and test results demonstrate the correctness of these formulations. The implementation of these verification algorithms in a production environment can reduce the possibility of rejecting good parts, thereby reducing costs.

Performance Evaluation of Occupant Classification Systems

The new FMVSS 208 Federal Regulation requires restraint systems to focus on occupants other than the 50th percentile male. The new focus includes small adults and children. As a result, restraint systems may need to perform differently for several occupant classes, thereby creating a need for occupant classification systems (OCS). A typical regulation compliance strategy is to suppress the restraint system when a child occupies the front passenger seat and to enable the restraints when an adult occupies the seat. The regulation provides specific weight and height ranges to define these classes of seat occupants. The evolution of OCS technologies produced a need for test methodologies and objective metrics to measure classification system capability. The application of the statistical one-sided tolerance interval to OCS systems has proven invaluable in measuring classification performance and driving system improvements. The one-sided tolerance method is based on a single continuous variable, such as weight. A single common threshold, or tolerance limit, is used to compare two competing populations, such as 6-year-old versus 5th percentile female populations. Output of the method produces graphics demonstrating reliability as a function of potential threshold that objectively characterizes a system’s classification performance level. This paper also discusses the importance of applying the one-sided tolerance interval method to performance data that captures the noise sources that impact system performance. For occupant classification systems, noise sources include differences in test subjects’ sizes, how they sit in the seat, and how the seat is set-up. This paper also discusses the importance of sample size selection. Two methods of determining a sample size are presented. The first method uses the one-sided tolerance interval method equation directly. The second method simulates a noise source and selects a sample size where the noise standard deviation converges to its population variance. Once the mean, standard deviation, and sample size for each test case is known, the proposed method computes the reliability of each test case evaluated for a range of potential thresholds. A review of the resulting reliability curves characterizes classification performance. If an acceptable range of thresholds exists, the resulting range is referred to as a “threshold window.” System improvements can be directed toward those test cases that constrain the “threshold window.” This paper proposes a statistical method that can provide a solid measure of the robust capability of an OCS that classifies based on a single continuous variable (such as weight) to distinguish between occupant classes. This statistical method enables the careful balance necessary in setting thresholds.Copyright