Some circular coverage problems

Morgenthaler, George W.

doi:10.1093/biomet/48.3-4.313

Cited by 10 publications

(3 citation statements)

References 12 publications

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“…Patnaik [12] has shown that when the standard deviations are equal but the means are not, the radial error distribution may be determined in terms of the non-central Chi-square distribution. Related work is given by Cohen [2], Chew and Boyce [1], Morgenthaler [10], Scheuer [13], and Gilliland [4].…”

Section: Frameworkmentioning

confidence: 99%

Control Charts for Radial Error

McCool

2006

Quality Technology & Quantitative Management

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In applications such as the drilling of holes or placement of components at a targeted location, the quality characteristic of interest is the radial distance of the center from its desired location. Control charts for radial error are established for the case where the center displacement errors in two orthogonal directions are normally and independently distributed with the same variance about the true center location. It is shown that a second chart based on the ratio of individual observed values of radial error can be used to distinguish between a radial shift in the means of the error distributions and an increase in their variability.

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Section: Frameworkmentioning

confidence: 99%

Control Charts for Radial Error

McCool

2006

Quality Technology & Quantitative Management

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“…Morgenthaler (1961) and Guenther and Terragno (1964) both derive the expected fraction of the target destroyed by a single weapon, assuming that the impact point has a Gaussian distribution centered on ( and with variances × 2 and a 2 . The result is…”

Section: Uniform Circular Targetmentioning

confidence: 99%

“…To meet this difficulty Breaux (1968) transforms the above into a numerically stable form. The resulting expression has the added advantage that E 1 (f),E 2 (f),... , En(f) are all available as partial sums of the same series: Morgenthaler (1961) considers a more general problem in which each weapon has an individual aiming-point; the resulting expressions are so cumbersome that he must resort to simulation. He also replaces a salvo of n weapons with an annulus of appropriate area having its center distributed according to a circular Gaussian distribution centered on the target.…”

mentioning

confidence: 99%