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Full-Text Articles in Mathematics
Length Bias In The Measurements Of Carbon Nanotubes, Paul H. Kvam
Length Bias In The Measurements Of Carbon Nanotubes, Paul H. Kvam
Department of Math & Statistics Faculty Publications
To measure carbon nanotube lengths, atomic force microscopy and special software are used to identify and measure nanotubes on a square grid. Current practice does not include nanotubes that cross the grid, and, as a result, the sample is length-biased. The selection bias model can be demonstrated through Buffon’s needle problem, extended to general curves that more realistically represent the shape of nanotubes observed on a grid. In this article, the nonparametric maximum likelihood estimator is constructed for the length distribution of the nanotubes, and the consequences of the length bias are examined. Probability plots reveal that the corrected length …
Load Sharing Models, Paul H. Kvam, Jye-Chyi Lu
Load Sharing Models, Paul H. Kvam, Jye-Chyi Lu
Department of Math & Statistics Faculty Publications
Consider a system of components whose lifetimes are governed by a probability distribution. Load sharing refers to a model of stochastic interdependency between components that operate within a system. If components are set up in a parallel system (see Parallel, Series, and Series–Parallel Systems) for example, the system survives as long as at least one component is operating. In a typical load-sharing system, once a component fails, the remaining components suffer an increase in failure rate due to the extra “load” they must encumber due to the failed component.
Degradation Models, Suk Joo Bae, Paul H. Kvam
Degradation Models, Suk Joo Bae, Paul H. Kvam
Department of Math & Statistics Faculty Publications
Reliability testing typically generates product lifetime data, but for some tests, covariate information about the wear and tear on the product during the life test can provide additional insight into the product’s lifetime distribution. This usage, or degradation, can be the physical parameters of the product (e.g., corrosion thickness on a metal plate) or merely indicated through product performance (e.g., the luminosity of a light emitting diode). The measurements made across the product’s lifetime are degradation data, and degradation analysis is the statistical tool for providing inference about the lifetime distribution from the degradation data.