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Critical Fault-Detecting Time Evaluation In Software With Discrete Compound Poisson Models, Min-Hsiung Hsieh, Shuen-Lin Jeng, Paul Kvam
Critical Fault-Detecting Time Evaluation In Software With Discrete Compound Poisson Models, Min-Hsiung Hsieh, Shuen-Lin Jeng, Paul Kvam
Department of Math & Statistics Faculty Publications
Software developers predict their product’s failure rate using reliability growth models that are typically based on nonhomogeneous Poisson (NHP) processes. In this article, we extend that practice to a nonhomogeneous discrete-compound Poisson process that allows for multiple faults of a system at the same time point. Along with traditional reliability metrics such as average number of failures in a time interval, we propose an alternative reliability index called critical fault-detecting time in order to provide more information for software managers making software quality evaluation and critical market policy decisions. We illustrate the significant potential for improved analysis using wireless failure …
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 …