Profile control charts based on nonparametric LL-1 regression methods

Classical statistical process control often relies on univariate characteristics. In many contemporary applications, however, the quality of products must be characterized by some functional relation between a response variable and its explanatory variables. Monitoring such functional profiles has been a rapidly growing field due to increasing demands. This paper develops a novel nonparametric $L$-1 location-scale model to screen the shapes of profiles. The model is built on three basic elements: location shifts, local shape distortions, and overall shape deviations, which are quantified by three individual metrics. The proposed approach is applied to the previously analyzed vertical density profile data, leading to some interesting insights.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS501 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Uniform fractional factorial designs

The minimum aberration criterion has been frequently used in the selection of fractional factorial designs with nominal factors. For designs with quantitative factors, however, level permutation of factors could alter their geometrical structures and statistical properties. In this paper uniformity is used to further distinguish fractional factorial designs, besides the minimum aberration criterion. We show that minimum aberration designs have low discrepancies on average. An efficient method for constructing uniform minimum aberration designs is proposed and optimal designs with 27 and 81 runs are obtained for practical use. These designs have good uniformity and are effective for studying quantitative factors.Comment: Published in at http://dx.doi.org/10.1214/12-AOS987 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

On construction of optimal mixed-level supersaturated designs

Supersaturated design (SSD) has received much recent interest because of its potential in factor screening experiments. In this paper, we provide equivalent conditions for two columns to be fully aliased and consequently propose methods for constructing $E(f_{\mathrm{NOD}})$- and $\chi^2$-optimal mixed-level SSDs without fully aliased columns, via equidistant designs and difference matrices. The methods can be easily performed and many new optimal mixed-level SSDs have been obtained. Furthermore, it is proved that the nonorthogonality between columns of the resulting design is well controlled by the source designs. A rather complete list of newly generated optimal mixed-level SSDs are tabulated for practical use.Comment: Published in at http://dx.doi.org/10.1214/11-AOS877 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Optimized U-type Designs on Flexible Regions

The concept of a flexible region describes an infinite variety of symmetrical shapes to enclose a particular region of interest within a space. In experimental design, the properties of a function on the region of interest is analyzed based on a set of design points. The choice of design points can be made based on some discrepancy criterion. This paper investigates the generation of design points on a flexible region. It uses a recently proposed new measure of discrepancy for this purpose, the Central Composite Discrepancy. The optimization heuristic Threshold Accepting is used to generate low discrepancy Utype designs. The proposed algorithm is capable to construct optimal U-type designs under various flexible experimental regions in two or more dimensions. The illustrative results for the two dimensional case indicate that using an optimization heuristic in combination with an appropriate discrepancy measure, it is possible to produce high quality experimental designs on flexible regions.Central composite discrepancy, Experimental design, Flexible regions, Threshold accepting, U-type design

Visual tracking of highly articulated objects using massively parallel processors

Hand gesture recognition has the potential of simplifying human computer interactions. However, the human hand is a highly articulated object, capable of taking on many different appearances. In this work, we consider an analysis by synthesis approach to this difficult tracking problem. We attempt to overcome the vast amount of computation required by implementing the algorithm on commodity GPUs. We also collect a lengthy sequence of hand motions from five cameras in order to train and test our algorithm. We show that to achieve good tracking performance, it is important to understand the way that the hand moves. It is of secondary importance to have a good estimate of the hand shape and to be able to process the frames as quickly as possible. Under heavily controlled circumstances, we are able to achieve full tracking accuracy

Henri Temianka Correspondence; (lin)

https://digitalcommons.chapman.edu/temianka_correspondence/2322/thumbnail.jp

Profile modification to minimize spur gear dynamic loading

An analytical computer simulation program for dynamic modeling of low-contact-ratio spur gear systems is presented. The procedure computes the static transmission error of the gears operating under load and uses a fast Fourier transform to generate the frequency spectrum of the static transmission error at various tooth profile modifications. The dynamic loading response of an unmodified (perfect involute) gear pair was compared with that of gears with various profile modifications. Correlations were found between various profile modifications and the resulting dynamic loads. An effective error, obtained from frequency domain analysis of the static transmission error of the gears, gave a very good indication of the optimum profile modification to reduce gear dynamic loading. Design curves generated by dynamic simulation at various profile modifications are given for gear systems operated at various loads. Optimum profile modifications can be determined from these design curves for improved gear design