2,134 research outputs found
Profile control charts based on nonparametric -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 -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 - and -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
Understanding multistage experiments
Abstract: Current advanced manufacturing processes are composed of multiple complex stages which prohibit experimenters from conveniently employing traditional statistical experimental designs due to restrictions on randomisation. In this paper, we demonstrate, and summarise how split plot design and its variants have been used for multistage experimentation, and present several multistage experiment scenarios with comments for practitioners and researchers
Bayesian Analysis for Weighted Mean-squared Error in Dual Response Surface Optimization
Dual response surface optimization considers the mean and the variation simultaneously. The minimization of meansquared error (MSE) is an effective approach in dual response surface optimization. Weighted MSE (WMSE) is formed by imposing the relative weights, (k, 1−k), on the squared bias and variance components of MSE. To date, a few methods have been proposed for determining k. The resulting k from these methods is either a single value or an interval. This paper aims at developing a systematic method to choose a k value when an interval of k is given. Specifically, this paper proposes a Bayesian approach to construct a probability distribution of k. Once the distribution of k is constructed, the expected value of k can be used to form WMSE
Multivariate Exponentially Weighted Moving Average Control Chart for Monitoring Process Variability
and DSD-chart. Furthermore, the EWMA M-chart and V-chart can be plotted in one single figure. As for monitoring both process mean and process variability, the combined MEWMA and EWMA V-charts provide the best control procedure
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