Application of robust optimization to automated test assembly

In automated test assembly (ATA), 0-1 linear programming (0-1 LP) methods are applied to select questions (items) from an item bank to assemble an optimal test. The objective in this 0-1 LP optimization problem is to assemble a test that measures, in as precise a way as possible, the ability of candidates. Item response theory (IRT) is commonly applied to model the relationship between the responses of candidates and their ability level. Parameters that describe the characteristics of each item, such as difficulty level and the extent to which an item differentiates between more and less able test takers (discrimination) are estimated in the application of the IRT model. Unfortunately, since all parameters in IRT models have to be estimated, they do have a level of uncertainty to them. Some of the other parameters in the test assembly model, such as average response times, have been estimated with uncertainty as well. General 0-1 LP methods do not take this uncertainty into account, and overestimate the predicted level of measurement precision. In this paper, alternative robust optimization methods are applied. It is demonstrated how the Bertsimas and Sim method can be applied to take this uncertainty into account in ATA. The impact of applying this method is illustrated in two numerical examples. Implications are discussed, and some directions for future research are presented.     

Application of gradient based algorithms for robust shape optimization of a tensile test specimen

In case of technical applications such as automotive or aeronautic part optimization, uncertainties in design variables and other parameters have to be taken into account. Especially, scattering of material properties and mechanical loads have large influences on the component behavior. Due to the difficulty in calculating of sensitivities, usually stochastic algorithms are used for robust and reliability optimization. That entails a large number of function calls and long computation time. Therefore, the stochastic responses with expectation value and variances will be approximated by response surfaces in this contribution. Based on the practical example of a tensile test specimen a deterministic optimization and optimization under uncertainties will be done. The results of the different optimizations will be compared and the influence of the uncertainties will be shown and discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Estimating production test properties from test measurement data

A complex sequence of tests on components and the system is a part of many manufacturing processes. Statistical imperfect test and repair models can be used to derive the properties of such test sequences but require model parameters to be specified. We describe a technique for estimating such parameters from typical data that are available from past testing. A Gaussian mixture model is used to illustrate the approach and as a model that can represent the wide variety of statistical properties of test data, including outliers, multimodality and skewness. Model fitting was carried out using a Bayesian approach, implemented by MCMC. Copyright © 2011 John Wiley & Sons, Ltd.     

Modularization modeling and simulation of turbine test rig main test system

Comprehensive applications of modularization modeling method have proven its effectiveness and versatility in system simulation field. This paper establishes the modularization numerical model of a turbine test rig main test system by using a finite volume numerical system developed. The simulation study based on an experiment is conducted. The comparison with available experimental data indicates that the general trends of simulation curves are in agreement with test curves and that there is obvious thermal stratification phenomenon at different positions along combustion gas flow direction. Accordingly, it can be concluded that the analysis of experimental data is reasonable and the established numerical system is effective. It is also found that the modeling of valve spool throttling and the modeling of components-wall heat transfer are two key factors of affecting simulation accuracy.     

Goodness of wit test

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Goodness of wit test Goodness of wit test #14: Outcome analysis     

Goodness of wit test

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Goodness of wit test     

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Goodness of wit test Goodness of wit test #12: Straightforward!     

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Goodness of wit test     

Whitehead test modules

A (right -) module is said to be a Whitehead test module for projectivity (shortly: a p-test module) provided for each module , implies is projective. Dually, i-test modules are defined. For example, is a p-test abelian group iff each Whitehead group is free. Our first main result says that if is a right hereditary non-right perfect ring, then the existence of p-test modules is independent of ZFC + GCH. On the other hand, for any ring , there is a proper class of i-test modules. Dually, there is a proper class of p-test modules over any right perfect ring.

A non-semisimple ring is said to be fully saturated (-saturated) provided that all non-projective (-generated non-projective) modules are i-test. We show that classification of saturated rings can be reduced to the indecomposable ones. Indecomposable 1-saturated rings fall into two classes: type I, where all simple modules are isomorphic, and type II, the others. Our second main result gives a complete characterization of rings of type II as certain generalized upper triangular matrix rings, . The four parameters involved here are skew-fields and , and natural numbers . For rings of type I, we have several partial results: e.g. using a generalization of Bongartz Lemma, we show that it is consistent that each fully saturated ring of type I is a full matrix ring over a local quasi-Frobenius ring. In several recent papers, our results have been applied to Tilting Theory and to the Theory of -modules.

     

Functorial test modules

In this article we introduce a slight modification of the definition of test modules which is an additive functor τ on the category of coherent Cartier modules. We show that in many situations this modification agrees with the usual definition of test modules. Furthermore, we show that for a smooth morphism $f:X\to Y$ of F-finite schemes one has a natural isomorphism $f^{!}°\tau ?\tau °f^{!}$. If f is quasi-finite and of finite type we construct a natural transformation $\tau °f_{?}\to f_{?}°\tau$.     

The short-cut test

The short-cut test detects existence and uniqueness of “Laplacians” on finitely ramified, graph-directed fractals. Previous results by Sabot, Nussbaum and the author are improved and extended. It opens up the way for further studies because it combines well established spectral, dynamical and analytic techniques. Its algorithmic and recursive structure is designed to provide computable and flexible criteria.     

Nonparametric test of restricted interchangeability

Exact and large sample distributions of the rank order test under the null hypothesis of restricted interchangeability are obtained. Under given regularity conditions and under Pitman's shift in location alternative, the asymptotic relative efficiency of this nonparametric test in comparison with Votaw's (1948, Ann. Math. Statist., 19, 447–473) likelihood ratio test is given.     

Non-unbiasedness of Cramer-von Mises test

This paper shows that for any given level of significanceα ∈ (0,1), and any sample sizen, the Cramer-von Mises test is not unbiased.     

Implementation of a unimodularity test

This paper describes implementation and computational results of a polynomial test of total unimodularity. The test is a simplified version of a prior method. The program also decides two related unimodularity properties. The software is available free of charge in source code form under the Boost Software License.     

Adaptive minimax test of independence

The paper is concerned with the adaptive minimax problem of testing the independence of the components of a d-dimensional random vector. The functions under alternatives consist of smooth densities supported on [0, 1]d and separated away from the product of their marginals in L2-norm. We are interested in finding the adaptive minimax rate of testing and a test that attains this rate. We focus mainly on the tests for which the error of the first kind an can decrease to zero as the number of observations increases. We show also how this property of the test affects its error of the second kind.     

Isotropic distributions of test matrices

In 1946, von Neumann and his collaborators used a special distribution of random matrices as a model for estimatinga priori the machine precision needed to solve large linear systems. The present paper identifiesisotropy as a group-theoretic property of this distribution, shows that its matrices are almost never ill-conditioned, and explains how to use other isotropically distributed random matrices for testing the accuracy of numerical methods for solving linear systems and associated error diagnostics.

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Zusammenfassung Die zur Lösung linearer Gleichungssysteme benötigte Genauigkeit wurde schon 1946 durch von Neumann und seine Mitarbeiter mittels speziell verteilter Zufallsmatrizen geschätzt. In der vorliegenden Arbeit erscheint dieIsotropie als gruppentheoretische Eigenschaft dieser Verteilung. Ferner wird gezeigt, dass die Zufallsmatrizen fast nie schlecht konditioniert sind. Schliesslich diskutieren die Autoren die Verwendung anderer isotrop verteilter Zufallsmatrizen zur Prüfung von Genauigkeit und a-priori-Fehlerschranken bei Algorithmen zur Lösung linearer Gleichungssysteme.

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Dedicated to Eduard Stiefel

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The main results of this paper were reported in [3], and communicated in 1976 to those working on the LINPACK project.