Unbalanced Model Research Articles

Laboratory tests of steel simple torsionally unbalanced models

AbstractThe objective of this work is to obtain estimations of the amplification factors α and δ used for torsion design of buildings, from experiments. For this study, simple one‐storey torsionally unbalanced (TU) steel models were considered. Models consisted of a deck supported on four columns with a selected arrangement of hinges at column ends. Two theoretical structural eccentricities (e = 0.05 and 0.15) were considered. Models were excited with a simple long‐period pendulum consisting of a hanging platform with a forced‐vibration generator on it. Eight models were tested at several excitation levels (frequencies and force magnitudes) in both ranges of behaviour: elastic and inelastic. Experiments were conducted at three frequency ratios of excitation. Registered accelerations of the pendulum platform indicate that the experimental set‐up leads to excitations that resemble narrow‐band seismic ground motions. Frame shear force estimations, based on accelerations recorded at both deck sides, indicate that torsion design factors (α and δ) depend on eccentricity. Estimations of frame shears based on measurements indicate that for normalized eccentricities e ⩾ 0.025, the amplification α can be between 2 and 3; while δ factor resulted between 0.0 and 1.6. Copyright © 2006 John Wiley & Sons, Ltd.

Robust R-Estimation of a Consensus Value from Multi-Center Studies

We consider multi-center experiments (for determining a consensus value) conducted in possibly heterogeneous set-ups leading to unbalanced heteroscedastic one-way random effects models. When normality of both the random components and their homoscedasticity are in doubt, standard statistical methods may not be valid. Two robust R-estimators (for the common location parameter), based on signed-rank statistics, are proposed and their properties studied. When large heteroscedasticity is present or the distribution of random effect is abnormal, the proposed estimators perform better than the classical weighted least squares and selected estimators. This feature is illustrated with an arsenic in oyster tissue problem, along with some other simulation studies.

Comparison of One-Sided Tolerance Limits in Unbalanced One-Way Random Models

ABSTRACT The objective of this article is to provide and evaluate a new method for constructing tolerance limits in unbalanced one-way random models via generalized inference. A simulation study is conducted to compare the proposed method with that of Krishnamoorthy and Mathew (2004). The simulation results suggest that the proposed method performs well in all designs considered.

Bayesian Tolerance Intervals for the Unbalanced One-Way Random Effects Model

Statistical intervals, properly calculated from sample data, are likely to be substantially more informative to decision makers than obtaining a point estimate alone and are often of paramount interest to practitioners and thus management (and are usually a great deal more meaningful than statistical significance or hypothesis tests). In this note, a simulation-based approach for determining Bayesian tolerance intervals in an unbalanced one-way random effects model is illustrated. Reference and probability matching priors are first derived for a more general mixed linear model from which the priors for β, σ2ε, and ν in the case of the random effects model follow easily, where β is the grand mean, σ2ε is the variance of random errors, and ν = σ2γ/σ2ε is the ratio of the random effect to noise variances. A tensile-strength example illustrates the flexibility and unique features of the Bayesian simulation method for the construction of tolerance intervals. Although this example has only one random effect, the method can be applied similarly to other unbalanced data sets and models with multiple variance components. In the last section, a procedure is discussed to obtain Bayesian tolerance intervals for the three-component balanced hierarchical design model.

Modeling the dynamic regulation of nitrogen fixation in the cyanobacterium Trichodesmium sp.

A physiological, unbalanced model is presented that explicitly describes growth of the marine cyanobacterium Trichodesmium sp. at the expense of N(2) (diazotrophy). The model involves the dynamics of intracellular reserves of carbon and nitrogen and allows the uncoupling of the metabolism of these elements. The results show the transient dynamics of N(2) fixation when combined nitrogen (NO(3)(-), NH(4)(+)) is available and the increased rate of N(2) fixation when combined nitrogen is insufficient to cover the demand. The daily N(2) fixation pattern that emerges from the model agrees with measurements of rates of nitrogenase activity in laboratory cultures of Trichodesmium sp. Model simulations explored the influence of irradiance levels and the length of the light period on fixation activity and cellular carbon and nitrogen stoichiometry. Changes in the cellular C/N ratio resulted from allocations of carbon to different cell compartments as demanded by the growth of the organism. The model shows that carbon availability is a simple and efficient mechanism to regulate the balance of carbon and nitrogen fixed (C/N ratio) in filaments of cells. The lowest C/N ratios were obtained when the light regime closely matched nitrogenase dynamics.

Ground deformation at Soufrière Hills Volcano, Montserrat during 1998–2000 measured by radar interferometry and GPS

We examine the motion of the ground surface on the Soufrière Hills Volcano, Montserrat between 1998 and 2000 using radar interferometry (InSAR). To minimise the effects of variable atmospheric water vapour on the InSAR measurements we use independently-derived measurements of the radar path delay from six continuous GPS receivers. The surfaces providing a measurable interferometric signal are those on pyroclastic flow deposits, mainly emplaced in 1997. Three types of surface motion can be discriminated. Firstly, the surfaces of thick, valley-filling deposits subsided at rates of 150–120 mm/year in the year after emplacement to 50–30 mm/year two years later. This must be due to contraction and settling effects during cooling. The second type is the near-field motion localised within about one kilometre of the dome. Both subsidence and uplift events are seen and though the former could be due to surface gravitational effects, the latter may reflect shallow (< 1 km) pressurisation effects within the conduit/dome. Far-field motions of the surface away from the deeply buried valleys are interpreted as crustal strains. Because the flux of magma to the surface stopped from March 1998 to November 1999 and then resumed from November 1999 through 2000, we use InSAR data from these two periods to test the crustal strain behaviour of three models of magma supply: open, depleting and unbalanced. The InSAR observations of strain gradients of 75–80 mm/year/km uplift during the period of quiescence on the western side of the volcano are consistent with an unbalanced model in which magma supply into a crustal magma chamber continues during quiescence, raising chamber pressure that is then released upon resumption of effusion. GPS motion vectors agree qualitatively with the InSAR displacements but are of smaller magnitude. The discrepancy may be due to inaccurate compensation for atmospheric delays in the InSAR data.

One- and Two-Sided Tolerance Intervals for General Balanced Mixed Models and Unbalanced One-Way Random Models

In this article we develop procedures for one- and two-sided tolerance intervals for normal general linear models in which there exists a set of independent scaled chi-squared random variables. The proposed procedures are based on the concept of generalized pivotal quantities and are applicable to general mixed models provided that balanced data are available. However, this study focuses on situations involving unbalanced data. Specific attention is given to the unbalanced one-way random model. It is shown that the use of generalized pivotal quantities allows the construction of the tolerance intervals of interest fairly straightforward. Some practical examples are given to illustrate the proposed procedures. Furthermore, detailed statistical simulation studies are conducted to evaluate their performance, showing that the proposed procedures can be recommended for practical use.

Modeling the coverage probability of a confidence interval on the among-group variance component in the unbalanced random one-way model

The coverage probability of an approximate confidence interval on the among-group variance component, σ α 2 , in a one-way random model is modeled using generalized linear models techniques. The purpose of the proposed modeling is to derive an empirical relationship between the coverage probability on one hand, andk, n., o, and the model’s variance components on the other hand, wherek is the number of groups, n. is the total number of observations, and o is a measure of imbalance for the design used. The latter quantities serve as control variables in the derived model, and the coverage probability is treated as the response variable. Contour plots generated from this model can be easily used to depict the effects of the control variables on the coverage probability. In particular, the plots are utilized to compare four methods for constructing approximate confidence intervals on σ α 2 . Additional advantages of the derived model include prediction of the coverage probability for a given method using only specified values of the control variables, and the determination of operating conditions that result in improved coverage probability within the region of interest.

Evaluating the Life Cycles of Education-Supporting Lotteries

This article examines the history of total lottery sales for eleven education-supporting lottery states. Controlling for the influence of multistate games, state income differentials, and unemployment, unbalanced fixed-effects models investigating four measures of lottery sales indicate that nominal lottery sales continue to climb, but sales adjusted for inflation are either falling or soon will. Per capita sales across all states have not grown much beyond the first several years in the lottery life cycles, but per student sales are still rising due to declining school-age populations and purchases of lottery tickets made by other than state residents. Forecasts for real per capita lottery sales are provided for each of the states in the sample through 2030.

Design and Implementation of 100 Gbit/s OTDM Packet-interleaved MAN/LAN for Future Ultrafast Burst-mode Interconnection

In this paper, detailed data frame format and schematic node structure is investigated and designed for 100 Gbit/s OTDM packet-interleaved metropolitan area network and local area network (MAN/LAN) under unidirectional ring-like folded bus architecture with optional statistic multiplexing extension, CoS and flow control extension and multiple data rate access extension. Several kinds of media access control (MAC) methods are introduced to achieve fair and efficient access among upstream and downstream nodes with the consideration of future burst-mode interconnection application. Also, an improved cyclic reservation multiple access method is proposed and validated to provide fair and efficient access at the aspect of node access rate, access delay and access delay variation under unbalanced pareto on-off burst mode traffic model. Finally, several component technologies, such as optical pulses generator and TOAD are presented and analyzed for the implementation of OTDM packet-interleaved MAN/LAN.

Conceptualizing automated palletizing systems

The present paper addresses the determination of decision parameters in conceptualizing automated palletizing systems (APS). Conceptualizing is the process of developing an initial system design solution for a complex real-world material-handling problem. Such an initial solution is preliminary in nature and reflects the interaction between the problem environment (e.g. throughput needs, cost) and the material-handling system environment (e.g. equipment, operating system practices). The decision parameters for the concept are grouped in two categories: configuration options and operational strategies. In the system configuration stage, a system type is chosen among end-of-line, multi-line and multi-line-with-sortation. The number and length of the accumulation lines and the number of palletizers are also determined in this stage. Operational strategies are listed with regard to assigning the accumulation lanes to the items, selection of a dispatching rule and the setting of conveyor speeds. An ‘unbalanced conveyor model’ is developed for carton dispatching rules as an analytical alternative to an existing balanced conveyor model and its results are verified by simulation. Two dispatching rules are compared based on cost performance.

One-Sided Tolerance Limits in Balanced and Unbalanced One-Way Random Models Based on Generalized Confidence Intervals

We consider the problem of deriving one-sided tolerance intervals in the one-way random model with balanced as well as unbalanced data, under the usual normality assumptions. The problems investigated deal with the computation of such intervals for the observable random variable, as well as the unobservable random effect in the one-way random model. The tolerance limits are derived using the concept of a generalized confidence interval. Some approximations are derived for the tolerance limits, and their performance is investigated by simulation. The simulation results show that the proposed tolerance limits are quite satisfactory for practical use.

Estimation of Heritability in Heteroscedastic One‐Way Unbalanced Random Model

AbstractA modified estimator of heritability is proposed under heteroscedastic one way unbalanced random model. The distribution, moments and probability of permissible values (PPV) for conventional and modified estimators are derived. The behaviour of two estimators has been investigated, numerically, to devise a suitable estimator of heritability under variance heterogeneity. The numerical results reveal that under balanced case the heteroscedasticity affects the bias, MSE and PPV of conventional estimator, marginally. In case of unbalanced situations, the conventional estimator underestimates the parameter when more variable group has more observations and overestimates when more variable group has less observations, MSE of the conventional estimator decreases when more variable group has more observations and increases when more variable group has less observations and PPV is marginally decreased. The MSE and PPV are comparable for two estimators while the bias of modified estimator is less than the conventional estimator particularly for small and medium values of the parameter. These results suggest the use of modified estimator with equal or more observations for more variable group in presence of variance heterogeneity.

A Combined Invariant Test for a Null Variance Ratio

AbstractThis paper investigates the properties of a test that combines the Wald and LMPI (locally most powerful invariant) tests of variance components in unbalanced mixed models. The combined test statistic is easily computed and its null distribution may be approximated by a central F distribution with the degrees of freedom of the numerator adjusted in accordance with the degree of imbalance of the design. Numerical methods are used to show that the approximation is accurate over a wide range of conditions and that the efficiency of the combined test, relative to the power envelope, is satisfactorily high overall.

The Effect of Design Imbalance on the Power of the F‐test of a Variance Component in the One‐Way Random Model

AbstractThe ANOVA‐based F‐test used for testing the significance of the random effect variance component is a valid test for an unbalanced one‐way random model. However, it does not have an uniform optimum property. For example, this test is not uniformly most powerful invariant (UMPI). In fact, there is no UMPI test in the unbalanced case (see Khuri, Mathew, and Sinha, 1998).The power of the F‐test depends not only on the design used, but also on the true values of the variance components. As Khuri (1996) noted, we can gain a better insight into the effect of data imbalance on the power of the F‐test using a method for modelling the power in terms of the design parameters and the variance components. In this study, generalized linear modelling (GLM) techniques are used for this purpose. It is shown that GLM, in combination with a method of generating designs with a specified degree of imbalance, is an effective way of studying the behavior of the power of the F‐test in a one‐way random model.

Between group variance component interval estimation for the unbalanced heteroscedastic one-way random effects model

The studied topic is motivated by the problem of interlaboratory comparisons. This paper focuses on the confidence interval estimation of the between group variance in the unbalanced heteroscedastic one-way random effects model. Several interval estimators are proposed and compared by means of the simulation study. The most recommended (safest) is the confidence interval based on Bonferroni's inequality.

Graphical evaluation of the adequacy of the method of unweighted means

A graphical technique is introduced to assess the adequacy of the method of unweighted means in providing approximate F -tests for an unbalanced random model. These tests are similar to those obtained under a balanced ANOVA. The proposed technique is simple and can easily be used to determine the effects of imbalance and values of the variance components on the adequacy of the approximation. The one-way and two-way random models are used to illustrate the proposed methodology. Extensions to higher-order models are also mentioned.

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Evaluation of a plastic shoe

Hoof-related lameness in horses is common; however, very few critical studies have been performed to evaluate the ability of different shoes to reduce lameness. Dr. Chris Kawcak, with Drs. David Frisbie and Wayne McIlwraith, worked with Val Perino, an MS student, to develop a project intended to compare horses that were unshod, shod with steel shoes, and shod with plastic shoes (Dynamix shoes) in both balanced and controlled, unbalanced states. The specific aims of the study were to compare clinical lameness, ground reaction force, and hoof strain in unshod, traditionally shod, and Dynamix shod horses in both balanced and controlled, unbalanced states. This led to the hypothesis that Dynamix shod horses would have less clinical lameness, increased ground reaction force, and less hoof strain than unshod and traditionally shod horses. Six horses, ages 3 to 5 years, were chosen for the study and treated in accordance with ACUC protocol. The first groups of measurements were on hooves that were trimmed for normal balance. The left front hooves of all horses were then trimmed in an unbalanced manner starting on week 18. Lameness was graded in each horse at a jog according to a subjective lameness scoring system. Each horse was also jogged across a Tekscan sensor mat at a controlled speed. The force, pressure, and contact area were determined for each hoof. Rosette strain gauges were also applied to the prepared hoof at the medial and lateral quarters in both parallel and perpendicular fashion. Data were analyzed by using a mixed model analysis of variance and least squares mean when appropriate. A P value less than .05 was considered significant. Horses were significantly more lame when they wore Dynamix shoes without the clips compared with clips. The controlled, unbalanced model induced a level of lameness that was appropriate for seeing the effects of treatment. It was also found that the horses were less lame in Dynamix shoes compared with when they were unshod in both balanced and unbalanced states. Ground reaction force was highest in the Dynamix treatment group compared with the traditionally shod group. However, the force was higher in the unshod and Dynamix treatment groups when the hooves were unbalanced, which does not correlate with the increased lameness seen when the hooves were unbalanced. The controlled, unbalanced treatment significantly reduced lateral coronary band compression as seen by a reduction in lateral transverse hoof strain. In conclusion, the Dynamix shoe appears to reduce lameness in both balanced and unbalanced states; however, the clips appear to be an essential component of the design. This is the first time that the Tekscan technology has been used to assess abnormal hoof conformation and the investigators are currently planning to further evaluate the Tekscan system against a force plate to determine the meaning of these data. (From Colorado State University Orthopaedic Researach Center Laboratory Report. The complete study was published as: Perino, V MS Thesis. Colorado State University. 2002.) Copyright 2002, Elsevier Science (USA). All rights reserved. 0737-0806/02/2208-0008$35.00/0 doi:10.1053/jevs.2002.37110 Fig 1. (A) Natural Balance shoe, (B) Egg Bar shoe, and (C) Dynamix shoe.

COMPARISON OF CONFIDENCE INTERVALS ON THE AMONG-GROUP VARIANCE COMPONENT FOR THE UNBALANCED ONE-WAY RANDOM MODEL

ABSTRACT The purpose of this paper is to compare four methods for constructing approximate confidence intervals on the among-group variance component for the unbalanced random one-way model. Monte-Carlo simulation is used to compare the estimated coverage probabilities of these intervals. The comparison is based on a method for generating designs having specified degrees of imbalance. Two of these methods, namely, the one by Thomas and Hultquist [5] and the modified harmonic mean method, appear to be the best in most cases considered.