A Functional-Based Distribution Diagnostic for a Linear Model with Correlated Outcomes: Technical Report

Despite the widespread popularity of linear models for correlated outcomes (e.g. linear mixed modesl and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated marginal residual vector by the Cholesky decomposition of the inverse of the estimated marginal variance matrix. Linear functions or the resulting "rotated" residuals are used to construct an empirical cumulative distribution function (ECDF), whose stochastic limit is characterized. We describe a resampling technique that serves as a computationally efficient parametric bootstrap for generating representatives of the stochastic limit of the ECDF. Through functionals, such representatives are used to construct global tests for the hypothesis of normal margional errors. In addition, we demonstrate that the ECDF of the predicted random effects, as described by Lange and Ryan (1989), can be formulated as a special case of our approach. Thus, our method supports both omnibus and directed tests. Our method works well in a variety of circumstances, including models having independent units of sampling (clustered data) and models for which all observations are correlated (e.g., a single time series).

Calculation of the average travel distance in a low-level picker-to-part system considering any distribution function within the aisles

The estimation of the average travel distance in a low-level picker-to-part order picking system can be done by analytical methods in most cases. Often a uniform distribution of the access frequency over all bin locations is assumed in the storage system. This only applies if the bin location assignment is done randomly. If the access frequency of the articles is considered in the bin location assignment to reduce the average total travel distance of the picker, the access frequency over the bin locations of one aisle can be approximated by an exponential density function or any similar density function. All known calculation methods assume that the average number of orderlines per order is greater than the number of aisles of the storage system. In case of small orders this assumption is often invalid. This paper shows a new approach for calculating the average total travel distance taking into account that the average number of orderlines per order is lower than the total number of aisles in the storage system and the access frequency over the bin locations of an aisle can be approximated by any density function.

Fracture strength of drilled wafers: study of the stress concentration factor and determination of the weibull distribution of the fracture stress

In the photovoltaic field, the back contact solar cells technology has appeared as an alternative to the traditional silicon modules. This new type of cells places both positive and negative contacts on the back side of the cells maximizing the exposed surface to the light and making easier the interconnection of the cells in the module. The Emitter Wrap-Through solar cell structure presents thousands of tiny holes to wrap the emitter from the front surface to the rear surface. These holes are made in a first step over the silicon wafers by means of a laser drilling process. This step is quite harmful from a mechanical point of view since holes act as stress concentrators leading to a reduction in the strength of these wafers. This paper presents the results of the strength characterization of drilled wafers. The study is carried out testing the samples with the ring on ring device. Finite Element models are developed to simulate the tests. The stress concentration factor of the drilled wafers under this load conditions is determined from the FE analysis. Moreover, the material strength is characterized fitting the fracture stress of the samples to a three-parameter Weibull cumulative distribution function. The parameters obtained are compared with the ones obtained in the analysis of a set of samples without holes to validate the method employed for the study of the strength of silicon drilled wafers.

Three particle effects in the pair distribution function for He [superscript 4] gas,

"Supported in part by the Atomic Energy Commission."

Path integral calculation of the three-particle direct and exchange contributions to the pair distribution function and of the third virial coefficient for He4 gas /

Thesis--Illinois.

A model for the distribution function for significant wave height /

"January 1981."

On the Quotient Function Employed in the Blind Source Separation Problem

MSC 2010: 42C40, 94A12

Chaos-Galerkin solution of stochastic Timoshenko bending problems

This paper presents an accurate and efficient solution for the random transverse and angular displacement fields of uncertain Timoshenko beams. Approximate, numerical solutions are obtained using the Galerkin method and chaos polynomials. The Chaos-Galerkin scheme is constructed by respecting the theoretical conditions for existence and uniqueness of the solution. Numerical results show fast convergence to the exact solution, at excellent accuracies. The developed Chaos-Galerkin scheme accurately approximates the complete cumulative distribution function of the displacement responses. The Chaos-Galerkin scheme developed herein is a theoretically sound and efficient method for the solution of stochastic problems in engineering. (C) 2011 Elsevier Ltd. All rights reserved.

Defining risk acceptance criteria in occupational settings: A case study in the furniture industrial sector

The use of appropriate acceptance criteria in the risk assessment process for occupational accidents is an important issue but often overlooked in the literature, particularly when new risk assessment methods are proposed and discussed. In most cases, there is no information on how or by whom they were defined, or even how companies can adapt them to their own circumstances. Bearing this in mind, this study analysed the problem of the definition of risk acceptance criteria for occupational settings, defining the quantitative acceptance criteria for the specific case study of the Portuguese furniture industrial sector. The key steps to be considered in formulating acceptance criteria were analysed in the literature review. By applying the identified steps, the acceptance criteria for the furniture industrial sector were then defined. The Cumulative Distribution Function (CDF) for the injury statistics of the industrial sector was identified as the maximum tolerable risk level. The acceptable threshold was defined by adjusting the CDF to the Occupational, Safety & Health (OSH) practitioners’ risk acceptance judgement. Adjustments of acceptance criteria to the companies’ safety cultures were exemplified by adjusting the Burr distribution parameters. An example of a risk matrix was also used to demonstrate the integration of the defined acceptance criteria into a risk metric. This work has provided substantial contributions to the issue of acceptance criteria for occupational accidents, which may be useful in overcoming the practical difficulties faced by authorities, companies and experts.

Defining risk acceptance criteria in occupational settings: A case study in the furniture industrial sector

The use of appropriate acceptance criteria in the risk assessment process for occupational accidents is an important issue but often overlooked in the literature, particularly when new risk assessment methods are proposed and discussed. In most cases, there is no information on how or by whom they were defined, or even how companies can adapt them to their own circumstances. Bearing this in mind, this study analysed the problem of the definition of risk acceptance criteria for occupational settings, defining the quantitative acceptance criteria for the specific case study of the Portuguese furniture industrial sector. The key steps to be considered in formulating acceptance criteria were analysed in the literature review. By applying the identified steps, the acceptance criteria for the furniture industrial sector were then defined. The Cumulative Distribution Function (CDF) for the injury statistics of the industrial sector was identified as the maximum tolerable risk level. The acceptable threshold was defined by adjusting the CDF to the Occupational, Safety & Health (OSH) practitioners’ risk acceptance judgement. Adjustments of acceptance criteria to the companies’ safety cultures were exemplified by adjusting the Burr distribution parameters. An example of a risk matrix was also used to demonstrate the integration of the defined acceptance criteria into a risk metric. This work has provided substantial contributions to the issue of acceptance criteria for occupational accidents, which may be useful in overcoming the practical difficulties faced by authorities, companies and experts.

Convergence of the mass-transport steepest descent scheme for the sub-critical Patlak-Keller-Segel model

Variational steepest descent approximation schemes for the modified Patlak-Keller-Segel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical masses. As a consequence, we recover the recent result about the global in time existence of weak-solutions to the modified Patlak-Keller-Segel equation for the logarithmic interaction kernel in any dimension in the sub-critical case. Moreover, we show how this method performs numerically in one dimension. In this particular case, this numerical scheme corresponds to a standard implicit Euler method for the pseudo-inverse of the cumulative distribution function. We demonstrate its capabilities to reproduce easily without the need of mesh-refinement the blow-up of solutions for super-critical masses.

Rockfall hazard and risk assessments along roads at a regional scale: Example in Swiss Alps

Unlike fragmental rockfall runout assessments, there are only few robust methods to quantify rock-mass-failure susceptibilities at regional scale. A detailed slope angle analysis of recent Digital Elevation Models (DEM) can be used to detect potential rockfall source areas, thanks to the Slope Angle Distribution procedure. However, this method does not provide any information on block-release frequencies inside identified areas. The present paper adds to the Slope Angle Distribution of cliffs unit its normalized cumulative distribution function. This improvement is assimilated to a quantitative weighting of slope angles, introducing rock-mass-failure susceptibilities inside rockfall source areas previously detected. Then rockfall runout assessment is performed using the GIS- and process-based software Flow-R, providing relative frequencies for runout. Thus, taking into consideration both susceptibility results, this approach can be used to establish, after calibration, hazard and risk maps at regional scale. As an example, a risk analysis of vehicle traffic exposed to rockfalls is performed along the main roads of the Swiss alpine valley of Bagnes.