Tail asymptotics for the maximum of perturbed random walk

Consider a random walk $S=(S_n:n\geq 0)$ that is ``perturbed'' by a stationary sequence $(\xi_n:n\geq 0)$ to produce the process $(S_n+\xi_n:n\geq0)$. This paper is concerned with computing the distribution of the all-time maximum $M_{\infty}=\max \{S_k+\xi_k:k\geq0\}$ of perturbed random walk with a negative drift. Such a maximum arises in several different applications settings, including production systems, communications networks and insurance risk. Our main results describe asymptotics for $\mathbb{P}(M_{\infty}>x)$ as $x\to\infty$. The tail asymptotics depend greatly on whether the $\xi_n$'s are light-tailed or heavy-tailed. In the light-tailed setting, the tail asymptotic is closely related to the Cram\'{e}r--Lundberg asymptotic for standard random walk.Comment: Published at http://dx.doi.org/10.1214/105051606000000268 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

An Analysis of the Physical Properties of Recovered CCA-Treated Wood from Residential Decks

A large volume of CCA-treated wood removed from residential decks is disposed of in landfills every year, and better environmentally conscious alternatives are needed. Recycling CCA-treated wood from the decks could be a feasible alternative, but there is a lack of knowledge regarding the physical properties of the material. This research analyzed the chemical and mechanical properties of spent CCA-treated wood from residential decks to evaluate the material for reuse in other applications. Several of the joists and the decking of removed decks were found to be below the originally stated retention level. The joists had higher retention levels, and length of service was not a factor in level of chemical retention in the decking or joists. The spent decking had similar stiffness properties, but the bending strength was lower than recently treated material. As with the chemical properties, the mechanical properties were not affected by the amount of time the deck was in service. Overall, it was found that the preservative retention properties were lower than expected, the stiffness was equal to, and the strength was lower than, recently CCA-treated wood. This does not indicate that the material is unusable, but aids in determining suitable applications where recycled CCA-treated wood can be used

Differentiating Defects in Red Oak Lumber by Discriminant Analysis Using Color, Shape, and Density

Defect color, shape, and density measures aid in the differentiation of knots, bark pockets, stain/mineral streak, and clearwood in red oak, (Quercus rubra). Various color, shape, and density measures were extracted for defects present in color and X-ray images captured using a color line scan camera and an X-ray line scan detector. Analysis of variance was used to determine which color, shape, and density measures differed between defects. Discriminant classifiers were used to test which defect measures best discriminated between different defects in lumber.The ANOVA method of model measure selection was unable to provide a direct method of selecting the optimum combination of measures; however, it did provide insight as to which measure should be selected in cases of confusion between defects. No single sensor measure provided overall classification accuracy greater than 70%, indicating the need for multisensor and multimeasure information for defect classification. When used alone, color measures resulted in the highest overall defect classification accuracy (between 69 and 70%). Shape and density measures resulted in the lowest overall classification accuracy (between 32 and 53%); however, when used in combination with other measures, they contributed to a 5-10% increase in defect classification accuracy. It was determined that defect classification required multisensor information to obtain the highest accuracy. For classifying defects in red oak, sensor measures should include two color mean values and two standard deviation values, a shape measure, and a X-ray standard deviation value

Estimating hardwood sawmill conversion efficiency based on sawing machine and log characteristics

Increased problems of hardwood timber availability have caused many sawmiller, industry analysts, and planners to recognize the importance of sawmill conversion efficiency. Conversion efficiency not only affects sawmill profits, but is also important on a much broader level. Timber supply issues have caused resource planners and policy makers to consider the effects of conversion efficiency on the utilization and depletion of the timber resource. Improvements in sawmill conversion efficiency would favorably impact sawmill profits, and would be equivalent in effect to extending existing supplies of standing timber. An equation was developed to estimate lumber recovery factor for hardwood sawmills based on the characteristics of sawing machines and log resources. Variables included in the model were headrig type, headrig kerf, average log diameter and length, and the influence of total sawing variation. The estimated coefficients significantly influenced lumber recovery factor. The model should be helpful in assessing conversion efficiency trends and potential benefits from gains in sawmill efficiency

Uma análise das resoluções apresentadas por alunos do ensino médio de uma questão envolvendo frações

Anais do II Seminário Seminário Estadual PIBID do Paraná: tecendo saberes / organizado por Dulcyene Maria Ribeiro e Catarina Costa Fernandes — Foz do Iguaçu: Unioeste; Unila, 2014O presente trabalho apresenta uma análise dos resultados de uma questão envolvendo o conteúdo de fração que foi aplicada em uma avaliação diagnóstica, que foi aplicada a alunos do 1o ano do Ensino Médio de uma escola da rede pública da cidade de Cornélio Procópio, por alunas que fazem parte do Programa Institucional de Bolsa a Iniciação a Docência (PIBID) da Universidade Tecnológica Federal do Paraná. Os resultados indicam que mesmo no Ensino Médio os alunos apresentam dificuldades para estruturar corretamente as frações e realizar operações simples, no caso, adição de frações com o mesmo numerado

Relative kerf and sawing variation values for some hardwood sawing machines

Information on the conversion efficiency of sawing machines is important to those involved in the management, maintenance, and design of sawmills. Little information on the conversion characteristics of hardwood sawing machines has been available. This study, based on 266 studies of 6 machine types, provides an analysis of the machine characteristics of kerf width, within-board, between-board, and total sawing variations and wood loss per sawline. Machine conversion efficiency was found to be explained by feedworks and setworks type, and sawblade thickness and type. This analysis of machine characteristics provides information for a rational choice of sawing machines for hardwood sawmills

Relative performance of hardwood sawing machines

Only limited information has been available to hardwood sawmiller on the performance of their sawing machines. This study analyzes a large database of individual machine studies to provide detailed information on 6 machine types. These machine types were band headrig, circular headrig, band linebar resaw, vertical band splitter resaw, single arbor gang resaw and double arbor gang resaw. Kerf width and within-board, between-board and total sawing variation values are given with an analysis of their origin in individual machine characteristics. Feedworks and setworks type and sawblade thickness and type generally determined machine type performance

A Simulation Model for a Hardwood Sawmill Decision Support System

The paper describes a sawmill simulation model developed as a component of an integrated decision support system for hardwood sawmills. Discussions focus primarily on some of the essential features of the simulator and how it can be used as a tool for designing sawmill facilities and in the evaluation of sawing policies and production plans. Further discussed are some of the discrete-event simulation modeling techniques used in developing the simulator