Relatórios de Pesquisa

This work presents an alternative model for statistical control of the process when we have autocorrelated data. The traditional methods suggest the control chart as the most appropriate tool to be used for the identification of the two different sources of variation for all types of processes. The prediction models based on time series play an important role when the main purpose is to control those processes that produce series of autocorrelated data. Box -Jenkins models deal specifically with those situations of autocorrelated data and this brings up its importance as a prediction model in time series analysis.A case study conducted in a chemical industry is presented as an example of one application of the suggested model, once it deals with an autocorrelated process in which the initial data extend its influence on subsequent data for a certain period o time. The main variable of interest in this case study is the contamination of iron in the final product. This variable has been evaluated since the beginning of the process attempting to control the contamination of iron in the product in a level such that its utilization does not cause any damage to the customer. With this adjusted model the purpose is to control the residuals (predicted – observed) which should remain inside the interval determined by the control limits with mean zero.

rp-2008-2.pdf

Lambert (1992, \textit{Technometrics} \textbf{34}, 1--14) described the zero-inflated Poisson (ZIP) regression, a class of models for count data with an excess of zeros. In this paper, Lambert's methodology is extended to accommodate correlated genetic effects in the regression structure of the Poisson and mixture parameters. In addition, an inter correlation structure between these random genetic effects is introduced, and used to infer pleiotropy, an expression of the extent to which the mixture and Poisson parameters are influenced by common genes. The methods described here are implemented and illustrated with data on number of mastitis cases from Norwegian Red cows. Bayesian analysis yields posterior distributions useful for studying environmental and genetic variability, as well as genetic correlation. The model is assessed using posterior predictive checks.

rp-2007-36.pdf

Using two physical problems involving the so-called fractional telegraph equation, two new addition theorems associated with the generalized Mittag-Leffler function are shown. As a by-product new sum rules associated with the two parameters Mittag-Leffler function and with the classical confluent hypergeometric function, which is the most general function involving two parameters, are also shown.

Using methods of differential and integral calculus, is presented and discussed the calculation of a fractional Green's function, associated with the unidimensional case of the so-called general fractional telegraph equation with a spatial variable. This is a fractional partial differential equation with constant coefficients. The equation is solved by means of the juxtaposition of transforms, i.e., is introduced the Laplace transform in the time variable and the Fourier transform in the spatial variable. Several particular cases are discussed in terms of the parameters. Some known results are recovered. As a by-product of our main result, we obtain two new relations involving the two parameters Mittag-Leffler function.