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The estimation of variance components and estimable vectors is carried out for nonorthogonal mixed models. To do that we use a decomposition of the design space in several orthogonal blocks. We assume the random vectors to have null mean vectors and null cross covariance matrices.

The role of Experimental Design is very well known, considering applications to a broad range of areas, such as Agriculture, Biology, Medicine, Industry, Education, Economy, Engineering and Food Consumption Sciences. Motivated by the variety of problems faced in the several areas and simultaneously taking advantage of the emerging technological developments, new theoretical results, as well as new designs and structures, have been developed by researchers and practitioners accordingly to the needs. Experimental Design got a place among the most important statistical methodologies and, mainly because of allowing to separate variation sources, since the last century it has been strongly recommended for Health Sciences studies. In this area, particular attention has been devoted to Randomized Complete Block Designs and to Balanced Incomplete Block Designs (BIBD) - which allow testing simultaneously a number of treatments bigger than the block size. Thus, after a brief review of some particular BIBD properties and of BIBDR - Balanced Incomplete Blocks with Block Repetition, an applications to Health Sciences simulated data is illustrated, by exploring R software.

This paper presents a study of the evolution the study of the product of two normally distributed variables. From first approaches in the middle of the 20th Century until the most recent ones from this decade. Nowadays, existence of an unique formula for the product was not proved. Partial results using different approaches: Bessel Functions, Numerical Integration, Pearson Type Function, …

In water supply systems with distribution networkthe most critical aspects of control and Monitoring of water quality, which generates crises system, are the effects of cross-contamination originated by the network typology. The classics of control of quality systems through the application of Shewhart charts are generally difficult to manage in real time due to the high number of charts that must be completed and evaluated. As an alternative to the traditional control systems with Shewhart charts, this study aimed to apply a simplified methodology of a monitoring plan quality parameters in a drinking water distribution, by applying Hotelling’s T2 charts and supplemented with Shewhart charts with Bonferroni limits system, whenever instabilities with processes were detected.