Desempenho do delineamento composto central em experimentos com alto coeficiente de variação

• Autor(a) principal: Mendonça, Layanne Andrade
• Data de Publicação: 2012
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: LOCUS Repositório Institucional da UFV
• Texto Completo: http://locus.ufv.br/handle/123456789/4052
• topic: Delineamento composto central; Superfície de resposta; Delineamentos econômicos; Central composite design; Surface parameters; Economic designs; CNPQ::CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::PLANEJAMENTO DE EXPERIMENTOS

The present work had the purpose of evaluating the performance of the rotational central composite design (RCCD) in relation to the estimated response surface parameters, under conditions of simulated experimental errors that provide high coefficients of variation. The big impulse of the response methodology was given by Box and Wilson (1951), who developed methods of process optimization in industrial researches. Within these methods, the RCCD may be mentioned as an economic design for the response surface, due to the reduced number of level combinations in the studied factors, when compared to the full factorial. However, it is known that these designs are efficient where experimental mistakes are usually small and the conditions of the experiment are easily controlled. However, given the reduced number of tests by the RCCD, it has become important to verify its potential in designing treatments to adjust response surfaces on experiments related to agrarian sciences, that present, naturally, larger random error. For such, the treatment designs, full factorial and rotational central composite have been used to plan the combinations between the coded levels of two factors (A and B). A second-order model has been established for two factors A and B without interaction among them, named true response surface. A full 5x5 factorial has been established, with the combinations between the coded levels of factors A and B and 40 repetitions per treatment. In total, 1000 experimental units have been built. Afterwards, 100 simulations have been made for the experimental errors ε present in the experiment under normal conditions with average zero and variations σε2. The parameter σε has been specified in 32, 48, 64 and 80, to provide the residual coefficients of variation (CV) equal to 25, 37, 50 and 60 %. The choice of these coefficients of variation has been made in order to include the classifications created by Ferreira (1991), quoted by Silva et al. (2011), and Pimentel Gomes (1985) for the agrarian areas. The observed values of Y have been obtained from the sum of the true values of Y ( ) obtained from the true response surface, with residuals ( ), generated by the simulation. In each type of design (RCCD and full factorial), three, six, nine and twelve repetitions per treatment have been established. According to the combinations between the types of treatment, coefficients of variation and number of repetitions per treatment, 100 adjustments of the response surface have been realized, from which the averages of the coefficient of determination, the average distances between the true and the estimated critical point (CPD) and between the coefficients of variation estimated and simulated (CVD), besides the success percentage and confidence interval of each parameter and the percentage of success from the response surface. Afterwards, a regression of these measures as been made, evaluated based on the design, coefficient of variation and number of repetitions per treatment. The superiority of performance of the full factorial in relation to the RCCD increase in relation to the increase of the CV and the reducing of the number of repetitions per treatment. The RCCD has been recommended under more controlled experimental conditions, for being a more economic treatment design. However, knowing the difficulty of controlling the random error on experiments for the agrarian areas, in experiments of this nature the full factorial or the RCCD were recommended with a larger number of repetitions per treatment. It has also been concluded that the increase of the CV prejudices the adjustment quality of the full factorial and mainly of the RCCD and this prejudice can be compensated with the increase in the number of repetitions per treatment. It has been seen that the adjustment quality provided by the treatment design does not depend only of their quantity, but mostly on the sufficient amount of experimental units to provide proper estimates of the effects of the known and unknown factors.