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Master's Dissertation
DOI
https://doi.org/10.11606/D.11.2019.tde-20191218-125711
Document
Author
Full name
Gilson Medeiros e Silva
Institute/School/College
Knowledge Area
Date of Defense
Published
Piracicaba, 1987
Supervisor
Title in Portuguese
O emprego dos esquemas fatoriais fracionados e do confundimento na experimentação
Keywords in Portuguese
ANÁLISE FATORIAL
DELINEAMENTO EXPERIMENTAL
Abstract in Portuguese
O objetivo principal deste trabalho é estudar a utilização dos esquemas fatoriais completo com e sem confundimento e do fatorial fracionado com e sem confundimento para as séries 2n e 3n. Com este intuito apresentamos o desenvolvimento teórico desses esquemas, empregando a notação mais tradicional como também a geometria finita. Os dados utilizados foram gerados por simulação através do modelo matemático inteiramente ao acaso do fatorial 26, onde efeitos principais e as interações foram fixadas. Os erros foram tirados de uma tabela com distribuição normal com µ = 0 e σ 2 = 1. Variamos o desvio padrão dos erros normais e assim estruturamos 4 experimentos. Montamos para cada experimento, quadros de análise de variância sem confundimento, com uma e duas interações confundidas quando o fatorial é completo, e para ½ da repetição foram montados quadros sem confundimento e com uma interação confundida. Também foram calculadas as eficiências. Com base nestes resultados mostramos as melhores interações para serem confundidas como também as maiores eficiências, e vemos que o fatorial fracionado é mais eficiente do que o fatorial completo. Também observamos que a eficiência nos casos estudados não mudam de um experimento para outro mesmo que a variância dos erros aumente.
Title in English
The use of fractional factorial designs and confounding in experimentation
Abstract in English
The main objective of this work is to study the utilization of the complete factorial scheme with and without confounding and of the fractional factorial scheme with and without confounding for the series 2n and 3n. With this purpose, we present the theoretical development of these schemes, employing the most traditional notation as well as the finite geometry. The employed data were generated from simulation according to the unique mathematics model at random of the 26 factorial, where the main effects and the interactions were fixed. The errors had been taken from normal distribution table with µ = 0 e σ 2 = 1. We vary the standard model deflection of the common errors and then we organize the experiments. We built for each experiment tables of variance analyses without confounding, with one and two confused interactions when the factorial scheme is complete, and for a half of the repetition was built tables without confounding and with one confused interaction. It was also calculated the efficiency. Based on these results we showed the best interactions to be confused as well as the best efficiencies, and then we noticed that the fractional factorial scheme is more efficient than the complete factorial scheme. We also noticed that the efficiency, in the studied cases, didn't change from one experiment to the other, even if the errors variance raise
 
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Publishing Date
2019-12-19
 
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