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Nested design is a specific kind of experimental design in which each level of each element occurs with all levels of different factors without relationships. The aim of this article is to estimate the variance components of the interferometry model by two methods and to compare them and obtain the least measurement error for these estimators, and depending on the viscosity chemical experiment we obtained the least measurement line through the comparison between the two methods. we conclude that, the variance components estimated by the maximum penalized likelihood method are less than the variance components estimated by the maximum likelihood method. Conversely, the mean squared error of the parameters estimated by the maximum likelihood method is less than the mean squared error of the parameters estimated by the maximum penalized likelihood method.
Thus, the parameters estimated using maximum penalized likelihood method have the least measurement error, and therefore are more accurate and acceptable than the parameters estimated using the maximum likelihood method.