Ds-optimal experimental plans for robust parameter design (Spanish text)

This dissertation develops a methodology to obtain experimental plans for Parameter Design studies as an alternative to two classical approaches to the topic: Taguchi crossed designs and combined designs such as the central composite designs suggested by some western statisticians.; The dissertation includes firstly a discussion about the limitations that both types of designs present in some real-life industrial situations. The basic theory of D-Optimality and Ds-Optimality of experimental plans is then briefly presented, as it constitutes the basis for the designs that are proposed next.; The proposed procedure is based upon the formulation of an adequate model for control and noise factor effects in the response variable and the finding of optimal designs to estimate the relevant parameters of the model (Ds-Optimality). The model proposed is a generalisation of others proposed by some authors, including the possible presence of qualitative factors. The dissertation analyses the relevance of the different model parameters, depending on the criterion decision used.; An original methodology is presented to obtain in this framework continual Ds-optimal designs when all factors are quantitative. Using this methodology, designs have been obtained for the cases where there are two or three control factors, combined with one, two or three noise factors. Some regularities appearing in these optimal theoretical designs have been also researched.; Exact experimental plans with a small number of runs are also proposed for these cases as an alternative to classical designs. The comparison with previous ones results favourable to the new proposed designs.; The methodology is finally applied to obtain a D-s optimal experimental plan for a more complex actual industrial problem in a spot welding process, where the model for the response variable has six control factors and four noise factors, being some of these qualitative factors. Originally the problem was solved using a Taguchi crossed design. In this dissertation it was confirmed that using the proposed methodology a different design would have been obtained which could have improved both the efficacy and efficiency of the research with quite less effort.