Three projects for the design of experiments: choice experiments, Kriging and split-plot designs

This PhD thesis is composed of three projects related to the design and analysis of experiments. The first project pertains to the construction of optimal designs for choice experiments. It has been developed also in collaboration with professor Jesús Fernando López-Fidalgo during my first PhD visiting period at the University of Navarra, Pamplona, Spain. Our thanks to Prof. Patrizia Pinelli, Department of Statistics, Computer Science and Applications - PHYTOLAB Laboratory, Scientific and Technological Pole, University of Florence, for providing us the HPLC analysis for the real case-study faced in this first project. The second project is related to computer experiments and Kriging modelling, applied to solve a complex engineering problem in the railway field. Regarding the second project about Kriging, we want to acknowledge Prof. Ing. Luciano Cantone, Department of Engineering for Enterprise "Mario Lucertini", University of Rome "Tor Vergata", for providing us the data and the engineering details for the problem under study. The third project deals with randomization issues in a split-plot design, due to production process requirements of a product in the field of mechanical engineering. This last project has been developed also in collaboration with professor G. Geoffrey Vining during my second PhD visiting period at the Virginia Tech University, Blacksburg, Virginia, USA. Moreover, we want also to acknowledge Dott. Ing. Francesco Bertocci and Esaote SpA, Florence, Italy for the collaboration and contribution to the engineering and technological features.In what follows, a brief summary for each project is reported. 1. OPTIMAL APPROXIMATE CHOICE DESIGNS WITH CORRELATED PREFERENCES THROUGH A COMPOUND CRITERION In this project, we propose an innovative approach for the construction of heterogeneous choice designs with correlated choice preferences. Differently from existing research in the choice design literature that make use of an exact design framework to build optimal choice designs, we propose the construction of optimal heterogeneous choice designs based on an approximate design theory, and under the Panel Mixed Logit model structure that explicitly takes account of the correlation between the responses of a respondent facing a sequence of choice-sets. Our proposed approach allows us to obtain optimal heterogeneous choice designs composed of groups of choice-sets to be administered to a proportion of respondents according to the optimal weights. We show the efficiency of our proposal through an application to a real case study that concerns the analysis of the consumers’ preferences for coffee, integrating a choice experiment with the consumer sensory tests. To this end, we develop our proposal under a compound design criterion. Moreover, we present the estimation results of the Panel Mixed Logit model related to the proposed optimal heterogeneous choice design we applied to our real case study, which are very satisfactory, by further confirming the validity of our innovative proposal. LATIN HYPERCUBE DESIGNS BASED ON STRONG ORTHOGONAL ARRAYS AND KRIGING MODELLING TO IMPROVE THE PAYLOAD DISTRIBUTION OF TRAINS This projects deals with computer experiments and Kriging modelling to improve the braking performance for freight trains. We focus on the payload distribution along the train, so as to reduce the effects of in-train forces, e.g. compression and tensile forces, among vehicles during a train emergency braking. The topic is particularly relevant for Railway Undertakings, especially in Europe, where a series of codes regulates international freight traffic. To this end, we propose a novel approach to improve the payload distribution of trains through a suitable design for the computer experiment and Kriging modelling. More precisely, we build a Latin Hypercube design based on strong orthogonal arrays for the computer experiment that achieves very good space-filling properties with a relatively low number of experimental runs. Kriging models with anisotropic covariance functions are subsequently applied to find the optimal payload distribution able to reduce the in-train forces. Moreover, differently from other researches in this field, where the entire train was characterized by a unique payload distribution, in the present application we consider that the train is divided in several sections, each one composed of different wagons. Therefore, each train section is characterized by its own payload distribution: having different train sections gives the possibility to optimize trains that deliver their payload along their route. Furthermore, it also allows for better understanding of the best payload distribution along the entire train, so as by further improving the freight train efficiency in terms of braking performance. THE IMPACT OF NOT RANDOMIZING A SPLIT-PLOT EXPERIMENT AND HOW TO DETECT ITS EFFECT This project deals with lacking of randomization in an industrial split-plot experiment. More precisely, a split-plot design is planned to improve the production process of an ultrasound transducer for medical imaging. Due to constraints on how the company could conduct the experiment, some of the factors in the design are not randomized. To this end, we focus on the possible consequent impact of lacking of randomization in the split-plot design. More precisely, we carry out a simulation study based on the real one, in order to examine the implications of lacking of randomization on the factor estimates and on the corresponding residual values.