Discrete choice experiments are used when choice alternatives can be described in terms of attributes. The objective is to infer the value that respondents attach to attribute levels. Respondents are presented sets of profiles based on attributes specified at certain levels and asked to select the profile they consider best. When the number of attributes or attribute levels becomes large, the profiles in a single choice set may be too numerous for respondents to make precise decisions. One strategy for reducing the size of choice sets is the sub-setting of attributes. However, the optimality of these reduced size choice sets has not been examined in the literature. We examine the optimality of reduced size choice sets for 2^n experiments using information per profile (IPP) as the optimality criteria. We propose a new approach for calculating the IPP of designs obtained by dividing attributes into two or more subsets with one, two, and in general, r overlapping attributes, and compare the IPP of the reduced size designs with the original full designs. Next we examine the IPP of choice designs based on 3^n factorial experiments. We calculate the IPP of reduced size designs obtained by sub-setting attributes in 3^n plans and compare them to the original full designs. / Statistics

Choice-based conjoint experiments are used when choice alternatives can be described in terms of attributes. The objective is to infer the value that respondents attach to attribute levels. This method involves the design of profiles on the basis of attributes specified at certain levels. Respondents are presented sets of profiles called choice sets, and asked to select the one they consider best. Sets with no dominating or dominated profiles are called Pareto Optimal sets. Information Per Profile (IPP) is used as an optimality criteria to compare designs with different numbers of profiles. For a 2^n experiment, the optimality of connected main effects plans based on two consecutive choice sets, Sl and Sl+1, has been examined in the literature. In this thesis we examine the IPP of both consecutive and non-consecutive choice sets and show that IPP can be maximized under certain conditions. We show that non-consecutive choice sets have higher IPP than consecutive choice sets for n ≥ 4. We also examine the optimality of connected first-order-interaction designs based on three choice sets and show that non-consecutive choice sets have higher IPP than consecutive choice sets under certain conditions. Further, we examine the D-, A- and E-optimality of consecutive and non-consecutive PO choice sets with maximum IPP. Finally, we consider 3^n choice experiments. We look for the optimal PO choice sets and examine their IPP, D-, A- and E-optimality, as well as comparing consecutive and non-consecutive choice sets. / Statistics

<p dir="ltr">Energy consciousness initiatives have seen a recent uptick to curb the ever growing concerns of global warming. Heat Pumps are a crucial piece of technology for these efforts, as they consume lower energy than the requirement they satisfy and are typically used for refrigeration and HVAC systems. Hybrid Heat Pump Water Heater (HPWH) technologies have seen increased adoption, and the improvement of these technologies could pay dividends in the long run. </p><p dir="ltr">This project explores the optimal design space of HPWHs within the context of the Department of Energy Guidelines for their performance rating and compares several up and coming refrigerants with lower GWP than the current market dominant refrigerant, R-134a, to provide consistent performance with improvements on the environmental front along with potential cost improvements on the manufacturing front. For this purpose, Dymola, a simulation software that employs the Modelica language for modeling complex dynamic systems, is employed to study the transient behavior of a market example Heat Pump Water Heater. </p><p dir="ltr">The results of these simulations were validated using experimental data gathered in the laboratory using relevant instrumentation on the physical device and manufacture specified performance ratings to compare the validity of the simulation results. The results of the study indicated the presence of a multi-dimensional design space with a defined set of possible combinations for device implementation. Within that feasible region, there exist multiple trajectories of iso-preference which alter the overall device performance, and the careful study of these parameters and their implications on the device performance can lead to a more robust design pathway for future improvements of the device. The work also contextualizes these improvements by quantifying the relative importance of different parameters upon the final performance of the device, showing how to identify which parameters to focus on when embarking upon an improvement journey. Additionally, preliminarily ideal specifications for the device operation under different refrigerants studied were also identified to provide similar or better performance to the current device. </p><p dir="ltr">The study showed that when matching mass flux rates, R-152a, R-290, and R-600a outperform R-134a in terms of expected COP. Of the 3, only R-290 uses a smaller compressor size than the baseline R-134a cycle for achieving the required heating capacity. The other refrigerants studied do not improve upon the COP of the cycle, but do have benefits over R-134a in terms of their respective GWPs. </p><p dir="ltr">The results suggest that with the considered alterations, R-290 systems within the current charge restrictions (<150g) can be developed and achieve the same heating performance with slight improvements on COP and therefore potentially UEF values. </p><p dir="ltr">The study also shows that all refrigerants considered could achieve the required heating capacity with a considerably downsized condenser and appropriately reduced subcooling. It highlighted the trends being consistent across refrigerants and implemented a final alternative refrigerant through the identified optimization steps to arrive at a new configuration without revalidating the trends, showing that newer optimal configurations could be identified with minimal time spent in the simulation environment. </p><p dir="ltr">Finally, the study explored alternative control possibilities by way of overheating the water beyond its required setpoint and enabling a control based mixing at the outlet to reduce the energized time of the device and leveraging the exceptional insulation capabilities for thermal storage.</p>