Design of Experiments (DOE) is an important topic in statistics. Efficient experimentation can help an investigator to extract maximum information from a dataset. In recent times, DOE has found new and challenging applications in science, engineering and technology. In this thesis, two different experimental design problems, motivated by the need for modeling the growth of nanowires are studied.;In the first problem, we consider issues of determining an optimal experimental design for estimation of parameters of a complex curve characterizing nanowire growth that is partially exponential and partially linear. A locally D-optimal design for the non-linear change-point growth model is obtained by using a geometric approach. Further, a Bayesian sequential algorithm is proposed for obtaining the D-optimal design. The advantages of the proposed algorithm over traditional approaches adopted in recent nano-experiments are demonstrated using Monte-Carlo simulations.;The second problem deals with generating space-filling design in feasible regions of complex response surfaces with unknown constraints. Two different types of sequential design strategies are proposed with the objective of generating a sequence of design points that will quickly carve out the (unknown) infeasible regions and generate more and more points in the (unknown) feasible region. The generated design is space-filling (in certain sense) within the feasible region. The first strategy is model independent, whereas the second one is model-based. Theoretical properties of proposed strategies are derived and simulation studies are conducted to evaluate the performance of proposed strategies. The strategies are developed assuming that the response function is deterministic, and extensions are proposed for random response functions.
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