This thesis consists of two parts. The first part focuses on design and analysis for computer experiments and the second part deals with binary time series and its application to kinetic studies in micropipette experiments. The first part of the thesis addresses three problems. The first problem is concerned with optimal design of computer experiments. Latin hypercube designs (LHDs) have been used extensively for computer experiments. A multi-objective optimization approach is proposed to find good LHDs by combining correlation and distance performance measures. Several examples are presented to show that the obtained designs are good in terms of both criteria. The second problem is related to the analysis of computer experiments. Kriging is the most popular method for approximating complex computer models. Here a modified kriging method is proposed, which has an unknown mean model. Therefore it is called blind kriging. The unknown mean model is identified from experimental data using a Bayesian variable selection technique. Many examples are presented which show remarkable improvement in prediction using blind kriging over ordinary kriging. The third problem is related to computer experiments with nested and branching factors. Design and analysis of experiments with branching and nested factors are challenging and have not received much attention in the literature. Motivated by a computer experiment in a machining process, we develop optimal LHDs and kriging methods that can accommodate branching and nested factors. Through the application of the proposed methods, optimal machining conditions and tool edge geometry are attained, which resulted in a remarkable improvement in the machining process. The second part of the thesis deals with binary time series analysis with application to cell adhesion frequency experiments. Motivated by the analysis of repeated adhesion tests, a binary time series model incorporating random effects is developed in this chapter. A goodness-of-fit statistic is introduced to assess the adequacy of distribution assumptions on the dependent binary data with random effects. Application of the proposed methodology to real data from a T-cell experiment reveals some interesting information. These results provide some quantitative evidence to the speculation that cells can have ¡§memory¡¨ in their adhesion behavior.