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 randomly generated LHD can have a systematic pattern: the variables may be highly correlated or the design may not have good space-filling properties. There are procedures for finding good LHDs by minimizing the pairwise correlations or maximizing the inter-site distances. We show that these two criteria need not be equivalent or even in close agreement. Therefore, a multi-objective optimization approach is proposed to find good LHDs by combining correlation and distance performance measures. A new exchange algorithm for efficiently generating such designs is also proposed. Several examples are presented to show that the new algorithm is fast, and 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. The most popular kriging method, known as ordinary kriging, uses a constant mean in the model. 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. Moreover, the blind kriging predictor is easier to interpret and more robust to misspecification in the correlation parameters.

The third problem is related to computer experiments with nested and branching factors. In many experiments, some of the factors exist only within the level of another factor. Such factors are often called nested factors. A factor within which other factors are nested is called a branching factor. For example, suppose we want to experiment with two processing methods. The factors involved in these two methods can be different. Thus, in this experiment the processing method is a branching factor and the other factors are nested within the branching factor. 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. Repeated adhesion frequency assay is the only published method for measuring the kinetic rates of cell adhesion. Cell adhesion plays an important role in many physiological and pathological processes. Traditional analysis of adhesion frequency experiments assumes that the adhesion test cycles are independent Bernoulli trials. This assumption can often be violated in practice. 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. The asymptotic distribution of the goodness-of-fit statistic is derived and its finite-sample performance is examined via a simulation study. Application of the proposed methodology to real data from a T-cell experiment reveals some interesting information, including the dependency between repeated adhesion tests. These results provide some quantitative evidence to the speculation that cells can have “memory” in their adhesion behavior.