The majority of research in experimental design has, to date, been focused on designs when there is only one type of response variable under consideration. In a decision-making process, however, relying on only one objective or criterion can lead to oversimplified, sub-optimal decisions that ignore important considerations. Incorporating multiple, and likely competing, objectives is critical during the decision-making process in order to balance the tradeoffs of all potential solutions. Consequently, the problem of constructing a design for an experiment when multiple types of responses are of interest does not have a clear answer, particularly when the response variables have different distributions. Responses with different distributions have different requirements of the design.

Computer-generated optimal designs are popular design choices for less standard scenarios where classical designs are not ideal. This work presents a new approach to experimental designs for dual-response systems. The normal, binomial, and Poisson distributions are considered for the potential responses. Using the D-criterion for the linear model and the Bayesian D-criterion for the nonlinear models, a weighted criterion is implemented in a coordinate-exchange algorithm. The designs are evaluated and compared across different weights. The sensitivity of the designs to the priors supplied in the Bayesian D-criterion is explored in the third chapter of this work.

The final section of this work presents a method for a decision-making process involving multiple objectives. There are situations where a decision-maker is interested in several optimal solutions, not just one. These types of decision processes fall into one of two scenarios: 1) wanting to identify the best N solutions to accomplish a goal or specific task, or 2) evaluating a decision based on several primary quantitative objectives along with secondary qualitative priorities. Design of experiment selection often involves the second scenario where the goal is to identify several contending solutions using the primary quantitative objectives, and then use the secondary qualitative objectives to guide the final decision. Layered Pareto Fronts can help identify a richer class of contenders to examine more closely. The method is illustrated with a supersaturated screening design example.

Mixture experiments are useful when the interest is in determining how changes in the proportion of an experimental component affects the response. This research focuses on the modeling and design of mixture experiments when the response is categorical namely, binary and ordinal. Data from mixture experiments is characterized by the perfect collinearity of the experimental components, resulting in model matrices that are singular and inestimable under likelihood estimation procedures. To alleviate problems with estimation, this research proposes the reparameterization of two nonlinear models for ordinal data -- the proportional-odds model with a logistic link and the stereotype model. A study involving subjective ordinal responses from a mixture experiment demonstrates that the stereotype model reveals useful information about the relationship between mixture components and the ordinality of the response, which the proportional-odds fails to detect.

The second half of this research deals with the construction of exact D-optimal designs for binary and ordinal responses. For both types, the base models fall under the class of Generalized Linear Models (GLMs) with a logistic link. First, the properties of the exact D-optimal mixture designs for binary responses are investigated. It will be shown that standard mixture designs and designs proposed for normal-theory responses are poor surrogates for the true D-optimal designs. In contrast with the D-optimal designs for normal-theory responses which locate support points at the boundaries of the mixture region, exact D-optimal designs for GLMs tend to locate support points at regions of uncertainties. Alternate D-optimal designs for binary responses with high D-efficiencies are proposed by utilizing information about these regions.

The Mixture Exchange Algorithm (MEA), a search heuristic tailored to the construction of efficient mixture designs with GLM-type responses, is proposed. MEA introduces a new and efficient updating formula that lessens the computational expense of calculating the D-criterion for multi-categorical response systems, such as ordinal response models. MEA computationally outperforms comparable search heuristics by several orders of magnitude. Further, its computational expense increases at a slower rate of growth with increasing problem size. Finally, local and robust D-optimal designs for ordinal-response mixture systems are constructed using MEA, investigated, and shown to have high D-efficiency performance.

Optimal experimental design for generalized linear models is often done using a pseudo-Bayesian approach that integrates the design criterion across a prior distribution on the parameter values. This approach ignores the lack of utility of certain models contained in the prior, and a case is demonstrated where the heavy focus on such hopeless models results in a design with poor performance and with wild swings in coverage probabilities for Wald-type confidence intervals. Design construction using a utility-based approach is shown to result in much more stable coverage probabilities in the area of greatest concern.

The pseudo-Bayesian approach can be applied to the problem of optimal design construction under dependent observations. Often, correlation between observations exists due to restrictions on randomization. Several techniques for optimal design construction are proposed in the case of the conditional response distribution being a natural exponential family member but with a normally distributed block effect . The reviewed pseudo-Bayesian approach is compared to an approach based on substituting the marginal likelihood with the joint likelihood and an approach based on projections of the score function (often called quasi-likelihood). These approaches are compared for several models with normal, Poisson, and binomial conditional response distributions via the true determinant of the expected Fisher information matrix where the dispersion of the random blocks is considered a nuisance parameter. A case study using the developed methods is performed.

The joint and quasi-likelihood methods are then extended to address the case when the magnitude of random block dispersion is of concern. Again, a simulation study over several models is performed, followed by a case study when the conditional response distribution is a Poisson distribution.

Nonregular screening designs can be an economical alternative to traditional resolution IV 2^(k-p) fractional factorials. Recently 16-run nonregular designs, referred to as no-confounding designs, were introduced in the literature. These designs have the property that no pair of main effect (ME) and two-factor interaction (2FI) estimates are completely confounded. In this dissertation, orthogonal arrays were evaluated with many popular design-ranking criteria in order to identify optimal 20-run and 24-run no-confounding designs. Monte Carlo simulation was used to empirically assess the model fitting effectiveness of the recommended no-confounding designs. The results of the simulation demonstrated that these new designs, particularly the 24-run designs, are successful at detecting active effects over 95% of the time given sufficient model effect sparsity. The final chapter presents a screening design selection methodology, based on decision trees, to aid in the selection of a screening design from a list of published options. The methodology determines which of a candidate set of screening designs has the lowest expected experimental cost.

This dissertation explores different methodologies for combining two popular design paradigms in the field of computer experiments. Space-filling designs are commonly used in order to ensure that there is good coverage of the design space, but they may not result in good properties when it comes to model fitting. Optimal designs traditionally perform very well in terms of model fitting, particularly when a polynomial is intended, but can result in problematic replication in the case of insignificant factors. By bringing these two design types together, positive properties of each can be retained while mitigating potential weaknesses. Hybrid space-filling designs, generated as Latin hypercubes augmented with I-optimal points, are compared to designs of each contributing component. A second design type called a bridge design is also evaluated, which further integrates the disparate design types. Bridge designs are the result of a Latin hypercube undergoing coordinate exchange to reach constrained D-optimality, ensuring that there is zero replication of factors in any one-dimensional projection. Lastly, bridge designs were augmented with I-optimal points with two goals in mind. Augmentation with candidate points generated assuming the same underlying analysis model serves to reduce the prediction variance without greatly compromising the space-filling property of the design, while augmentation with candidate points generated assuming a different underlying analysis model can greatly reduce the impact of model misspecification during the design phase. Each of these composite designs are compared to pure space-filling and optimal designs. They typically out-perform pure space-filling designs in terms of prediction variance and alphabetic efficiency, while maintaining comparability with pure optimal designs at small sample size. This justifies them as excellent candidates for initial experimentation.

This dissertation presents methods for addressing research problems that currently can only adequately be solved using Quality Reliability Engineering (QRE) approaches especially accelerated life testing (ALT) of electronic printed wiring boards with applications to avionics circuit boards. The methods presented in this research are generally applicable to circuit boards, but the data generated and their analysis is for high performance avionics. Avionics equipment typically requires 20 years expected life by aircraft equipment manufacturers and therefore ALT is the only practical way of performing life test estimates. Both thermal and vibration ALT induced failure are performed and analyzed to resolve industry questions relating to the introduction of lead-free solder product and processes into high reliability avionics. In chapter 2, thermal ALT using an industry standard failure machine implementing Interconnect Stress Test (IST) that simulates circuit board life data is compared to real production failure data by likelihood ratio tests to arrive at a mechanical theory. This mechanical theory results in a statistically equivalent energy bound such that failure distributions below a specific energy level are considered to be from the same distribution thus allowing testers to quantify parameter setting in IST prior to life testing. In chapter 3, vibration ALT comparing tin-lead and lead-free circuit board solder designs involves the use of the likelihood ratio (LR) test to assess both complete failure data and S-N curves to present methods for analyzing data. Failure data is analyzed using Regression and two-way analysis of variance (ANOVA) and reconciled with the LR test results that indicating that a costly aging pre-process may be eliminated in certain cases. In chapter 4, vibration ALT for side-by-side tin-lead and lead-free solder black box designs are life tested. Commercial models from strain data do not exist at the low levels associated with life testing and need to be developed because testing performed and presented here indicate that both tin-lead and lead-free solders are similar. In addition, earlier failures due to vibration like connector failure modes will occur before solder interconnect failures.

Encouraging stair use may increase physical activity among college students. The overall goals of this study were to quantitatively and qualitatively evaluate a stair use initiative, which included a mural painting contest in a residential hall. The number of individuals exiting the stairs were counted and interview data were obtained regarding the visibility of the signs and murals and whether the signs or murals influenced stair use. Focus groups and interviews were conducted with the community assistants (CAs) and staff members involved with the project to obtain qualitative data on their perceptions and opinions of the mural painting event. It was hypothesized that the average number of individuals per half hour who used the stairs would significantly increase from baseline to post-test. To examine changes over time in individuals exiting the stairs, a quasi-experimental design was used with one baseline measurement and multiple posttests (n=5). Stair use was determined by counting individuals exiting the stairwells. Time differences in exiting stair use were examined with repeated measures analysis of variance (ANOVA). Descriptive statistics and t-tests were used to analyze interview data. Qualitative data were analyzed using a thematic analysis approach. There was a significant time effect on stair use (F=7.512, p =0.000) and a significant interaction between staircase and time (F=7.518, p=0.000). There was no significant interaction of gender over time (F=.037, p=0.997). A repeated measures ANOVA was conducted on each staircase individually and showed that significant time differences were only found in the Southwest staircase. Based on exit interviews (n=28), most students saw the directional signs (61%) and murals (89.3%). However, neither the signs (71.4%) nor the murals (82.1%) were perceived as influential on stair use. Data from the focus groups and interviews revealed that the mural painting contest did not occur as intended, because the contest piece did not take place. In conclusion, solely having residents of a residential hall paint murals in stairwells was insufficient for increasing stair use. A mural painting contest may be a viable approach if properly planned and implemented.

In mixture-process variable experiments, it is common that the number of runs is greater than in mixture-only or process-variable experiments. These experiments have to estimate the parameters from the mixture components, process variables, and interactions of both variables. In some of these experiments there are variables that are hard to change or cannot be controlled under normal operating conditions. These situations often prohibit a complete randomization for the experimental runs due to practical and economical considerations. Furthermore, the process variables can be categorized into two types: variables that are controllable and directly affect the response, and variables that are uncontrollable and primarily affect the variability of the response. These uncontrollable variables are called noise factors and assumed controllable in a laboratory environment for the purpose of conducting experiments. The model containing both noise variables and control factors can be used to determine factor settings for the control factor that makes the response "robust" to the variability transmitted from the noise factors. These types of experiments can be analyzed in a model for the mean response and a model for the slope of the response within a split-plot structure. When considering the experimental designs, low prediction variances for the mean and slope model are desirable. The methods for the mixture-process variable designs with noise variables considering a restricted randomization are demonstrated and some mixture-process variable designs that are robust to the coefficients of interaction with noise variables are evaluated using fraction design space plots with the respect to the prediction variance properties. Finally, the G-optimal design that minimizes the maximum prediction variance over the entire design region is created using a genetic algorithm.

The emergence of new technologies as well as a fresh look at analyzing existing processes have given rise to a new type of response characteristic, known as a profile. Profiles are useful when a quality variable is functionally dependent on one or more explanatory, or independent, variables. So, instead of observing a single measurement on each unit or product a set of values is obtained over a range which, when plotted, takes the shape of a curve. Traditional multivariate monitoring schemes are inadequate for monitoring profiles due to high dimensionality and poor use of the information stored in functional form leading to very large variance-covariance matrices. Profile monitoring has become an important area of study in statistical process control and is being actively addressed by researchers across the globe. This research explores the understanding of the area in three parts. A comparative analysis is conducted of two linear profile-monitoring techniques based on probability of false alarm rate and average run length (ARL) under shifts in the model parameters. The two techniques studied are control chart based on classical calibration statistic and a control chart based on the parameters of a linear model. The research demonstrates that a profile characterized by a parametric model is more efficient monitoring scheme than one based on monitoring only the individual features of the profile. A likelihood ratio based changepoint control chart is proposed for detecting a sustained step shift in low order polynomial profiles. The test statistic is plotted on a Shewhart like chart with control limits derived from asymptotic distribution theory. The statistic is factored to reflect the variation due to the parameters in to aid in interpreting an out of control signal. The research also looks at the robust parameter design study of profiles, also referred to as signal response systems. Such experiments are often necessary for understanding and reducing the common cause variation in systems. A split-plot approach is proposed to analyze the profiles. It is demonstrated that an explicit modeling of variance components using generalized linear mixed models approach has more precise point estimates and tighter confidence intervals.