In accelerated life tests (ALTs), complete randomization is hardly achievable because of economic and engineering constraints. Typical experimental protocols such as subsampling or random blocks in ALTs result in a grouped structure, which leads to correlated lifetime observations. In this dissertation, generalized linear mixed model (GLMM) approach is proposed to analyze ALT data and find the optimal ALT design with the consideration of heterogeneous group effects.

Two types of ALTs are demonstrated for data analysis. First, constant-stress ALT (CSALT) data with Weibull failure time distribution is modeled by GLMM. The marginal likelihood of observations is approximated by the quadrature rule; and the maximum likelihood (ML) estimation method is applied in iterative fashion to estimate unknown parameters including the variance component of random effect. Secondly, step-stress ALT (SSALT) data with random group effects is analyzed in similar manner but with an assumption of exponentially distributed failure time in each stress step. Two parameter estimation methods, from the frequentist’s and Bayesian points of view, are applied; and they are compared with other traditional models through simulation study and real example of the heterogeneous SSALT data. The proposed random effect model shows superiority in terms of reducing bias and variance in the estimation of life-stress relationship.

The GLMM approach is particularly useful for the optimal experimental design of ALT while taking the random group effects into account. In specific, planning ALTs under nested design structure with random test chamber effects are studied. A greedy two-phased approach shows that different test chamber assignments to stress conditions substantially impact on the estimation of unknown parameters. Then, the D-optimal test plan with two test chambers is constructed by applying the quasi-likelihood approach. Lastly, the optimal ALT planning is expanded for the case of multiple sources of random effects so that the crossed design structure is also considered, along with the nested structure.

Fruit and vegetable (FV) consumption continues to lag far behind US Department of Agriculture (USDA) recommendations. Interventions targeting individuals' dietary behaviors address only a small fraction of dietary influences. Changing the food environment by increasing availability of and excitement for FV through local food production has shown promise as a method for enhancing intake. However, the extent to which local production is sufficient to meet recommended FV intakes, or actual intakes, of specific populations remains largely unconsidered. This study was the first of its kind to evaluate the capacity to support FV intake of Arizona's population with statewide production of FV. We created a model to evaluate what percentage of Dietary Guidelines for Americans (DGA) recommendations, as well as actual consumption, state-level FV production could meet in a given year. Intake and production figures were amended to include estimates of only fresh, non-tropical FV. Production was then estimated by month and season to illustrate fluctuations in availability of FV. Based on our algorithm, Arizona production met 184.5% of aggregate fresh vegetable recommendations, as well as 351.9% of estimated intakes of Arizonans, but met only 29.7% of recommended and 47.8% of estimated intake of fresh, non-tropical fruit. Much of the excess vegetable production can be attributed to the dark-green vegetable sub-group category, which could meet 3204.6% and 3160% of Arizonans' aggregated recommendations and estimated intakes, respectively. Only minimal seasonal variations in the total fruit and total vegetable categories were found, but production of the five vegetable sub-groups varied between the warm and cool seasons by 19-98%. For example, in the starchy vegetable group, cool season (October to March) production met only 3.6% of recommendations, but warm season (April to November) production supplied 196.5% of recommendations. Results indicate that Arizona agricultural production has the capacity to meet a large proportion of the population's FV needs throughout much of the year, while at the same time remaining a major producer of dark-green vegetables for out-of-state markets.