Reliability growth is not a new topic in either engineering or statistics and has been a major focus for the past few decades. The increasing level of high-tech complex systems and interconnected components and systems implies that reliability problems will continue to exist and may require more complex solutions. The most heavily used experimental designs in assessing and predicting a systems reliability are the "classical designs", such as full factorial designs, fractional factorial designs, and Latin square designs. They are so heavily used because they are optimal in their own right and have served superbly well in providing efficient insight into the underlying structure of industrial processes. However, cases do arise when the classical designs do not cover a particular practical situation. Repairable systems are such a case in that they usually have limitations on the maximum number of runs or too many varying levels for factors. This research explores the D-optimal design criteria as it applies to the Poisson Regression model on repairable systems, with a number of independent variables and under varying assumptions, to include the total time tested at a specific design point with fixed parameters, the use of a Bayesian approach with unknown parameters, and how the design region affects the optimal design. In applying experimental design to these complex repairable systems, one may discover interactions between stressors and provide better failure data. Our novel approach of accounting for time and the design space in the early stages of testing of repairable systems should, theoretically, in the final engineering design improve the system's reliability, maintainability and availability.

Nowadays product reliability becomes the top concern of the manufacturers and customers always prefer the products with good performances under long period. In order to estimate the lifetime of the product, accelerated life testing (ALT) is introduced because most of the products can last years even decades. Much research has been done in the ALT area and optimal design for ALT is a major topic. This dissertation consists of three main studies. First, a methodology of finding optimal design for ALT with right censoring and interval censoring have been developed and it employs the proportional hazard (PH) model and generalized linear model (GLM) to simplify the computational process. A sensitivity study is also given to show the effects brought by parameters to the designs. Second, an extended version of I-optimal design for ALT is discussed and then a dual-objective design criterion is defined and showed with several examples. Also in order to evaluate different candidate designs, several graphical tools are developed. Finally, when there are more than one models available, different model checking designs are discussed.