Reliability experiments provide important information regarding the life of a product, including how various factors may affect product life. Current analyses of reliability data usually assume a completely randomized design. However, reliability experiments frequently contain subsampling which is a restriction on randomization. A typical experiment involves applying treatments to test stands, with several items placed on each test stand. In addition, raw materials used in experiments are often produced in batches. In some cases one batch may not be large enough to provide materials for the entire experiment and more than one batch must be used. These batches lead to a design involving blocks. This dissertation proposes two methods for analyzing reliability experiments with random blocks and subsampling. The first method is a two-stage method which can be implemented in software used by most practitioners, but has some limitations. Therefore, a more rigorous nonlinear mixed model method is proposed.