Decisions in destructive acceptance sampling by attributes and in a simple random walk game

The dissertation contains two parts. The first part deals with assessing the quality of populations. One aim of this part is to provide methods that allow us to make trustworthy decisions. Here, we study statistical sampling methods that estimate how many items with a specific attribute remain in populations after removing samples of items. One removes samples from the population, for example when destructive inspection is required. Decisions to accept or reject the populations are made based on Bayesian analyses of those samples. To make these decisions broadly applicable, we develop an efficient way to tabulate them as sampling plans. We show that classical methods are misapplied when aiming to assess the quality of a population reduced by sampling. We show that the sampling plans in ISO 2859-2 can have a specific consumer’s risk above 44%, despite a stated (classical) consumer’s risk limit of 10%. Classical plans fail here because they assess the entire population, including the sample. This sample may be a large portion of the population. Another aim is to use information from previous tests to reduce the sampling effort and still make trustworthy decisions. To assess the quality of a population over time, we develop a hidden Markov model for the occurrence of failures via parametric lifetime distributions. We flexibilize lifetime models by allowing their parameters to vary in time. However, we assume that the parameters are constant within certain time windows. As a result, the predictions are more realistic and hence more suitable as basis for decisions. For example, we use the predictions to derive acceptance criteria ensuring that remaining populations stay satisfactory from each inspection until the next. The derived acceptance criteria allow for sequential testing at each inspection time. Incorporation of information from previous tests reduces the sampling effort.