Estimating Bayesian tolerance intervals for a two - factor factorial model

Quality improvement efforts have become the cornerstone of all manufacturing processes. Quality can be defined in terms of variability reduction, and since variability is a statistical concept, statistical techniques such as statistical quality control present techniques for assessing process variation. Methods such as experimental design provide a way to ascertain factor relationships and give a basis for computing variability that arises from each process variable, ultimately providing a way of calculating total process variability. This in turn results in variance components and eventually variance component estimation. As with any statistical model, estimates may be classified in any one of two ways, point estimates or interval estimates. Interval estimates that provide information about an entire population, and not only information on a few observations from a sample or knowledge about only a population parameter, are known as tolerance intervals. Wolfinger (1998) provided a Bayesian simulationbased approach for ascertaining three types of tolerance intervals using a balanced one-way random effects model. In this study, the method initially proposed by Wolfinger (1998), is extended in order to estimate tolerance intervals for the balanced two-way crossed classification random effects model with interaction. The suggested and derived techniques will be applied to the thermal impedance data initially collected by Houf and Berman (1988), and the method presented by Wolfinger (1998) will be expanded to also include the estimation of tolerance intervals for averages of observations from new or unknown measurements. This Bayesian approach provides a thorough but yet simplistic paradigm to using tolerance intervals in manufacturing settings.Thesis (MSc) -- Faculty of Science, Statistics, 202