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The improvement of quality has become a very important part of any manufacturing process. Since variation observed in a process is a function of the quality of the manufactured items, estimating variance components and tolerance intervals present a method for evaluating process variation. As apposed to confidence intervals that provide information concerning an unknown population parameter, tolerance intervals provide information on the entire population, and, therefore address the statistical problem of inference about quantiles and other contents of a probability distribution that is assumed to adequately describe a process. According to Wolfinger (1998), the three kinds of commonly used tolerance intervals are, the (; ) tolerance interval (where is the content and is the confidence), the - expectation tolerance interval (where is the expected coverage of the interval) and the fixed - in - advance tolerance interval in which the interval is held fixed and the proportion of process measurements it contains, is estimated. Wolfinger (1998) presented a simulation based approach for determining Bayesian tolerance intervals in the case of the balanced one - way random effects model. In this thesis, the Bayesian simulation method for determining the three kinds of tolerance intervals as proposed by Wolfinger (1998) is applied for the estimation of tolerance intervals in a balanced univariate normal model, a balanced one - way random effects model with standard N(0; 2 " ) measurement errors, a balanced one - way random effects model with student t - distributed measurement errors and a balanced two - factor nested random effects model. The proposed models will be applied to data sets from a variety of fields including flatness measurements measured on ceramic parts, measuring the amount of active ingredient found in medicinal tablets manufactured in small batches, measurements of iron concentration in parts per million determined by emission spectroscopy and a South - African data set collected at SANS Fibres (Pty.) Ltd. concerned with measuring the percentage increase in length before breaking of continuous filament polyester. In addition, methods are proposed for comparing two or more quantiles in the case of the balanced univariate normal model. Also, the Bayesian simulation method proposed by Wolfinger (1998) for the balanced one - way random effects model will be extended to include the estimation of tolerance intervals for averages of observations from new or unknown batches. The Bayesian simulation method proposed for determining tolerance intervals for the balanced one - way random effects model with student t - distributed measurement errors will also be used for the detection of possible outlying part measurements. One of the main advantages of the proposed Bayesian approach, is that it allows explicit use of prior information. The use of prior information for a Bayesian analysis is however widely criticized, since common non - informative prior distributions such as a Jeffreysâ prior can have an unexpected dramatic effect on the posterior distribution. In recognition of this problem, it will also be shown that the proposed non - informative prior distributions for the quantiles and content of fixed - in - advance tolerance intervals in the cases of the univariate normal model, the proposed random effects model for averages of observations from new or unknown batches and the balanced two - factor nested random effects model, are reference priors (as proposed by Berger and Bernardo (1992c)) as well as probability matching priors (as proposed by Datta and Ghosh (1995)). The unique and flexible features of the Bayesian simulation method were illustrated since all mentioned models performed well for the determination of tolerance intervals.

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Bibliography: leaves 175-179. / xvi, 179 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / The theme of this thesis is the theory and application of crossover designs. Both classical and Bayesian approaches are considered. / Thesis (Ph.D.)--University of Adelaide, Dept. of Statistics, 1998

Thesis (D.Sc.)--University of Adelaide, Department of Statistics, 1980. / Consists mainly of 33 articles and papers reprinted from journals.

Thesis (Ph.D.) -- University of Adelaide, Dept. of Statistics, 1986.

Thesis (M. Phil.)--University of Hong Kong, 1997. / Includes bibliographical references (leaf 129-133).