In a composite sampling procedure initial samples (increments) are drawn from a lot and physically mixed to form composite samples. Subsamples are then taken from these composite samples and tested to determine the lot quality, usually the lot mean, μ_x. Composite sampling procedures typically are employed with bulk materials, for which high testing costs preclude estimation of μ_x using the arithmetic average of values from several individually tested increments. Because of the physical averaging that occurs when increments are mixed to form composite samples, it is possible to estimate μ_x with specified precision with greater economy using a composite sampling procedure than using a noncompositing procedure. This dissertation extends and interprets the work of Brown and Fisher on modeling procedures that involve subsampling mixtures of sampled material. Models are developed for sampling from segmented or nonsegmented lots, allowing for more than one finite composite, testing error, within-increment variability, or two subsampling stages. The result of each model is a formula expressing the variance of the estimator of μ_x in terms of model parameters. Each such formula is contrasted with the corresponding formula derived from the customarily employed random effects linear model. / Ph. D.