Statistical quality control is the application of statistical methods to problems for which it is of interest to evaluate, establish, or verify the quality of a product. The two basic areas of statistical quality control that have received both the greatest attention in the literature and the widest acceptance in industry are acceptance sampling and statistical process control. In the majority of such techniques, a single characteristic of an item is used to describe its quality. In such cases, one of two basic types of product quality measures is typically used: attributes product quality measures and variables product quality measures. Variables product quality measures evaluate an item’s quality by measuring its quality characteristic on a continuous scale. Attributes product quality measures assign a 0 to an item if its characteristic is conforming to some specification, and 1 if its characteristic is nonconforming. Although attributes and variables product quality measures have many appropriate applications, there are many situations m which product quality is best described by classifying a single characteristic of the item using three or more discrete levels. A multilevel discrete product quality measure is a function that assigns a numerical value to such an item corresponding to the level in which it is classified. Several acceptance sampling plans and control charts that incorporate the use of multilevel discrete product quality measures are defined here. In addition to the multilevel discrete product quality measure, each of the defined methods utilizes a quality value function. A quality value function assigns a numerical value to an item based on the classification it receives from the multilevel discrete product quality measure. Each of the defined multilevel acceptance sampling plans and multilevel control charts is evaluated with respect to its probabilistic behavior. In addition, the problem of parameter selection and quality value function specification is addressed for each of the defined techniques. The cases considered are the 3-level case, the 4-level case, and the general j-level case. / Ph. D.