ABSTRACT
The fluctuations in the quality of a manufactured product, such as integrated circuits, steel bars, and cotton fabric, are a result of the variations in the raw materials, machines, and workers used to manufacture them. We measure quality by recording the value of a numerical variable X defined on the population of manufactured objects. Examples of such variables include the thickness of an epitaxial layer deposited on a silicon wafer, the compressive strength of concrete, the tensile strength of a steel cable, etc. Sometimes the variable is categorical as when we classify each item inspected as conforming or nonconforming. In all cases the product is required to meet a standard usually stated in the form of lower and upper control limits on the variable X.
