Publisher Summary This chapter considers quality control and a key statistical technique in manufacturing and production processes. A variety of control charts, including not only the Shewhart control charts but also more sophisticated ones, based on moving averages and cumulative sums, are considered. The determination of whether a process is in or out of control is greatly facilitated by the use of control charts, which are determined by two numbers—the upper and lower control limits. To employ such a chart, the data generated by the manufacturing process are further divided into subgroups and subgroup statistics. The successive items produced have measurable characteristics, whose mean and variance are fixed when the process is in control. The chapter also shows how to construct control charts based on subgroup averages and on subgroup standard deviations. These control charts can be used to indicate a change in the quality of the items produced and are considered in situations where each item produced has a random number of defects. Three different control charts are also presented that do not consider each subgroup value in isolation—moving average, exponential weighted moving average, and cumulative sum control charts.