This paper, presented orally to the Gordon Research Conference on Statistics in Chemistry in July 1960, traces the development of process inspection schemes from the original methods of Shewhart to the new charts using cumulative sums, and surveys the present practice in the operation of schemes based on cumulative sums. In spitc of the completely different appearance of the visual records kept for Shewhart and cumulative sum charts, a continuous sequence of development from the one type of scheme to the other can be established. The criteria by which a particular process inspection scheme is chosen are also developed and the practical choice of schemes is described.