Quality improvement methods must be understood by those who operate them. This has often been taken to imply that only crude statistical methods are suitable for use on the shop floor. But with the important proviso that proper explanation and motivation are needed, practical understanding of subtle procedures may well run ahead of theoretical work. Many of the major advances in statistical method made in this century have arisen in industrial contexts; and there is no reason to suppose matters will change in this respect in the future. The implications of these facts for industrial management and for the training of statisticians are explored.