A Mathematical Framework for Statistical Process Control

Abstract

Only one year after SHEWHART’s [10] first paper on control charts had appeared in the Bell System Technical Journal, BECKER, PLAUT & RUNGE [1] published their monograph on Statistical Process Control (SPC) in 1927. In their monograph they develop most of the mathematical tools necessary for judging and comparing lots and processes, but don’t mention SHEWHART’s control chart as a simple and effective graphical method for performing process monitoring. Since then almost 70 years passed resulting in a simply indeterminable body of literature. But, unfortunately, the majority of publications in the field of SPC concentrates on methodological and technical problems, thus omitting a thorough fundamental discussion of the problem itself. The result is that Statistical Process Control resembles a more or less unorganized pile of technical tools derived from different approaches. Practitioners are invited to just select one of these tools, and often feel overwhelmed. Even experts in Statistical Process Control must often surrender faced with the ever increasing number of different alternatives for one and the same situation. This survey aims in clarifying the confused state in Statistical Process Control by working out its foundations and introducing a natural order within the existing methodology.