Shewhart's Idea of Predictability and Modern Statistics

Shewhart's view on statistical control as presented in his 1931 book is connected to predictability and it seems to be inspired by philosophical theories. At that time, there was no proper statistical framework available when Shewhart implemented his ideas on statistical control. This was not a problem for standard settings for which the original Shewhart control chart was developed, but there are currently several much more complicated situations where the standard tools of Shewhart do not suffice without modification. We will discuss whether current statistical notions like hypothesis testing (both the standard Neyman-Pearson theory and other forms like sequential statistics and equivalence testing), prediction intervals and tolerance intervals can be useful in these other settings. We will also discuss alternative settings of statistical control proposed in the literature including Bayesian settings.