ABSTRACT
In the 1930s, Shewhart, motivated by industrial quality control problems, introduced the control chart that raises a warning when a current observation becomes larger than a specific tolerance level. This chart is referred to as the Shewhart control chart. This chapter shows that the Shewhart-type rules have certain optimality properties for detecting changes of arbitrarily magnitude. It turns out that the likelihood ratio based Shewhart detection rule, which consists in comparing the running likelihood ratio to a threshold, is optimal with respect to Bayesian as well as maximin criteria, maximizing the instantaneous probability of detection.
