Different criteria of optimality are used in different subcultures of statistical
surveillance. One aim with this review is to bridge the gap between the different areas.
The shortcomings of some criteria of optimality are demonstrated by their
implications. Some commonly used methods are examined in detail, with respect to
optimality. The examination is made for a standard situation in order to focus on the
inferential principles. A uniform presentation of methods, by expressions of likelihood
ratios, facilitates the comparisons between methods. The correspondences between
criteria of optimality and methods are examined. The situations and parameter values
for which some commonly used methods have optimality properties are thus
determined. A linear approximation of the full likelihood ratio method, which satisfies
several criteria of optimality, is presented. This linear approximation is used to
examine when linear methods are approximately optimal. Methods for complicated
situations are reviewed with respect to optimality and robustness.