Evaluations of likelihood ratio methods for surveillance

Abstract

Methods based on likelihood ratios are known to have several optimality properties. When control charts are used in practice, knowledge about several characteristics of the method is important for the judgement of which action is appropriate at an alarm. The probability of a false alarm, the delay of an alarm and the predictive value of an alarm are qualities (besides the usual ARL) which are described by a simulation study for the evaluations. Since the methods also have interesting optimality properties, the results also enlighten different criteria of optimality. Evaluations are made of the "The Likelihood Ratio Method" which utilizes an assumption on the intensity and has the Shiryaevoptimality. Also, the Roberts and the CUSUM method are evaluated. These two methods combine the likelihood ratios in other ways. A comparison is also made with the Shewhart method, which is a commonly used method.