Evaluations of likelihood ratio methods for surveillance. Differences and robustness

When a control chart is 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. Results for finite time are given for a shift in level of a Gaussian process. Evaluations are made of the full likelihood ratio method that has two parameters and can be made optimal for both the size and the intensity of a shift. Also, the Shiryaev-Roberts and the CUSUM methods are evaluated. These two methods have one parameter for the size of the shift. A comparison is also made with the commonly used Shewhart method. All methods are based on some likelihood ratio expressions. Differences and limiting equalities among the methods are demonstrated and also the robustness with respect to the choice of parameters.

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