Capability of Detection for Poisson Distributed Measurements by Normal Approximations

In the analysis of very small components, it is very important to know what concentration or amount of the analyte can be detected by the measurement method. When we determine whether the analysis sample is the same as the basic state, the capability of detection for the measurement method is defined as the amount that can be detected. The ISO 11843 series standardizes the capability of detection. ISO 11843 series has not described the capability of detection for Poisson distributed measures. The measurement results occasionally are count data. When the capability of detection can be exactly measured, it can be derived numerically, but it is very difficult to be derived analytically. There are various approximation methods having their own distinct features for a Poisson distribution. However, so far it is not known which approximation is best from the viewpoint of estimating the capability of detection. In this paper, the evaluation of the capability of detection for Poisson distributed measurements is described. A number of approximation methods are proposed from the viewpoint of the capability of detection for the measurement method. The best approximation method is then compared with the exact method.