Analytical Sciences

A Practical Method for Determining Minimum Detectable Values in Pulse-Counting Measurements

Yoichiro FURUKAWA,* Manabu IWASAKI,** and Akihiro TANAKA***

*DENKI KAGAKU KOGYO KABUSHIKI KAISHA, Central Research Institute, 3-5-1 Asahimachi, Machida, Tokyo 194-8560, Japan
**Department of Computer and Information Science, Seikei University, 3-3-1 Kichijoji-Kitamachi, Musashino, Tokyo 180-8633, Japan
***ULVAC-PHI, Incorporated, 370 Enzo, Chigasaki, Kanagawa 253-8522, Japan

The purpose of this paper is to propose a statistical method for determining minimum detectable values in a pulse-counting measurements. The output of x-ray, electron and ion-spectroscopy detectors is a series of pulses that vary in their arrival frequency according to a Poisson distribution. The analysis presented here relates this to a Normal distribution, making it consistent with the standards and methodology recommended by IUPAC and in the ISO 11843 series of international standards. The theory and limitations of doing this are presented using two types of approximations: a Simple approximation and a Square Root approximation. The variance, critical values of the response variables, capability of detection criteria and the minimum detectable values are then defined. Finally, the validity of the approximations is checked using experimental data. It is concluded that the methodology is accurate enough for practical use.

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