Foreword

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This document was prepared by Technical Committee ISO/TC 69, Application of statistical methods, Subcommittee SC 6, Measurement methods and results.

This third edition cancels and replaces the second edition ( ISO 11843-6:2019 ), which has been technically revised.

The main changes are as follows:

the symbols were modified to conform to ISO 11843-1 ;
a list of symbols was moved from Annex A to Clause 4;
in 6.3, explanatory text of how to determine the minimum detectable value was added;
Clause 8 was revised to provide a description of the appropriate approach for determining whether or not the target substance has been detected;
typographic and obvious errors were corrected.

A list of all parts in the ISO 11843 series can be found on the ISO website.

Any feedback or questions on this document should be directed to the user’s national standards body. A complete listing of these bodies can be found at www.iso.org/members.html.

Introduction

Many types of instruments use the pulse-counting method for detecting signals. X-ray, electron and ion-spectroscopy detectors, such as X-ray diffractometers (XRD), X-ray fluorescence spectrometers (XRF), X-ray photoelectron spectrometers (XPS), Auger electron spectrometers (AES), secondary ion mass spectrometers (SIMS) and gas chromatograph mass spectrometers (GCMS) are of this type. These signals consist of a series of pulses produced at random and irregular intervals. They can be understood statistically using a Poisson distribution and the methodology for determining the minimum detectable value can be deduced from statistical principles.

Determining the minimum detectable value of signals is sometimes important in practical work. The value provides a criterion for deciding when “the signal is certainly not detected”, or when “the signal is significantly different from the background noise level”^[ 1 ^]to[ 8 ^]. For example, it is valuable when measuring the presence of hazardous substances or surface contamination of semi-conductor materials. RoHS (Restrictions on Hazardous Substances) sets limits on the use of six hazardous materials (hexavalent chromium, lead, mercury, cadmium and the flame retardant agents, perbromobiphenyl, PBB, and perbromodiphenyl ether, PBDE) in the manufacturing of electronic components and related goods sold in the EU. For that application, XRF and GCMS are the testing instruments used. XRD is used to measure the level of hazardous asbestos and crystalline silica present in the environment or in building materials.

Although the methodology employed to determine the minimum detection values has long been established in the field of chemical analysis, it has hitherto remained undefined within the domain of pulse count measurements. The necessity of establishing a methodology for determining the minimum detectable value in this field is duly acknowledged^[ 9 ^].

In this document the Poisson distribution is approximated by the normal distribution, ensuring consistency with the IUPAC approach laid out in the ISO 11843 series . The conventional approximation is used to generate the variance, the critical value of the response variable, the capability of detection criteria and the minimum detectability level^[ 10 ^].

In this document:

α is the probability of erroneously detecting that a system is not in the basic state, when really it is in that state;
β is the probability of erroneously not detecting that a system is not in the basic state when the value of the state variable is equal to the minimum detectable value(x_D).

1 Scope

This document presents methods for determining the critical value of the response variable and the minimum detectable value in Poisson distribution measurements. It is applicable when variations in both the background noise and the signal are describable by the Poisson distribution. The conventional approximation is used to approximate the Poisson distribution by the normal distribution consistent with ISO 11843-3 and ISO 11843-4 .

The accuracy of the normal approximation as compared to the exact Poisson distribution is discussed in Annex B.

2 Normative references

3 Terms and definitions

4 Symbols

5 Measurement system and data handling

6 Computation by approximation

6.1 The critical value based on the normal distribution

6.2 Determination of the critical value of the response variable

6.3 Sufficient capability of the detection criterion

6.4 Confirmation of the sufficient capability of detection criterion

7 Reporting the results from an assessment of the capability of detection

8 Reporting the results from an application of the method

Bibliography