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Aims: The purpose of this work was to derive a simple Excel spreadsheet and a set of standard tables of most probable number (MPN) values that can be applied by users of International Standard Methods to obtain the same output values for MPN, SD of the MPN, 95% confidence limits and test validity. With respect to the latter, it is considered that the Blodgett concept of 'rarity' is more valuable than the frequently used approach of improbability (vide de Man).
Methods and Results: The paper describes the statistical procedures used in the work and the reasons for introducing a new set of conceptual and practical approaches to the determination of MPNs and their parameters. Examples of MPNs derived using these procedures are provided. The Excel spreadsheet can be downloaded from http://www.wiwiss.fu-berlin.de/institute/iso/mitarbeiter/wilrich/index.html.
Conclusions: The application of the revised approach to the determination of MPN parameters permits those who wish to use tabulated values, and those who require access to a simple spreadsheet to determine values for nonstandard test protocols, to obtain the same output values for any specific set of multiple test results. The concept of 'rarity' is a more easily understood parameter to describe test result combinations that are not statistically valid. Provision of the SD of the log MPN value permits derivation of uncertainty parameters that have not previously been possible.
Significance and Impact of the Study: A consistent approach for the derivation of MPNs and their parameters is essential for coherence between International Standard Methods. It is intended that future microbiology standard methods will be based on the procedures described in this paper.
Background: We deal with interlaboratory experiments (collaborative studies) in which k participating laboratories, selected randomly from a population of laboratories, use samples from one and the same material or matrix. They perform binary microbiological measurements for which the measurement results are either “0” (target microorganisms not detected) or “1” (target microorganisms detected). The performance of such a measurement method is described by its probability of detection (POD) function, i.e., the POD as a function of the contamination of the sample (CFU per gram or CFU per milliliter), or by the level of detection (LODp), i.e., the contamination level of the sample that is detected (measurement result “1”) with a specified probability p. Objective: We derive an approximate statistical analysis that is simple enough to be implemented in a spreadsheet application.
Methods: Under the assumption of a Poisson distribution of the number of CFU in the samples, we estimate the mean POD function of the laboratories and the SD of the laboratory effect based on a complementary log-log model, a special case of the Generalized Linear Model in the special situation in which the contamination level is known by means other than the POD. The estimates are obtained by maximization of the Laplace approximation of the likelihood function. By simulation, a bias correction factor for the estimate of the SD is obtained. With the estimated POD function, LODs can be estimated. The model can also be used to evaluate the relative LOD of an alternative method with repect to a reference method.
Results: The EXCEL program PODLOD-interlab_ver1.xls for this method of statistical analysis can be downloaded from http://www.wiwiss.fu-berlin.de/fachbereich/vwl/iso/ehemalige/wilrich.
Highlights: A simple approximate statistical method for the estimation of the POD and LOD is derived. The method also allows the estimation of the RLOD of an alternative Microbiological Methods Received December 11, 2018. Accepted by AH April 5, 2019. Estimation of the POD Function and the LOD of a Binary Microbiological Measurement Method from an Interlaboratory Experiment Basil Jarvis, Ross Biosciences Ltd, Upton Bishop, Ross-on-Wye HR9 7UR, United Kingdom; Cordula Wilrich, Bundesanstalt für Materialforschung und –prüfung, Unter den Eichen 87, D-12205 Berlin, Germany; Peter-Theodor Wilrich, Freie Universität Berlin, Institut für Statistik und Ökonometrie, Garystrasse 21, D-14195 Berlin, Germany.
DOI: https://doi.org/10.5740/jaoacint.18-0412
method with respect to reference method. The method is implemented in an EXCEL program that can be downloaded from http://www.wiwiss.fu-berlin.de/fachbereich/vwl/iso/ehemalige/wilrich.
In connection with the use of chemically unstable gases (especially acetylene and ethylene oxide) accidents keep on happening - amongst them also quite serious ones. These gases are known to be chemically unstable. A chemically unstable sas is a flammable gas that is able to react exolosivelv even in the absence of air or oxveen. The investigation of accidents showed that the Chemical instability of flammable gases played an important role in the severity of accidents. Therefore, this hazardous property was included in the global harmonizatiön of the Classification of Chemicals. The Classification of chemically unstable flammable gases and mixtures is an amendment to Chapter 2.2 “Flammable gases” of the UN Globally Harmonized System of Classification and Labelling of Chemicals (GHS), because most chemically unstable gases are flammable as well. The proposal to add them to the GHS originated from the experts of an informal working group of the UN Sub-Committee of Expert on the GHS (UNSCEGHS) headed by BAM, Germany. The UNSCEGHS has decided to include it in the Fourth Revised Edition of the GHS. The respective method for determining whether a gas is chemically unstable or not, is included in the UN Manual of Tests and Criteria. This paper presents some experimental investigations of these gases, the test methods, examples of new classifications and results from CHEMSAFE
Länderübergreifende und vereinheitlichte Kriterien zur Einstufung von gefährlichen Chemikalien und zu ihrer Gefahrenkommunikation sind ein wichtiges Element für die Sicherheit im Umgang mit Gefahrstoffen. Das globale System zur Einstufung und Kennzeichnung von Chemikalien – das Globally Harmonized System der Vereinten Nationen (UN) – oder kurz GHS – unterstützt dieses Anliegen und hat auch Eingang in die europäischen Rechtsvorschriften gefunden. Die Vereinten Nationen (UN) haben sich nunmehr einiger systematischer Probleme im GHS angenommen und verändern in diesem Zuge auch das Einstufungssystem für Explosivstoffe. Die Fachdiskussionen im Kreis der Experten bei UN sind komplex und nicht leicht zu verfolgen. Es soll daher hier ein Zwischenstand über die bislang vorliegenden Ergebnisse der damit befassten Arbeitsgruppen dargestellt werden.
One of the fundamental principles of the UN-GHS (Globally Harmonized System of Classification and Labelling of Chemicals) is that all hazards of a chemical should be assigned and communicated. There is no general prioritization of hazards in the sense that certain hazard classes are not applicable if another one has been assigned. In contrast to health and environmental hazards, there are physical or chemical factors which preclude certain combinations of physical hazard classes. So far, there is no common understanding as to which combinations are relevant and which not. For example, should a pyrophoric liquid be classified as flammable liquid in addition, or is this redundant and unnecessary? In the course of the implementation of the GHS by countries or sectors and the actual application by industry all over the world, such questions become more and more important. For many of the combinations an unambiguous decision based on theGHS alone is not possible, thus confirming that the question which physical hazard classes might be assigned simultaneously to a chemical is not trivial. As one more milestone on the path to a globally harmonized system for the classification of hazardous chemicals, this should be discussed and ultimately solved on a global basis. It is the hope that this presentaion might serve as an impetus for such discussions.