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Organisationseinheit der BAM
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.
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.
Estimation of the POD function and the LOD of a qualitative microbiological measurement method
(2009)
Qualitative microbiological measurement methods in which the measurement results are either 0 (microorganism not detected) or 1 (microorganism detected) are discussed. The performance of such a measurement method is described by its probability of detection as a function of the contamination (CFU/g or CFU/mL) of the test material, or by the LODp, i.e., the contamination that is detected (measurement result 1) with a specified probability p. A complementary log-log model was used to statistically estimate these performance characteristics. An intralaboratory experiment for the detection of Listeria monocytogenes in various food matrixes illustrates the method. The estimate of LOD50% is compared with the Spearman-Kaerber method.
Trial Design for Testing and Evaluation of Metal Detectors Used in Humanitarian Landmine Clearance
(2006)
ITEP project 2.1.1.2 - Final report - Reliability model for test and evaluation of metal detectors
(2004)
Metal detectors used in demining have been tested within the frame of the International Test and
Evaluation Programme project ITEP 2.1.1.2. Detection reliability tests were performed in accordance
with the CEN workshop agreement describing specifications for test and evaluation (CWA 14747:2003). Results of these tests are aimed to verify and should help to optimise the proposed testing
procedures.
The detection of defects in aircraft components or parts of a power plant or mines in the ground is connected with the task to distinguish between signals caused be the item searched for and noisy signals from other sources. The reliability of the system is the better the better the system is in detecting the wanted signal and avoiding false alarms caused by noise. It is usual to measure the reliability of diagnostic systems in terms of ROC-curves (Re-ceiver Operating Characteristics) and POD-curves (Probability of Detec-tion). The ROC curves describe the POD versus Probability of False Alarm with growing system sensitivity along the curve. POD curves describe the Probability of Detection for a fixed sensitivity for a variation of item sizes or depths. Reliability of the whole system is always a composition of the physics
and technique, application influences and the human factors. For the scien-tific understanding and possibilities of improvement, decomposition accord-ing to a modular model is helpful. The authors present their experiences with the reliability evaluation of metal detectors for humanitarian demining and an NDT system of mechanized ultrasonic phased array testing of copper welds. The special concern in demining is the influence of soil types, detec-tors and the experiences of human beings.
The total reliability of a mine searching system is driven by the triple of intrinsic
capability, which describes the physical-technical basis capability, the application and
environmental factors and the human factors. Some of them can be determined in
laboratory measurements but the human factor and a part of environment conditions
and their interaction with the device need to be treated statistically. That is why the
test & evaluation procedure described in CEN CWA 14747:2003, includes in addition
to parameter tests of metal detectors also the reliability or blind field tests under local
conditions with local personnel. A series of three big field trials had been
accomplished in the ITEP-project 2.1.1.2 Reliability Model for Test & Evaluation of
Metal Detectors to specify the optimum conditions for reliable trial results with
affordable effort. For each set of specific working conditions, characterized in terms
of a combination of one mine type in one soil with one detector handled by local
personnel, the searching system will show up a working performance in mine
detection rates as a function of mine depth and show up a certain overall false call
rate. During the ITEP-trials in Benkovac and Oberjettenberg the authors learnt to
determine this function separately for each mine type in each soil, which is especially
important for low metal mines in uncooperative soil which will be illustrated for the
mine PMA2 in different types of soil. The question of representativeness for field
conditions on the one hand and necessary statistical set up for the possibility to
distinguish between individual detector performances is still under discussion.
During the second European-American Workshop on NDE Reliability, September 99 in Boulder, the term NDE reliability was defined as the degree that an NDT system is capable of achieving its purpose regarding detection, characterization and false calls. The most common but also most expensive - way to determine this degree of capability in e.g. defect detection is to make just a performance demonstration using realistic test samples and to count the correct detections and false calls. For a more efficient way of reliability evaluation we propose to decompose the system into main modules e.g. according to the reliability formula set up on the first workshop: into f(IC) a function of IC the intrinsic capability, determined by the physics and the technique of the NDE method representing an ideal upper bound of the reliability and g(AP) a function of AP the industrial application factor like surface state or limited access to a component in general diminishing the ideal capability and finally h(HF) the function of the human factor which is in general also diminishing the ideal capability. The workshop proposed a rather plain mathematical shape for the formula R = f(IC) g(AP) h(HF) which should be considered merely as a philosophical expression but not as exact mathematical formula to be applied for evaluation of e.g. POD data. We propose to decompose the NDE system into modules in terms of functions of IC, AP and HF if appropriate or additional ones if necessary and then to analyze the mutual relationships of the terms via fault tree analysis. Finally the total reliability of the system is composed of the reliability of the subsystems via the rules of statistical systems theory.
First trials for this approach of data analysis will be presented via examples from NDE systems in the aerospace industry.