Qualidade de medições em química analítica. Estudo de caso: determinação de cádmio por espectrofotometria de absorção atômica com chama

Calculation of uncertainty of results represents the new paradigm in the area of the quality of measurements in laboratories. The guidance on the Expression of Uncertainty in Measurement of the ISO / International Organization for Standardization assumes that the analyst is being asked to give a parameter that characterizes the range of the values that could reasonably be associated with the result of the measurement. In practice, the uncertainty of the analytical result may arise from many possible sources: sampling, sample preparation, matrix effects, equipments, standards and reference materials, among others. This paper suggests a procedure for calculation of uncertainties components of an analytical result due to sample preparation (uncertainty of weights and volumetric equipment) and instrument analytical signal (calibration uncertainty). A numerical example is carefully explained based on measurements obtained for cadmium determination by flame atomic absorption spectrophotometry. Results obtained for components of total uncertainty showed that the main contribution to the analytical result was the calibration procedure.

Acreditação do Laboratório de Metrologia da Frilabo para Ensaios e Calibrações em Temperaturas

O trabalho desenvolvido centrou-se na preparação da acreditação NP EN ISO/IEC 17025 do Laboratório de Metrologia da empresa Frilabo para prestação de serviços na área das temperaturas, no ensaio a câmaras térmicas e na calibração de termómetros industriais. Considerando o âmbito do trabalho desenvolvido, são abordados nesta tese conceitos teóricos sobre temperatura e incertezas bem como considerações técnicas de medição da temperatura e cálculo de incertezas. São também referidas considerações sobre os diferentes tipos de câmaras térmicas e termómetros. O texto apresenta os documentos elaborados pelo autor sobre os procedimentos de ensaio a câmaras térmicas e respetivo procedimento de cálculo da incerteza. Também estão presentes neste texto documentos elaborados pelo autor sobre os procedimentos de calibração de termómetros industriais e respetivo procedimento de cálculo da incerteza. Relativamente aos ensaios a câmara térmicas e calibração de termómetros o autor elaborou os fluxogramas sobre a metodologia da medição da temperatura nos ensaios, a metodologia de medição da temperatura nas calibrações, e respetivos cálculos de incertezas. Nos diferentes anexos estão apresentados vários documentos tais como o modelo de folha de cálculo para tratamento de dados relativos ao ensaio, modelo de folha de cálculo para tratamento de dados relativo às calibrações, modelo de relatório de ensaio, modelo de certificado de calibração, folhas de cálculo para gestão de clientes/equipamentos e numeração automática de relatórios de ensaio e certificados de calibração que cumprem os requisitos de gestão do laboratório. Ainda em anexo constam todas as figuras relativas à monitorização da temperatura nas câmara térmicas como também as figuras da disposição dos termómetros no interior das câmaras térmicas. Todas as figuras que aparecem ao longo do documento que não estão referenciadas são da adaptação ou elaboração própria do autor. A decisão de alargar o âmbito da acreditação do Laboratório de Metrologia da Frilabo para calibração de termómetros, prendeu-se com o facto de que sendo acreditado como laboratório de ensaios na área das temperaturas, a realização da rastreabilidade dos padrões de medida internamente, permitiria uma gestão de recursos otimizada e rentabilizada. A metodologia da preparação de todo o processo de acreditação do Laboratório de Metrologia da Frilabo, foi desenvolvida pelo autor e está expressa ao longo do texto da tese incluindo dados relevantes para a concretização da referida acreditação nos dois âmbitos. A avaliação de todo o trabalho desenvolvido será efetuada pelo o organismo designado IPAC (Instituto Português de Acreditação) que confere a acreditação em Portugal. Este organismo irá auditar a empresa com base nos procedimentos desenvolvidos e nos resultados obtidos, sendo destes o mais importante o Balanço da Melhor Incerteza (BMI) da medição também conhecido por Melhor Capacidade de Medição (MCM), quer para o ensaio às câmaras térmicas, quer para a calibração dos termómetros, permitindo desta forma complementar os serviços prestados aos clientes fidelizados à Frilabo. As câmaras térmicas e os termómetros industriais são equipamentos amplamente utilizados em diversos segmentos industriais, engenharia, medicina, ensino e também nas instituições de investigação, sendo um dos objetivos respetivamente, a simulação de condições específicas controladas e a medição de temperatura. Para entidades acreditadas, como os laboratórios, torna-se primordial que as medições realizadas com e nestes tipos de equipamentos ostentem confiabilidade metrológica1, uma vez que, resultados das medições inadequados podem levar a conclusões equivocadas sobre os testes realizados. Os resultados obtidos nos ensaios a câmaras térmicas e nas calibrações de termómetros, são considerados bons e aceitáveis, uma vez que as melhores incertezas obtidas, podem ser comparadas, através de consulta pública do Anexo Técnico do IPAC, com as incertezas de outros laboratórios acreditados em Portugal. Numa abordagem mais experimental, pode dizer-se que no ensaio a câmaras térmicas a obtenção de incertezas mais baixas ou mais altas depende maioritariamente do comportamento, características e estado de conservação das câmaras, tornando relevante o processo de estabilização da temperatura no interior das mesmas. A maioria das fontes de incerteza na calibração dos termómetros são obtidas pelas características e especificações do fabricante dos equipamentos, que se traduzem por uma contribuição com o mesmo peso para o cálculo da incerteza expandida (a exatidão de fabricante, as incertezas herdadas de certificados de calibração, da estabilidade e da uniformidade do meio térmico onde se efetuam as calibrações). Na calibração dos termómetros as incertezas mais baixas obtêm-se para termómetros de resoluções mais baixas. Verificou-se que os termómetros com resolução de 1ºC não detetavam as variações do banho térmico. Nos termómetros com resoluções inferiores, o peso da contribuição da dispersão de leituras no cálculo da incerteza, pode variar consoante as características do termómetro. Por exemplo os termómetros com resolução de 0,1ºC, apresentaram o maior peso na contribuição da componente da dispersão de leituras. Pode concluir-se que a acreditação de um laboratório é um processo que não é de todo fácil. Podem salientar-se aspetos que podem comprometer a acreditação, como por exemplo a má seleção do ou dos técnicos e equipamentos (má formação do técnico, equipamento que não seja por exemplo adequado à gama, mal calibrado, etc…) que vão efetuar as medições. Se não for bem feita, vai comprometer todo o processo nos passos seguintes. Deve haver também o envolvimento do todos os intervenientes do laboratório, o gestor da qualidade, o responsável técnico e os técnicos, só assim é que é possível chegar à qualidade pretendida e à melhoria contínua da acreditação do laboratório. Outro aspeto importante na preparação de uma acreditação de um laboratório é a pesquisa de documentação necessária e adequada para poder tomar decisões corretas na elaboração dos procedimentos conducentes à referida. O laboratório tem de mostrar/comprovar através de registos a sua competência. Finalmente pode dizer-se que competência é a palavra chave de uma acreditação, pois ela manifesta-se nas pessoas, equipamentos, métodos, instalações e outros aspetos da instituição a que pertence o laboratório sob acreditação.

Power systems reliability calculation based on fuzzy data mining

This paper presents a methodology supported on the data base knowledge discovery process (KDD), in order to find out the failure probability of electrical equipments’, which belong to a real electrical high voltage network. Data Mining (DM) techniques are used to discover a set of outcome failure probability and, therefore, to extract knowledge concerning to the unavailability of the electrical equipments such us power transformers and high-voltages power lines. The framework includes several steps, following the analysis of the real data base, the pre-processing data, the application of DM algorithms, and finally, the interpretation of the discovered knowledge. To validate the proposed methodology, a case study which includes real databases is used. This data have a heavy uncertainty due to climate conditions for this reason it was used fuzzy logic to determine the set of the electrical components failure probabilities in order to reestablish the service. The results reflect an interesting potential of this approach and encourage further research on the topic.

Contribution of the evaluation strategy and the use of hearing protection for the uncertainty associated with occupational exposure to noise

Doctoral Thesis for PhD degree in Industrial and Systems Engineering

Tractable valuations under uncertainty

I put forward a concise and intuitive formula for the calculation of the valuation for a good in the presence of the expectation that further, related, goods will soon become available. This valuation is tractable in the sense that it does not require the explicit resolution of the consumerís life-time problem.

A peripheral dose calculation model for estimating second cancer risk after breast radiotherapy

AbstractBreast cancer is one of the most common cancers affecting one in eight women during their lives. Survival rates have increased steadily thanks to early diagnosis with mammography screening and more efficient treatment strategies. Post-operative radiation therapy is a standard of care in the management of breast cancer and has been shown to reduce efficiently both local recurrence rate and breast cancer mortality. Radiation therapy is however associated with some late effects for long-term survivors. Radiation-induced secondary cancer is a relatively rare but severe late effect of radiation therapy. Currently, radiotherapy plans are essentially optimized to maximize tumor control and minimize late deterministic effects (tissue reactions) that are mainly associated with high doses (» 1 Gy). With improved cure rates and new radiation therapy technologies, it is also important to evaluate and minimize secondary cancer risks for different treatment techniques. This is a particularly challenging task due to the large uncertainties in the dose-response relationship.In contrast with late deterministic effects, secondary cancers may be associated with much lower doses and therefore out-of-field doses (also called peripheral doses) that are typically inferior to 1 Gy need to be determined accurately. Out-of-field doses result from patient scatter and head scatter from the treatment unit. These doses are particularly challenging to compute and we characterized it by Monte Carlo (MC) calculation. A detailed MC model of the Siemens Primus linear accelerator has been thoroughly validated with measurements. We investigated the accuracy of such a model for retrospective dosimetry in epidemiological studies on secondary cancers. Considering that patients in such large studies could be treated on a variety of machines, we assessed the uncertainty in reconstructed peripheral dose due to the variability of peripheral dose among various linac geometries. For large open fields (> 10x10 cm2), the uncertainty would be less than 50%, but for small fields and wedged fields the uncertainty in reconstructed dose could rise up to a factor of 10. It was concluded that such a model could be used for conventional treatments using large open fields only.The MC model of the Siemens Primus linac was then used to compare out-of-field doses for different treatment techniques in a female whole-body CT-based phantom. Current techniques such as conformai wedged-based radiotherapy and hybrid IMRT were investigated and compared to older two-dimensional radiotherapy techniques. MC doses were also compared to those of a commercial Treatment Planning System (TPS). While the TPS is routinely used to determine the dose to the contralateral breast and the ipsilateral lung which are mostly out of the treatment fields, we have shown that these doses may be highly inaccurate depending on the treatment technique investigated. MC shows that hybrid IMRT is dosimetrically similar to three-dimensional wedge-based radiotherapy within the field, but offers substantially reduced doses to out-of-field healthy organs.Finally, many different approaches to risk estimations extracted from the literature were applied to the calculated MC dose distribution. Absolute risks varied substantially as did the ratio of risk between two treatment techniques, reflecting the large uncertainties involved with current risk models. Despite all these uncertainties, the hybrid IMRT investigated resulted in systematically lower cancer risks than any of the other treatment techniques. More epidemiological studies with accurate dosimetry are required in the future to construct robust risk models. In the meantime, any treatment strategy that reduces out-of-field doses to healthy organs should be investigated. Electron radiotherapy might offer interesting possibilities with this regard.RésuméLe cancer du sein affecte une femme sur huit au cours de sa vie. Grâce au dépistage précoce et à des thérapies de plus en plus efficaces, le taux de guérison a augmenté au cours du temps. La radiothérapie postopératoire joue un rôle important dans le traitement du cancer du sein en réduisant le taux de récidive et la mortalité. Malheureusement, la radiothérapie peut aussi induire des toxicités tardives chez les patients guéris. En particulier, les cancers secondaires radio-induits sont une complication rare mais sévère de la radiothérapie. En routine clinique, les plans de radiothérapie sont essentiellement optimisées pour un contrôle local le plus élevé possible tout en minimisant les réactions tissulaires tardives qui sont essentiellement associées avec des hautes doses (» 1 Gy). Toutefois, avec l'introduction de différentes nouvelles techniques et avec l'augmentation des taux de survie, il devient impératif d'évaluer et de minimiser les risques de cancer secondaire pour différentes techniques de traitement. Une telle évaluation du risque est une tâche ardue étant donné les nombreuses incertitudes liées à la relation dose-risque.Contrairement aux effets tissulaires, les cancers secondaires peuvent aussi être induits par des basses doses dans des organes qui se trouvent hors des champs d'irradiation. Ces organes reçoivent des doses périphériques typiquement inférieures à 1 Gy qui résultent du diffusé du patient et du diffusé de l'accélérateur. Ces doses sont difficiles à calculer précisément, mais les algorithmes Monte Carlo (MC) permettent de les estimer avec une bonne précision. Un modèle MC détaillé de l'accélérateur Primus de Siemens a été élaboré et validé avec des mesures. La précision de ce modèle a également été déterminée pour la reconstruction de dose en épidémiologie. Si on considère que les patients inclus dans de larges cohortes sont traités sur une variété de machines, l'incertitude dans la reconstruction de dose périphérique a été étudiée en fonction de la variabilité de la dose périphérique pour différents types d'accélérateurs. Pour de grands champs (> 10x10 cm ), l'incertitude est inférieure à 50%, mais pour de petits champs et des champs filtrés, l'incertitude de la dose peut monter jusqu'à un facteur 10. En conclusion, un tel modèle ne peut être utilisé que pour les traitements conventionnels utilisant des grands champs.Le modèle MC de l'accélérateur Primus a été utilisé ensuite pour déterminer la dose périphérique pour différentes techniques dans un fantôme corps entier basé sur des coupes CT d'une patiente. Les techniques actuelles utilisant des champs filtrés ou encore l'IMRT hybride ont été étudiées et comparées par rapport aux techniques plus anciennes. Les doses calculées par MC ont été comparées à celles obtenues d'un logiciel de planification commercial (TPS). Alors que le TPS est utilisé en routine pour déterminer la dose au sein contralatéral et au poumon ipsilatéral qui sont principalement hors des faisceaux, nous avons montré que ces doses peuvent être plus ou moins précises selon la technTque étudiée. Les calculs MC montrent que la technique IMRT est dosimétriquement équivalente à celle basée sur des champs filtrés à l'intérieur des champs de traitement, mais offre une réduction importante de la dose aux organes périphériques.Finalement différents modèles de risque ont été étudiés sur la base des distributions de dose calculées par MC. Les risques absolus et le rapport des risques entre deux techniques de traitement varient grandement, ce qui reflète les grandes incertitudes liées aux différents modèles de risque. Malgré ces incertitudes, on a pu montrer que la technique IMRT offrait une réduction du risque systématique par rapport aux autres techniques. En attendant des données épidémiologiques supplémentaires sur la relation dose-risque, toute technique offrant une réduction des doses périphériques aux organes sains mérite d'être étudiée. La radiothérapie avec des électrons offre à ce titre des possibilités intéressantes.

Accuracy of out-of-field dose calculation of tomotherapy and cyberknife treatment planning systems: A dosimetric study.

PURPOSE: Late toxicities such as second cancer induction become more important as treatment outcome improves. Often the dose distribution calculated with a commercial treatment planning system (TPS) is used to estimate radiation carcinogenesis for the radiotherapy patient. However, for locations beyond the treatment field borders, the accuracy is not well known. The aim of this study was to perform detailed out-of-field-measurements for a typical radiotherapy treatment plan administered with a Cyberknife and a Tomotherapy machine and to compare the measurements to the predictions of the TPS. MATERIALS AND METHODS: Individually calibrated thermoluminescent dosimeters were used to measure absorbed dose in an anthropomorphic phantom at 184 locations. The measured dose distributions from 6 MV intensity-modulated treatment beams for CyberKnife and TomoTherapy machines were compared to the dose calculations from the TPS. RESULTS: The TPS are underestimating the dose far away from the target volume. Quantitatively the Cyberknife underestimates the dose at 40cm from the PTV border by a factor of 60, the Tomotherapy TPS by a factor of two. If a 50% dose uncertainty is accepted, the Cyberknife TPS can predict doses down to approximately 10 mGy/treatment Gy, the Tomotherapy-TPS down to 0.75 mGy/treatment Gy. The Cyberknife TPS can then be used up to 10cm from the PTV border the Tomotherapy up to 35cm. CONCLUSIONS: We determined that the Cyberknife and Tomotherapy TPS underestimate substantially the doses far away from the treated volume. It is recommended not to use out-of-field doses from the Cyberknife TPS for applications like modeling of second cancer induction. The Tomotherapy TPS can be used up to 35cm from the PTV border (for a 390 cm(3) large PTV).

Probabilistic evidential assessment of gunshot residue particle evidence (Part I): likelihood ratio calculation and case pre-assessment using Bayesian networks

Well developed experimental procedures currently exist for retrieving and analyzing particle evidence from hands of individuals suspected of being associated with the discharge of a firearm. Although analytical approaches (e.g. automated Scanning Electron Microscopy with Energy Dispersive X-ray (SEM-EDS) microanalysis) allow the determination of the presence of elements typically found in gunshot residue (GSR) particles, such analyses provide no information about a given particle's actual source. Possible origins for which scientists may need to account for are a primary exposure to the discharge of a firearm or a secondary transfer due to a contaminated environment. In order to approach such sources of uncertainty in the context of evidential assessment, this paper studies the construction and practical implementation of graphical probability models (i.e. Bayesian networks). These can assist forensic scientists in making the issue tractable within a probabilistic perspective. The proposed models focus on likelihood ratio calculations at various levels of detail as well as case pre-assessment.

Example of Monte Carlo uncertainty assessment in the field of radionuclide metrology

This chapter presents possible uses and examples of Monte Carlo methods for the evaluation of uncertainties in the field of radionuclide metrology. The method is already well documented in GUM supplement 1, but here we present a more restrictive approach, where the quantities of interest calculated by the Monte Carlo method are estimators of the expectation and standard deviation of the measurand, and the Monte Carlo method is used to propagate the uncertainties of the input parameters through the measurement model. This approach is illustrated by an example of the activity calibration of a 103Pd source by liquid scintillation counting and the calculation of a linear regression on experimental data points. An electronic supplement presents some algorithms which may be used to generate random numbers with various statistical distributions, for the implementation of this Monte Carlo calculation method.

Offshoring and outsourcing under demand uncertainty -a supply chain management analysis

Outsourcing and offshoring or any combinations of these have not just become a popular phenomenon, but are viewed as one of the most important management strategies due to the new possibilities from globalization. They have been seen as a possibility to save costs and improve customer service. Executing offshoring and offshore outsourcing successfully can be more complex than initially expected. Potential cost savings resulting from of offshoring and offshore outsourcing are often based on lower manufacturing costs. However, these benefits might be conflicted by a more complex supply chain with service level challenges that can respectively increase costs. Therefore analyzing the total cost effects of offshoring and outsourcing is necessary. The aim of this Master´s Thesis was to to construct a total cost model using academic literature to calculate the total costs and analyze the reasonability of offshoring and offshore outsourcing production of a case company compared to insourcing production. The research data was mainly quantitative and collected mainly from the case company past sales and production records. In addition management level interviews from the case company were conducted. The information from these interviews was used for the qualification of the necessary quantitative data and adding supportive information that could not be gathered from the quantitative data. Both data collection and analysis were guided by a theoretical frame of reference that was based on academic literature concerning offshoring and outsourcing, statistical calculation of demand and total costs. The results confirm the theories that offshoring and offshore outsourcing would reduce total costs as both offshoring and offshore outsourcing options result in lower total annual costs than insourcing mainly due to lower manufacturing costs. However, increased demand uncertainty would make the alternative of offshore outsourcing more risky and difficult to manage. Therefore when assessing the overall impact of the alternatives, offshoring is the most preferable option. As the main cost savings in offshore outsourcing came from lower manufacturing costs, more specifically labour costs, the logistics costs in this case company did not have an essential effect in total costs. The management should therefore pay attention initially to manufacturing costs and then logistics costs when choosing the best production sourcing option for the company.

Discounted cash flow: accounting for uncertainty

Valuation is the process of estimating price. The methods used to determine value attempt to model the thought processes of the market and thus estimate price by reference to observed historic data. This can be done using either an explicit model, that models the worth calculation of the most likely bidder, or an implicit model, that that uses historic data suitably adjusted as a short cut to determine value by reference to previous similar sales. The former is generally referred to as the Discounted Cash Flow (DCF) model and the latter as the capitalisation (or All Risk Yield) model. However, regardless of the technique used, the valuation will be affected by uncertainties. Uncertainty in the comparable data available; uncertainty in the current and future market conditions and uncertainty in the specific inputs for the subject property. These input uncertainties will translate into an uncertainty with the output figure, the estimate of price. In a previous paper, we have considered the way in which uncertainty is allowed for in the capitalisation model in the UK. In this paper, we extend the analysis to look at the way in which uncertainty can be incorporated into the explicit DCF model. This is done by recognising that the input variables are uncertain and will have a probability distribution pertaining to each of them. Thus buy utilising a probability-based valuation model (using Crystal Ball) it is possible to incorporate uncertainty into the analysis and address the shortcomings of the current model. Although the capitalisation model is discussed, the paper concentrates upon the application of Crystal Ball to the Discounted Cash Flow approach.

Reactive power support pricing of distributed generators with primary energy source uncertainty

In this paper, a novel methodology to price the reactive power support ancillary service of Distributed Generators (DGs) with primary energy source uncertainty is shown. The proposed methodology provides the service pricing based on the Loss of Opportunity Costs (LOC) calculation. An algorithm is proposed to reduce the uncertainty present in these generators using Multiobjective Power Flows (MOPFs) implemented in multiple probabilistic scenarios through Monte Carlo Simulations (MCS), and modeling the time series associated with the generation of active power from DGs through Markov Chains (MC). © 2011 IEEE.

A method to incorporate the effect of taxonomic uncertainty on multivariate analyses of ecological data

Researchers in ecology commonly use multivariate analyses (e.g. redundancy analysis, canonical correspondence analysis, Mantel correlation, multivariate analysis of variance) to interpret patterns in biological data and relate these patterns to environmental predictors. There has been, however, little recognition of the errors associated with biological data and the influence that these may have on predictions derived from ecological hypotheses. We present a permutational method that assesses the effects of taxonomic uncertainty on the multivariate analyses typically used in the analysis of ecological data. The procedure is based on iterative randomizations that randomly re-assign non identified species in each site to any of the other species found in the remaining sites. After each re-assignment of species identities, the multivariate method at stake is run and a parameter of interest is calculated. Consequently, one can estimate a range of plausible values for the parameter of interest under different scenarios of re-assigned species identities. We demonstrate the use of our approach in the calculation of two parameters with an example involving tropical tree species from western Amazonia: 1) the Mantel correlation between compositional similarity and environmental distances between pairs of sites, and; 2) the variance explained by environmental predictors in redundancy analysis (RDA). We also investigated the effects of increasing taxonomic uncertainty (i.e. number of unidentified species), and the taxonomic resolution at which morphospecies are determined (genus-resolution, family-resolution, or fully undetermined species) on the uncertainty range of these parameters. To achieve this, we performed simulations on a tree dataset from southern Mexico by randomly selecting a portion of the species contained in the dataset and classifying them as unidentified at each level of decreasing taxonomic resolution. An analysis of covariance showed that both taxonomic uncertainty and resolution significantly influence the uncertainty range of the resulting parameters. Increasing taxonomic uncertainty expands our uncertainty of the parameters estimated both in the Mantel test and RDA. The effects of increasing taxonomic resolution, however, are not as evident. The method presented in this study improves the traditional approaches to study compositional change in ecological communities by accounting for some of the uncertainty inherent to biological data. We hope that this approach can be routinely used to estimate any parameter of interest obtained from compositional data tables when faced with taxonomic uncertainty.

Monte Carlo uncertainty propagation approaches in ADS burn-up calculations

In activation calculations, there are several approaches to quantify uncertainties: deterministic by means of sensitivity analysis, and stochastic by means of Monte Carlo. Here, two different Monte Carlo approaches for nuclear data uncertainty are presented: the first one is the Total Monte Carlo (TMC). The second one is by means of a Monte Carlo sampling of the covariance information included in the nuclear data libraries to propagate these uncertainties throughout the activation calculations. This last approach is what we named Covariance Uncertainty Propagation, CUP. This work presents both approaches and their differences. Also, they are compared by means of an activation calculation, where the cross-section uncertainties of 239Pu and 241Pu are propagated in an ADS activation calculation.

Review and comparison of effective delayed neutron fraction calculation methods with Monte Carlo codes

The calculation of the effective delayed neutron fraction, beff , with Monte Carlo codes is a complex task due to the requirement of properly considering the adjoint weighting of delayed neutrons. Nevertheless, several techniques have been proposed to circumvent this difficulty and obtain accurate Monte Carlo results for beff without the need of explicitly determining the adjoint flux. In this paper, we make a review of some of these techniques; namely we have analyzed two variants of what we call the k-eigenvalue technique and other techniques based on different interpretations of the physical meaning of the adjoint weighting. To test the validity of all these techniques we have implemented them with the MCNPX code and we have benchmarked them against a range of critical and subcritical systems for which either experimental or deterministic values of beff are available. Furthermore, several nuclear data libraries have been used in order to assess the impact of the uncertainty in nuclear data in the calculated value of beff .