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Masterarbeit, 2015
55 Seiten, Note: 2
I ABSTRACT
II ACKNOWLEDGEMENTS
III DEDICATION
IV TABLE OF CONTENTS
V LIST OF FIGURES
VII LIST OF TABLES AND DESIGNS
CHAPTER 1
1. INTRODUCTION TO UNCERTAINTY MEASUREMENT
1.1 The Definition of Uncertainty Measurement
1.1.1 The Explanation of the Definition
1.1.2 Specification of Measurand
1.1.3 Error, Precision and Uncertainty
1.2 Sources of Uncertainty
1.3 Estimation of Uncertainties
1.3.1 Model the Process
1.3.2 ‘Type A’ Evaluation of Standard Uncertainty
1.3.3 ‘Type B’ Evaluation of Standard Uncertainty
CHAPTER 2
2. GUM WORKBENCH®
2.1 The Software
2.2 Uncertainty Analysis Steps
CHAPTER 3
3. EVALUATION OF THE UNCERTAINTY USING THE GUM WORKBENCH SOFTWARE
3.1 Project
Calibration and Measurement Uncertainty of a Power Sensor at a Frequency of 19 GHz Using the Gum Workbench Software
3.1.1 Introduction
3.1.2 The Model Equation and the Input Quantities
3.1.3 Results
3.1.4 Uncertainty budget (Kx)
3.1.5 Discussion
3.2 Project
Calibration And Measurement Uncertainty Of Radio Frequency Field Strength Meters Using Broad-Band E Or H-Field Sensor in the Frequency Range up to 18GHz
3.2.1 Introduction
3.2.2 The Evaluation of Uncertainty and Results using GUM
3.2.3 Discussion
CHAPTER 4
4. DEVELOPMENT OF A SUPPORT USER GUIDE DESIGN FOR MEASUREMENT UNCERTAINTY ANALYSIS
4.1 Introduction
4.1.1 The Need of an Assistance System for the Evaluation of the Uncertainty
4.2 General User Guide Procedures
4.2.1 Understanding the Main Experiment
4.2.2 The Measurement Setup
4.2.3 Evaluation of the Uncertainty
4.2.4 Stating Results
4.3 Design Outline for the User Support
4.3.1 Design Outline for First Step
4.3.2 Design Outline for Second Step
4.3.3 Design Outline for Third Step
4.3.4 Design Outline for Fourth Step
4.4 Design Outline for Finding the Model Equation
CHAPTER 5
5. IMPLEMENTATION OF THE USER GUIDE DESIGN AND OTHER SUGGESTED IDEAS
5.1 Introduction
5.1.1 Ways of Implementation and Suggested Ideas
5.2 User Guide Design
6. CONCLUSION
7. REFERENCES
Assistance for the Determination of Measurement Uncertainty Analysis Scope of project:
In the “Guide to the Expression of Uncertainty in Measurement” (GUM), jointly issued by ISO and BIPM, a standard procedure for the determination of measurement uncertainty is defined. Yet, although this document is supported by many international organisations and the consideration of measurement uncertainty is of high importance in many fields of application, ranging from industrial quality control to scientific research, still often the determination of measurement uncertainty is omitted. This is mainly due to difficulties of the metrologists to apply the general rules of the GUM to the task at hand. To ease this task and support the determination of measurement uncertainty, the software GUM Workbench® performs all required mathematical evaluations based on a model of the measurement. Additionally, a concept for an assistance system as well as a graphic modelling editor has been developed to facilitate the definition of a suitable model. But, the existing concepts are not yet fit for practical testing under industrial conditions.
Thus, the project shall contribute to the further development of a prototypical implementation for an assistance solution supporting measurement uncertainty analysis within the existing framework. The main tasks in this project will be:
- Familiarisation with the topic of measurement uncertainty analysis and the handling of software GUM Workbench®.
- Definition of an design outline for the user support during measurement uncertainty analysis, including an analysis of required supporting function and the subsequent definition of a possible system structure.
- Selection of one aspect in the process and development of a draft for an adequate support solution, containing elements to enable partial automation or increase of efficiency for the process step as well as explanatory information for the users.
- Prototypical implementation and testing of the defined elements within the outlined framework.
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I would like to express my deepest gratitude and great appreciation to all those who have inspired me and guided me throughout the two years of my master program at Hochschule Coburg, starting from the first moment when deciding to start this program, through all hard working and studying till the last word of this research.
Special thanks to my advisor at Hochschule Coburg Prof. Dr. Gerhard Lindner for his invaluable support and great knowledge during this master program, also my gratitude goes to the AIMS office for the precious help and guidance during the program.
I would like also to express my deepest thanks to my advisor at Metrodata GmbH Dr.-Eng. Teresa Werner for her precious time and the great knowledge that she has always provided me in the field of uncertainty measurement.
Also my deepest and sincere gratitude to my dear friends in Coburg, Bremen and Shanghai, who have shared with me these unforgettable moments of hard working, joy and success, and to everyone who was part of this journey.
To the two brightest stars on my sky, who have enlighten every step of my way with caring and love, who have enriched every moment of my life with hope and happiness, who are already the reason of every success, achievement and every smile.
My dad and my mom, thank you, although I know that no words of gratitude would ever be enough.
Figure 1: GUM Workbench Software
Figure 2: Starting a new model and adding the description and title
Figure 3: Adding the Model Equation
Figure 4: Adding the Input Quantities
Figure 5: Adding the Input Types
Figure 6: The correlation matrix window
Figure 7: The uncertainty budget results
Figure 8: The final results with coverage factor
Figure 9: The Monte Carlo Simulation
Figure 10: Schematic of the measuring system
Figure 11: The description of project
Figure 12: Adding the model equations
Figure 13: Defining the input quantities
Figure 14: Defining each type of input quantities
Figure 15: The expanded uncertainty for DV and Kfcal
Figure 16: The standard uncertainty for DV and Kfcal
Figure 17: The uncertainty budget for input quantities
Figure 18: The results of Monte Carlo simulation for Kfcal
Figure 19: Listing input quantities
Figure 20: Adding type of each input
Table 1: The Observations Values of P
Table 2: The Observed Power Ratio P
Table 3: The Uncertainty Budget of Kx
Design 1: Understanding the main experiment procedure
Design 2: The measurement setup procedure
Design 3: Evaluation of the uncertainty procedure
Design 4: Stating results procedure
Design 5: Finding out the model equation procedure
Design 6: The tutorial / procedure window
Design 7: The quantity type description hint
Design 8: The physics and mathematics constant list
The uncertainty measurement is defined in metrological terminology as:
“Parameter, associated with the result of a measurement that characterises the dispersion of the values that could reasonably be attributed to the measurand.” [ 1]
For example the ‘parameter’, can be a standard deviation, a range, an interval (like a confidence interval) or half-interval (±u is a statement of a half-interval) or other measure of dispersion such as a relative standard deviation.
When phrasing the measurement uncertainty as a standard deviation, we use the term “Standard uncertainty” to be given for the parameter and we use the symbol “u” to represent it.
The uncertainty is related to each result of measurement experiment. A complete result of measurement usually includes reference of the uncertainty using the form of “x±U”, where x is the measurement result and U represents the uncertainty. This form of expressing a result is an indication to the meteorologists of the result that, with reasonable confidence, the result signifies that the value of the measurand is within this interval.
The measurand is simply a quantity, such as mass, concentration or length of a material, that is being measured. The term ‘value of the measurand’ is closely related to the conventional concept of ‘true value’ in traditional statistical terminology. From this different point ‘uncertainty’ has also been defined as:
“An estimate attached to a test result which characterises the range of values within which the true value is asserted to lie.” [ 2]
The understanding of this definition makes it easy to be explained to decision makers, who often use the phrase ‘true value’ as the value of interest for their judgments. Also it has the disadvantage that this true value itself can never be recognised and this generally requires more explanation.
The metrological definition agrees that uncertainty phrases ‘the dispersion of the values that could reasonably be attributed to the measurand’.
This is an important definition. It shows that although the uncertainty is related with a measurement result, the range quoted must relate to the possible range of values for the measurand. For example, the measurand can be the total mass of gold in a geological deposit. This differs from the definition of precision, which describes the range of results that would be observed if the measurement were done several times. In requesting information about ‘where the measurand value might be’, the definition of uncertainty needs the meteorologists to consider the effects that influence the results of measurement.
The influences clearly include the reasons of random diversities from a measurement to the next on scale of the measurement experiment. Also the sources of bias are important to be observed while the experiment, and might create more influences than can be observed by repeated measurement alone.
That is, measurement uncertainty normally asks for a range that states an allowance for both systematic and random effects.
To consider a simple analytical example, the measurement of concentration in a solid will typically involve extraction of material, weighings, volumetric operations and perhaps chromatography or spectrometry. Repeated measurement will result a propagation of values because of random variations in these procedures. But analysts know that it is seldom for the extraction to be completed and, for a given material, that fails to extract material will lead to a systematically low result. While good analytical practice always trials to low such influences to insignificance, some bias will remain.
In expressing the uncertainty about the value of the measurand, then, the analyst must take into account the understandable possibility of bias from such causes. (Usually, by taking into consideration the information as the range of analyte recoveries spotted on reference materials or from experiments.)
Same considerations should be applied in sampling. It is known that different samples taken from a bulk material will usually display real difference in value, which is clear from repeated measurement. It is also well known that sampling might be biased, for example by differential removal of materials, inadequate timing of sampling where temporal fluctuations occur, or by access restrictions. These effects will affect the relation between the value of the measurand and the spotted result. While good applying in sampling is intended to low these effects to insignificance, a careful assessment of uncertainty always considers the possibility of residual systematic influences.
Present guidance on measurement uncertainty shows it clear that uncertainty of measurement is not prepared to allow ‘overall error’. This would prevent, for example, mistakes caused by transcription errors or overall misapply of the measurement protocol.
However, sampling can lead to high scales of uncertainty (e.g. 80% of the concentration value), simply through the normal application of an accepted measurement protocol to a highly heterogeneous material.
Even when procedures seem to be correct, there will be also slight differences in the actual procedures because of the confusion in the measurement protocols, and the small modifications that are made to protocols in real-world sampling situations. Whether these high scales of uncertainty guide to unacceptable scales of reliability in the decisions that are based upon them depends upon a strict evaluation of fitness for purpose.
When an end-user is presented with a concentration result extracted for a bulk sample in the form ‘x±U’, they will very naturally be explained that interval as including the range of values attributable to the concentration in the sampling target. Implicit in this view is the idea that the measurand is ‘the (true) concentration (of the analyte) in the batch of material’, and that the uncertainty shows any necessary allowance for heterogeneity in the bulk. The analyst, by contrast, might mention to ‘the concentration in the laboratory sample analysed’, in a way of expressing ruling out the variation between laboratory samples. Clearly, a point of view shows the influence of sampling, while the other does not show. The influence on the uncertainty can, of course, be very considerable.
In metrological expressions, this distinction occurs because the two views are considering different measurands. One is considering ‘concentration in the sampling target’, the other ‘concentration in the laboratory sample’.
Another example might be ‘contaminant concentration at a factory outlet at the time of sampling’, compared to ‘the average contaminant concentration over a year’.
The mysteries in explanations can be avoided only by careful specification of the measurand. It is clearly necessary to clear the quantity (length, concentration, mass etc.). the explanation is equally important on the scope of the measurement, by including information on factors such as the time, location, or population to which the measurement result will be assumed to apply. It is never possible to ignore all mystery in completing the framing of the sampling protocol.
When a complex sample is taken by the combination of several increases from across a sampling target, and analysed as a single essential sample, that single determination of analyte concentration includes an estimate of the value of the measurand (i.e. the average composition of the purpose). The uncertainty on this single value shows the uncertainty in the estimate of the measurand value.
In contrast, if some separated primary samples are taken from the target, each analysed once, and the mean value calculated, this value will also be an estimate of the value of the measurand. However, the uncertainty will not be that of the measurement (expressed as standard deviation, s), but the standard error of the mean value (expressed as s/ V n). This later uncertainty on the mean can be reduced by taking more essential samples, whereas the uncertainty on the measurement cannot.
Some concepts such as accuracy, error, trueness, bias and precision are related to uncertainty.
Some of important differences are as follow:
- Difference between Uncertainty and Error: Error is a single difference between a result and a true “or reference” value, while uncertainty is a range of values attributable on the basis of the measurement result and other known effects.
- Difference between Uncertainty and Precision: Precision includes the effects that changes during observations (some random errors), while uncertainty includes allowances for all affects that may influence a result (systematic and random errors).
- Uncertainty is standing for correct application of measurement and sampling procedures, but it is not valid to make allowance for overall operator error.
One of the most important parts of finding out the uncertainty is the full understanding of process of the measurement and all sources that lead to uncertainty. This may explain why the skilled engineer or the skilled operator of the measurement experiment is best suited to perform the evaluation procedure. The defining of uncertainty sources starts by testing and analyzing in detail the process of measurement, which mainly includes a complete study of the measurement procedure and the measurement system, using of different of means, including computer simulations and flow diagrams.
There are so many possible sources of uncertainty in testing may include:
- The definition or the understanding of the experiment is incomplete. For example the requirements are not fully described or understood, as when the temperature is defined as “Room Temperature”.
- Incomplete fulfilment of the definition of the experiment procedure; also when the experiment conditions are clearly defined it may not be possible to produce the required conditions.
- Inappropriate knowledge of the effects of errors in the environmental conditions on the measurement procedure.
- Inadequate measurement of the environmental conditions.
- Sampling; the sample may not be actually representative.
- Parallax errors, personal bias in noticing the analogue measurement tools.
- The resolution of the measurement tool, or the discrimination threshold, or errors in the graduation of the scale.
- Some values referred to standards measurements (both reference and working) and reference materials.
- Modifications in the characteristics or performance of a measurement tool since its last calibration; incidence of drift.
- Some errors in constants values, corrections and other parameters used in data evaluation.
- Assumptions and approximations standardized in the measurement procedure and system.
Diversities in repeated observations experimented under fairly identical conditions; such random effects may be caused, for example, by short alternations in surrounding environment, for example temperature, humidity and air pressure, or by variability in the performance of the tester.
In addition to the uncertainty sources mentioned above, which are not always independent, some other unknown systematic effects which cannot be considered but which, nonetheless, may lead to an error. The presences of such errors may be concluded, for example the use of different procedure or system of the measurement experiment.
The main stage of estimating the uncertainty at the beginning of the experiment is to model the process of the measurement by a functional relationship, which identifies the input measured quantities which will be merged to get out the output quantity values, which also signalize the manner in which they are to be merged.
As an example in general terms, the functional relationship between the estimated input quantities, xi, and the output quantity, y is in the form
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For a more specific functional relationship, which should be identified if the output quantities are the summation or difference from the input quantities, if there are quotients or products, logarithmic quantities or power of input quantities.
The functional relationship should also define any correlated input quantities although in test measurements the incidence of such correlations is relatively irregular.
In many models of undertaking test measurements the functional relationship is basically simple and the test procedure provides the basis of a satisfactory model. The linear combination of measurements process is the regular form of the functional relationship.
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Where the coefficients, ci, represent the sensitivity coefficients, such as the temperature coefficient of expansion, or the partial derivative δ f/δ xi.
These coefficients play an important role in the functional relationship in order to find the combination of uncertainties.
An electrical example can be used to illustrate the modelling of the functional relationship. Resistance, R, may be measured in terms of voltage, V, and current, I, giving the functional relationship
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Also Power, P, may be measured in terms of current, I, and resistance, R, giving the functional relationship
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The combination of the contributing component uncertainties lead to find out the total uncertainty of a measurement is. Every single instrument reading or measurement may be affected by several factors and accurate consideration of each measurement took part in the test is important, thus, to find out and list all the factors that participate or affect the uncertainty. This step is the most important and critical step, which requires a complete understanding of the measurement tool, the objectives and the ideas of the test and the influence of the environment.
Next step is to identify the component uncertainties, by quantifying them by convenient means.
A primary approximate quantification is needed in order to authorize some components to be displayed to make an insignificant contribution to the total and not worthy of more rigid evaluation. In most cases a practical definition of insignificant would be a component uncertainty of not more than one fifth of the magnitude of the largest component uncertainty. 5
The ‘Type A’ evaluation of standard uncertainty can be applied when several independent observations have been made for one of the input quantities under the same conditions of measurement. If there is sufficient resolution in the measurement process there will be an observable scatter or spread in the values obtained.
We assumed the repeatedly measured input quantity Xi is the quantity Q. With n statistically independent observations (n > 1), the estimate of the quantity Q is q , the arithmetic mean or the average of the individual observed values qj (j = 1,2, ..., n).
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According to one of the following methods, the uncertainty of measurement associated with the estimate q can be evaluated:
- An estimate of the variance of the underlying probability distribution is the experimental variance s2(q) of values qj that is given by:
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Its (positive) square root is termed experimental standard deviation. The best estimate of the variance of the arithmetic mean q is the experimental variance of the mean given by:
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- For a measurement that is well-characterised and under statistical control a combined or pooled estimate of variance sp 2 may be available that characterises the dispersion better than the estimated standard deviation obtained from a limited number of observations. If in such a case the value of the input quantity Q is determined as the arithmetic mean q of a small number n of independent observations, the varianceof the mean may be estimated by:
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‘Type A’ evaluation is mainly used in:
- The statistical data which obtained by taking a random measurements made under same conditions from the measurement experiment.
- If the statistical data are available, an appropriate summaries of the data are used to find out the values of the unknown parameters from the probability distribution that shows the measurement process
- Measurement equation quantities whose parameters have been estimated using statistical methods are classified as Type A components.
Type B evaluation of standard uncertainty is associated with an estimate xi of an input quantity Xi by means other than the statistical analysis of a number of observations.
The standard uncertainty u(xi) is evaluated by scientific judgment based on all available information on the possible variability of Xi. Values belonging to this category may be derived from:
- The data included in the calibration certificates.
- The Uncertainty devoted to reference data from handbooks.
- The specifications of the manufacturer.
- Previous measurement data.
- General knowledge of, the properties and behaviors of relevant materials and tools; estimations made under this heading are on the basis of considered professional judgments by suitably qualified and experienced personnel and are quite common in many fields of testing.
The 'GUM Workbench' program is used to resolve the uncertainty of physical measurements and calibrations. The analysis and calculations follow the rules of the 'ISO “Guide to the expression of uncertainty in measurement”, and the requirement document EA-4/02 of the 'European cooperation for Accreditation of Laboratories'.
Computation examples of the EA-4/02 can be analyzed with the help of the program. They are included with the software package as example models.
GUM Workbench applies a systematical procedure in establishing an uncertainty analysis as needed by the EAL document. Beginning with the mathematical model relationship or the model equation which models the physical relationship of input and output quantities in the particular measurement experiment, the needed data for the analysis, as the standard uncertainty or the distribution of values, is interactively needed. The process is controlled by convenient classification of the input values according to the obtained information.
A table of the uncertainty budget is the results of this analysis.
This table concludes all used measurands with their values, the actual degrees of freedom, the assigned standard uncertainty and the sensitivity coefficient calculated from the model equation and their contribution to the standard uncertainty are the result of the measurement. In addition to the complete result of the examination, this is presented as a value with a related uncertainty and automatically or manually selected coverage factor. All values are rounded to an appropriate number of decimal places.
For the documentation of the process and the results, the uncertainty analysis together with all input data can be printed and presented as a report. All input are part of the printout and used as a structured documentation. You can also check your results and add your comments and observations before getting the results printed.
The model equation, the analysis and the values can be saved in a file with a chosen name. So, you will be having all data related to the experiment saved with all details.
You can also use any saved analysis or data as a starting point for new analysis for uncertainty involved the same model equation but with new or modified data. Therefore the program is mainly appropriate for the testing of the influence of different values and their following uncertainties on the result.
The following steps are to find out the uncertainty analysis using the GUM
Workbench software:
1. From the menu file select “NeW’ for starting a new analysis.
2. Select the option "Model'. Then provide a general description and a subject to your measurement experiment.
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Figure 2: Starting a new model and adding the description and title
3. In the Model Equation area, it has the model equation of the main experiment to be analyzed. The software will analyze the model equation and will find out a list of the input quantities.
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Figure 3: Adding the Model Equation
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Didaktik - Allgemeine Didaktik, Erziehungsziele, Methoden
Doktorarbeit / Dissertation, 86 Seiten
Diplomarbeit, 99 Seiten
Forschungsarbeit, 15 Seiten
Masterarbeit, 35 Seiten
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Doktorarbeit / Dissertation, 134 Seiten
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