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MARLAP Manual Volume III: Chapter 19, Measurement Uncertainty

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MARLAP Manual Volume III: Chapter 19, Measurement Uncertainty 19 MEASUREMENT UNCERTAINTY 19.1 Overview This chapter discusses the evaluation and reporting of measurement uncertainty. Laboratory measurements always involve uncertainty, which must be considered when analytical results are used as part of a basis for making decisions.1 Every measured result reported by a laboratory should be accompanied by an explicit uncertainty estimate. One purpose of this chapter is to give users of radioanalytical data an understanding of the causes of measurement uncertainty and of the meaning of uncertainty statements in laboratory reports. The chapter also describes proce- dures which laboratory personnel use to estimate uncertainties. This chapter has more than one intended audience. Not all readers are expected to have the mathematical skills necessary to read and completely understand the entire chapter. For this reason the material is arranged so that general information is presented first and the more tech- nical information, which is intended primarily for laboratory personnel with the required mathe- matical skills, is presented last. The general discussion in Sections 19.2 and 19.3 requires little previous knowledge of statistical metrology on the part of the reader and involves no mathe- matical formulas; however, if the reader is unfamiliar with the fundamental concepts and terms of probability and statistics, he or she should read Attachment 19A before starting Section 19.3. The technical discussion in Sections 19.4 and 19.5 requires an understanding of basic algebra and at least some familiarity with the fundamental concepts of probability and statistics. The discus- sion of uncertainty propagation requires knowledge of differential calculus for a com- Contents plete understanding. Attachments 19CE are intended for technical specialists. 19.1 Overview ..........................19-1 19.2 The Need for Uncertainty Evaluation .... 19-1 The major recommendations of the chapter 19.3 Evaluating and Expressing Measurement Uncertainty ........................19-3 are summarized in Section 19.3.9. 19.4 Procedures for Evaluating Uncertainty . 19-11 19.5 Radiation Measurement Uncertainty .... 19-34 19.2 The Need for Uncertainty 19.6 Recommendations ..................19-58 19.7 References ........................19-59 Evaluation Attachment 19A: Statistical Concepts and Terms19-63 Attachment 19B: Example Calculations ...... 19-77 Radiochemical laboratories have long recog- Attachment 19C: Multicomponent Measurement nized the need to provide uncertainties with Models ...........................19-83 their results. Almost from the beginning, lab- Attachment 19D: Estimation of Coverage Factors ...........................19-85 oratories have provided the counting uncer- Attachment 19E: Uncertainties of Mass and Volume tainty for each result, because it is usually Measurements .....................19-93 1 Planners and decisionmakers must also consider the variability of the analyte in sampled populations, as discussed in Appendix C; however, the focus of this chapter is on the uncertainty of measuring the analyte in each laboratory sample. JULY 2004 19-1 MARLAP Measurement Uncertainty easy to evaluate (see Sections 19.3.5 and 19.5.2). However, the counting uncertainty is only one component of the total measurement uncertainty. Over the years it has been recommended repeatedly that laboratories perform good evaluations of the total uncertainty of each measure- ment. In 1980 the Environmental Protection Agency published a report entitled Upgrading Environmental Radiation Data, which was produced by an ad hoc committee of the Health Physics Society. Two of the recommendations of this report were stated as follows (EPA 1980). Every reported measurement result (x) should include an estimate of its overall uncertainty (ux) which is based on as nearly a complete an assessment as possible. The uncertainty assessment should include every conceivable or likely source of inaccuracy in the result. More recently ANSI N42.23, American National Standard Measurement and Associated Instru- ment Quality Assurance for Radioassay Laboratories, recommended that service laboratories report both the counting uncertainty and the total propagated uncertainty. ISO/IEC 17025, General Requirements for the Competence of Testing and Calibration Laboratories, which was released as a standard in 1999, requires calibration and testing laboratories to have and apply procedures for estimating measurement uncertainties (ISO/IEC, 1999). The National Environ- mental Laboratory Accreditation Conference (NELAC) has also published a standard on labora- tory quality systems, which requires a radiochemical testing laboratory to report with each result its associated measurement uncertainty (NELAC, 2002, ch. 5). Note that the concept of traceability (see Chapter 18) is defined in terms of uncertainty. Trace- ability is defined as the property of the result of a measurement or the value of a standard whereby it can be related to stated references, usually national or international standards, through an unbroken chain of comparisons all having stated uncertainties (ISO, 1993a). Thus, a labora- tory cannot realistically claim that its measurement results are traceable to a standard unless there exists a chain of comparisons, each with an associated uncertainty, connecting its results to that standard. This chapter considers only measurement uncertainty. The claim is often made that field samp- ling uncertainties are so large that they dwarf laboratory measurement uncertainties. Although the claim may be true in some cases, MARLAP rejects this argument as an excuse for failing to per- form a full evaluation of the measurement uncertainty. A realistic estimate of the measurement uncertainty is one of the most useful quality indicators for a result. Although the need for good uncertainty evaluation has long been recognized, not all laboratories have been able to implement the recommendations fully. A certain level of mathematical sophis- tication is required. Implementation requires, at a minimum, a mastery of basic algebra, some knowledge of differential calculus and a grasp of many concepts of probability and statistics; but even more fundamentally it requires an understanding of the various aspects of the measurement MARLAP 19-2 JULY 2004 Measurement Uncertainty process in the laboratory, including chemical and physical principles as well as practical consid- erations. Implementation at a laboratory is certainly easier if there are those who understand both the measurement process and the mathematical methods, but in some cases it may be necessary to use a team approach that brings together all the required expertise. Today there is software that performs the mathematical operations for uncertainty evaluation and propagation, and some of the difficulties of implementation may disappear as such software becomes more widely available. Nevertheless analysts and technicians will still need to under- stand the concepts of measurement uncertainty and how they apply to particular measurement processes in the laboratory. 19.3 Evaluating and Expressing Measurement Uncertainty The methods, terms, and symbols recommended by MARLAP for evaluating and expressing measurement uncertainty are described in the Guide to the Expression of Uncertainty in Meas- urement, hereafter abbreviated as GUM, which was published by the International Organization for Standardization (ISO) in 1993 and corrected and reprinted in 1995 (ISO, 1995). The methods presented in the GUM are summarized in this chapter and adapted for application to radiochem- istry. The terminology and notation used by the GUM and this chapter may be unfamiliar or confusing to readers who are familiar with statistics but not metrology. Metrology (the science of measure- ment) uses the language and methods of probability and statistics, but adds to them its own terms, symbols, and approximation methods. 19.3.1 Measurement, Error, and Uncertainty The result of a measurement is generally used to estimate some particular quantity called the measurand. For example, the measurand for a radioactivity measurement might be the specific activity of 238Pu in a laboratory sample. The difference between the measured result and the actual value of the measurand is the error of the measurement. Both the measured result and the error may vary with each repetition of the measurement, while the value of the measurand (the true value) remains fixed. Measurement error may be caused by random effects and systematic effects in the measurement process. Random effects cause the measured result to vary randomly when the measurement is repeated. Systematic effects cause the result to tend to differ from the value of the measurand by a constant absolute or relative amount, or to vary in a nonrandom manner. Generally, both ran- dom and systematic effects are present in a measurement process. JULY 2004 19-3 MARLAP Measurement Uncertainty A measurement error produced by a random effect is a random error, and an error produced by a systematic effect is a systematic error. A systematic error is often called a bias (see also Attachment 19A).2 The distinction between random and systematic errors depends on the specifi- cation of the measurement process, since a random error in one measurement process may appear systematic in another. For example, a random error in the measurement of the specific activity of a radioactive standard solution may be systematic from the point of view of a laboratory that pur- chases the solution and uses it
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