Book contents
- Frontmatter
- Contents
- Dedication
- Preface
- 1 The importance of uncertainty in science and technology
- 2 Measurement fundamentals
- 3 Terms used in measurement
- 4 Introduction to uncertainty in measurement
- 5 Some statistical concepts
- 6 Systematic errors
- 7 Calculation of uncertainties
- 8 Probability density, the Gaussian distribution and central limit theorem
- 9 Sampling a Gaussian distribution
- 10 The t-distribution and Welch–Satterthwaite formula
- 11 Case studies in measurement uncertainty
- Appendix A Solutions to exercises
- Appendix B 95% Coverage factors, k as a function of the number of degrees of freedom, v
- Appendix C Further discussion following from the Welch–Satterthwaite formula
- References
- Index
7 - Calculation of uncertainties
Published online by Cambridge University Press: 06 July 2010
- Frontmatter
- Contents
- Dedication
- Preface
- 1 The importance of uncertainty in science and technology
- 2 Measurement fundamentals
- 3 Terms used in measurement
- 4 Introduction to uncertainty in measurement
- 5 Some statistical concepts
- 6 Systematic errors
- 7 Calculation of uncertainties
- 8 Probability density, the Gaussian distribution and central limit theorem
- 9 Sampling a Gaussian distribution
- 10 The t-distribution and Welch–Satterthwaite formula
- 11 Case studies in measurement uncertainty
- Appendix A Solutions to exercises
- Appendix B 95% Coverage factors, k as a function of the number of degrees of freedom, v
- Appendix C Further discussion following from the Welch–Satterthwaite formula
- References
- Index
Summary
Random errors, evaluated using statistical methods, create a Type A uncertainty. A known systematic error in a measured value should be corrected for, and after the correction has been made, the uncertainty in the correction contributes to the uncertainty in that value. The uncertainty in the correction, and hence in the value, may be Type A or Type B, depending on how the uncertainty is evaluated. The finally reported uncertainty of a measurand, called the combined uncertainty, is likely to have both Type A and Type B components, but becomes wholly Type B when subsequent use is made of it.
In this chapter we consider how to evaluate the combined uncertainty of a measurand. The procedure to be described makes no distinction between Type A and Type B uncertainties. It may appear then as if we have gone to unnecessary trouble in assigning types to uncertainties, but this classification is desirable since it emphasises the different methods by which they are evaluated. It is also useful as a reminder that, whereas an ‘error’ can be random or systematic, ‘uncertainty’ is a separate concept whose two types are distinguished from each other by different names, ‘Type A’ and ‘Type B’. However, once uncertainties have been classified, Type A and Type B uncertainties are treated identically thereafter.
- Type
- Chapter
- Information
- An Introduction to Uncertainty in MeasurementUsing the GUM (Guide to the Expression of Uncertainty in Measurement), pp. 97 - 125Publisher: Cambridge University PressPrint publication year: 2006
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