Roberti esa 2014 quantifying measurement uncertainty
7
© 2013 National Ecological Observatory Network, Inc. ALL RIGHTS RESERVED. QUANTIFYING MEASUREMENT UNCERTAINTY AN INTRODUCTION JOSH ROBERTI
-
Upload
questrcn -
Category
Environment
-
view
418 -
download
3
Transcript of Roberti esa 2014 quantifying measurement uncertainty
© 2013 National Ecological Observatory Network, Inc. ALL RIGHTS RESERVED.
QUANTIFYING MEASUREMENT UNCERTAINTY
AN INTRODUCTION
JOSH ROBERTI
© 2013 National Ecological Observatory Network, Inc. ALL RIGHTS RESERVED.
BACKGROUND: MEASUREMENT UNCERTAINTYThe first and most important step to calculating a measurement’s uncertainty is to identify all input quantities, Xi, on which Y (the measurand) depends:
The next step is to estimate the input quantities which may depend on other input quantities and be considered measurands themselves. The function will be simple or complex depending on the number of input variables and the number of correction factors (e.g., calibration coefficients).
Simple:
Complex:
(1)
(2)
(3)
© 2013 National Ecological Observatory Network, Inc. ALL RIGHTS RESERVED.
BACKGROUND: MEASUREMENT UNCERTAINTY
Two methods of evaluating standard uncertainty components: Type A and Type B.
Type A – First-hand statistical analyses, i.e., you crunch the stats
Type B – Not first-hand statistical analyses, i.e., the uncertainties are provided by someone else
or are reached via scientific judgment.
© 2013 National Ecological Observatory Network, Inc. ALL RIGHTS RESERVED.
BACKGROUND: MEASUREMENT UNCERTAINTY
Type A: input quantity X is estimated by the sample mean of n independent observations collected under controlled measurement conditions, e.g., .
The individual observations differ due to random effects. The experimental (sample) standard deviation of these observations characterizes the variability of these observations about their mean :
(4)
© 2013 National Ecological Observatory Network, Inc. ALL RIGHTS RESERVED.
BACKGROUND: MEASUREMENT UNCERTAINTYThe standard uncertainty associated with x, , is the estimated standard error of the sample mean:
This quantity measures the uncertainty in x as an estimate of X. Note that this example of a Type A evaluation is simply an application of the Central Limit Theorem.
(5)
© 2013 National Ecological Observatory Network, Inc. ALL RIGHTS RESERVED.
BACKGROUND: MEASUREMENT UNCERTAINTYType B: This type of evaluation assumes an a priori distribution for the data and is not based on a statistical analysis of repeated measurements of a measurand. In this case, the estimated standard uncertainty associated with the input estimate arises from the standard deviation of the assumed prior distribution. This type of uncertainty evaluation is often specified by the manufacturer.
Uniform: Triangular:
© 2013 National Ecological Observatory Network, Inc. ALL RIGHTS RESERVED.
BACKGROUND: MEASUREMENT UNCERTAINTY
Propagate the uncertainties:
Or:
(6)
(7)
