Novel mathematical and statistical approaches to uncertainty evaluation

Short Name: Uncertainty, Project Number: NEW04
Image showing mathematical equations on blackboard
Mathematical equations on blackboard

New approaches to complex risk assessment measurements

Measurement uncertainties are important in many applications, from ensuring precisely engineered components fit together to confirming batches of sensors meet specifications. Accurately determining the uncertainty or ‘doubt’ for a measured value is key to having confidence that a product meets specifications or safety criteria. New mathematical methods and statistical techniques are required to reliably extend uncertainty determination into complex areas such as risk assessments for safety or for determining smart meter testing strategies to ensure reliability.


The EMRP project Novel mathematical & statistical approaches to uncertainty evaluation (Uncertainty) developed new approaches for determining uncertainties in situations where complex simulations are combined The project also developed smart sampling techniques to reduce extensive computational times without compromising accuracy.


The Project:


  • Developed statistical methods for using probability to back calculate measurement results and the associated uncertainties. These were applied to the highly accurate Digital PCR technique used for counting the quantity of specific DNA sequences in biological samples.
  • Developed smart sampling methods and computer models to more rapidly determine a reliable result for computationally expensive calculations based on careful selection of input parameters and reducing the number of model iterations required.
  • Extended existing approaches on measurement uncertainty to conformity assessment and decision making to link the determination of calibration frequency to risk assessment criteria as informing decision making.


The project developed new approaches to uncertainty determination and increased the number of worked examples available so that these methods could be applied to similar situations by scientists and engineers. The worked examples will be included in future revisions of the Guide to the Expression of Uncertainty in Measurement (GUM), and its supplements. The project’s best practice guidance provides examples for some frequently encountered situations where models are used to determine measurement parameters. Fluid flow calibrations for installed flow meters and biochemistry immunoassays where very small concentrations of hormones or drugs require accurate detection are two examples which now have improved uncertainty determination methods. Other areas with worked uncertainty examples based on probability include computationally expensive processes such as fire engineering safety, and conformity testing using risk assessments important for large batch production processes like the roll out of smart energy meters across the EU.


EMPIR projects 15SIP05 TBCUnc and 17SIP05 CASoft build on this work.

Project website
The statistical inverse problem of scatterometry: Bayesian inference and the effect of different priors

Proc. SPIE 9526, Modeling Aspects in Optical Metrology V, 95260U (June 21, 2015)


Discrete and Continuous Dynamical Systems Series S

Numerical prediction of the flow rate through a flow meter with uncertain inflow profile

XXI IMEKO World Congress ”Measurement in Research and Industry”

Metrology of human-based measurements

17th International Congress of Metrology

Man as a Measurement Instrument

NCSLI Measure J. Meas. Sci.

Simplified evaluation of magnetic field fluctuation thermometry

Measurement Science and Technology

Alternative methods for uncertainty evaluation in EUV scatterometry

Proc. SPIE 8789, Modeling Aspects in Optical Metrology IV, 87890T (May 13, 2013); doi:10.1117/12.2020677