Optimised uncertainties

Overall costs - equation

Overall costs – equation

There are many and diverse ‘rules of thumb’ about how small measurement uncertainty has to be in order to make reliable decisions of conformity of product.

In recent years, an economic decision-theory approach has been applied in which an ‘optimum’ measurement uncertainty is derived by balancing the costs of measurement (D) against the consequence costs (C) of bad conformity decisions. This is arguably less arbitrary than rules such as 1/3 or 1/10 MPE.

Overall costs, according to the above equation, can be plotted over:

optimised USL

(II) a range of test uncertainties, for a given quantity value , close to a specification limit (USL), yielding the so-called “optimised uncertainty curve”:

Optimised uncertainty

AQL & LQL – traditional quality limits on sampling uncertainty

MPU – [max. permissible (alt. target) uncertainty] traditional limit on measurement uncertainty




Pendrill L R 2007 “Optimised Measurement Uncertainty and Decision-Making in Conformity Assessment”, NCSLi Measure, Vol. 2, no. 2, pp 76 – 86 Balancing the costs of testing against the consequence costs of in-correct decision-making

Pendrill L R 2008, “Operating ‘cost’ characteristics in sampling by variable and attributeAccred. Qual. Assur., 13, 619 – 631, DOI: 10.1007/s00769-008-0438-y Extending classical statistical significance tools to include measures of impact

L. R. Pendrill 2009, ”An Optimised Uncertainty Approach to Guard-banding in Global Conformity Assessment”, in Advanced Mathematical and Computational Tools in Metrology VIII, Data Modeling for Metrology and Testing in Measurement Science Series: Modeling and Simulation in Science, Engineering and Technology, Birkhauswer (Boston), 2009, ISBN: 978-0-8176-4592-2 http://www.worldscibooks.com/mathematics/7212.html

L R Pendrill 2014, “Using measurement uncertainty in decision-making & conformity assessment”, Metrologia 51 S206, doi:10.1088/0026-1394/51/4/S206


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