# 19. Calibration – Measurement Uncertainties Basics and Decision Rules

In measurement, uncertainty coming from measuring and surroundings will make evaluators need to decide whether to accept or reject the measurement result. This chapter will be talking about the introduction of measurement uncertainty and measurement decision rule, please refer to the following definitions:

•  Decision Rule
• Decision rule shall be applied for specification or standard declaration for laboratory
• Shall consider the respective risk level (e.g. error acceptance, error reject and hypothesis setting) before finalize decision rule.
• Used for balancing risks for accepting non conforming items (customer risk) or delay conforming items (production risk)
• Measurement Uncertainty
• An estimated for measurand’s true value range and potential distribution.
• If measurement uncertainty is smaller, that means the true value has smaller distribution and the error between measurand & true value is smaller.
• Better quality for the measurement.
• Measurement is all about obtaining measurand value, but measurand’s true value cannot be measured due to the following factors (but not limited to):
• Measuring equipment precision (limited resolution)
• Measuring equipment accuracy (error w.r.t. true value)
• Instability of measurand
• Environment impact
• Measuring methods

Therefore, the measurement uncertainty can cover measurand’s real value (within 95% of confidence interval), and can be presented as Y = Measurement value ± uncertainty (Y = y ± U)

Decision Rule of Thumb Diagram

For example of decision rule:

One regulation requires that commercial toys’ plasticizer content cannot exceed, but one company’s inspection result has plasticizer content of 0.07% with extended uncertainty of 0.04%. If we based on the following decision rules, which will pass or fail?

• Inspection result (ignoring uncertainty) cannot exceed 0.1%
• Inspection result considered measurement uncertainty, and if there is a possibility to exceed 0.1% then it shall be considered as fail.
• Inspection result cannot exceed 0.1%, but extended uncertainty is moderately low (cannot exceed one third of the upper tolerance).

Lastly, for the guidance of measurement uncertainty:

ISO guidance principle recommends to establish measurement uncertainty by:

• List all potential factor.
• Establish measurement mode.
• Calculate each factor’s standard uncertainty.
• Calculate combined standard uncertainty (Uc)

If expanded uncertainty is required, then:

• Calculate valid degrees of freedom (currently only applicable for calibration)
• Select confidence interval (default is 95%)
• Calculate coverage factors (k = 2.0 for testing results, calibration pending)
• Calculate expanded uncertainty U = k*Uc