Uncertainty for uncorrected measurement results in X-ray computed tomography

In a recent paper [1], a mathematical formalism for the uncertainty estimation of dimensional measurements obtained from X-ray computed tomography (CT) data was outlined. The formalism includes the treatment of both 'corrected'-when the final result is corrected for bias-and 'uncorrected' measurement results. Such formalism is mainly based on the ISO 15530 series and the VDI/VDE 2630-2.1 guidelines. However, the treatment of uncertainty in the 'uncorrected' case-not compensated for bias-is limited to the use of the root-sum-of-squares of standard uncertainties (RSSu) approach. The present paper expands to other possibilities for the uncertainty estimation of 'uncorrected' results that could be applied to CT measurements, namely the root-sum-of-squares of expanded uncertainties (RSSU), the algebraic sum of expanded uncertainty with the signed bias (SUMU), the enlargement of the expanded uncertainty by adding the absolute value of the bias (SUMU MAX), and the so-called U ε method that sums the expanded uncertainty with the absolute value of the bias scaled by a factor assigned for a 95% distribution coverage. In addition, the alternative of using a maximum permissible error (MPE) statement-typically specified by the manufacturer of the CT instrument to get a rough estimate of the expanded uncertainties of CT measurements is considered. Through a concrete example, by using dimensional X-ray CT data extracted from a metallic artifact that has internal features, these possibilities are analysed. From all the possibilities investigated, the RSSu method seems to be the most conservative for the estimation of expanded uncertainties associated with CT dimensional measurement that are not compensated for bias. On the other hand, uncertainty bounds estimated with the MPE-based approach vary little from a constant value, and, therefore, risk creating significant under-or over-estimation of the uncertainty intervals.