Exploring Accuracy and Uncertainty in Computed Tomography

Definitions to Understand

By Dirk Steiner / February 15, 2021
Figure 1: Precision and Accuracy

Precision and Accuracy:

For understanding the difference between accuracy and precision, consider a target like on a dartboard, illustrated in figure 1.

On the upper left the shots are all over the place and relative to the lower right, the precision and accuracy are both low. The top right shows what is sometimes called “good grouping,” all of the shots are very close to each other but not very close to the center which is the aiming point showing low accuracy but high precision. On the lower left all shots are around the center some are just scattered inside the second ring. That would be considered high accuracy but low precision.

Tolerance:

The term tolerance refers to the difference between the upper (maximum) limit and lower (minimum) limit of a dimension. In other words, tolerance is the maximum permissible variation in a dimension.

Uncertainty of Measurement:

In most cases when people are asking about accuracy, what they really mean is the uncertainty of measurement. Although a slightly clumsy term, “uncertainty of measurement” is the phrasing used by many standards that apply to CT scanning.


Figure 2: Uncertainty and Tolerance

Consider figure 2, the measurement came out with a reading of V1. The uncertainty of measurement is a value of how much the real value is likely to be at a certain confidence level.

Resolution:

The important parameter to know when evaluating a CT dataset is the smallest piece of information in it: voxel size. It is simply defined by the length (or diameter) of the field of view divided by number of voxels created in one direction.



Figure 3: CT System Components and Field of View

The voxel size doesn’t say anything about the smallest detail visible. If there is a pore the size of one voxel, that it would not be enough information to reliably detect it. A rule of thumb is that at least 2 x 2 x 2 voxels are needed to be able to see a single feature. For the purpose of metrology, that is not enough “meet” to create an accurate surface around the object. The term “resolution” is defined for the purpose of the specific application.

Error:

Error describes the CT system performance and is the deviation from a known measurement under specific conditions. A system is specified to perform maximum permissible error (MPE); there may be multiple different specifications for one system. The error is not the same as uncertainty of measurement. It represents a value that can be checked as part of an acceptance procedure or to monitor the system while in use. The error is measured under ideal conditions defined by the manufacturer often expressed as MPEXE=V μm *  (L / D mm)

Suitability:

Is the process suitable to use for a specific measurement task? Answer is black and white: yes or no.


Figure 4

Suitability typically also covers the question in situations as shown above. The measured value V1 is right inside the tolerance even with worst case uncertainty U considered. V2 is outside even if the best-case uncertainty is assumed. But what happens if the value V2 is within the tolerance, but the uncertainty could make the part fail? One approach is to make the tolerance tighter, but a lot of good parts might fail. The way commonly used standards deal with it is to perform a suitability study. Multiple approaches are available e.g. Gauge R&R, MSA, VDA5, VDI/VDE 2630. The study typically includes the entire process including operator and the object to be measured.