In this study, the repeatability of an operator is reported as two different values. The first percentage value indicates how well the operator performs in identifying the same de- fect regions for the inspection trials of the same part, report- ed as master cluster match percentage. For this measure, a match between two trials (from the same operator and part) is established if any element of the master cluster from the trial is matched with any element of the other trial. The total potential cluster matches, MRTMC
for each combination of
on all trials and T is the number of trials for the combination of operator and part.
operator and part is found as follows, MRTMC where Cj
= Cj *(T-1)!
The second repeatability value indicates how consistent the operator is in defining the specific shape and size of the de- fect regions of the same part across multiple trials, reported as the element match percentage. For each trial, the elements are checked for a match to an element on each of the other trials. The potential number of matches, MRTEl,
for operator
is the number of elements across all trials for operator j on this part.
j inspecting a particular part is found by Equation 2. MRTEl Ej
= Ej *(T-1)
A visual representation for the repeatability is presented in Figure 9. In this example, operator 1’s trial 1 contains seven elements for three defect regions, and trial 2 contains four
Equation 2 Equation 1 is the number of master clusters that operator j finds
elements for three defect regions for the same part. Opera- tor 1’s two inspection trials for the same part match two of three master clusters and seven of eleven elements. For this hypothetical example, operator 1’s repeatability is 67% for master cluster matching and 64% for element matching.
Defining Reproducibility
Reproducibility error is the variation in inspections between different operators on the same part. Similar to repeatabil- ity, reproducibility is also defined by two aspects in this pa- per: how well the operators perform in identifying the same defect regions and the specific size and shape of the defect regions between the inspection trials of the same part. For both measures, higher values indicate better reproducibility or agreement.
The first step in calculating reproducibility is to create a com- posite element map for all of the trials conducted by each op- erator for each part. This is shown in Figure 10 as the union of all trials (two in this example) for each operator. For each part, element matching is conducted between each operator’s composite element maps. This match- ing is done in the same manner as used for repeatabil- ity, and once again the goal is to deter- mine those elements that are in (nearly)
Figure 8. Search zone coefficient example of 1.5 for repeatability and reproducibility operations.
Figure 9. Defining repeatability of operator 1 for the two trials on one part. For this example, 2 of 3 master clusters match and 7 of 11 elements.
International Journal of Metalcasting/Summer 2011
Figure 10. Reproducibility of two operators with the same part. For this example, 3 of 4 master clusters match and 12 of 20 elements.
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