identical locations as any element from the other operator’s composite element map. The reproducibility search zone would theoretically have a radius equal to that of the elements, but 1.5 times this value is again used to account for any minor discrepancies in element placement.
The reproducibility is reported as two different percentage values. The first value indicates how well operators perform in identifying the same defect regions for the same part, reported as master cluster match percentage. For a master cluster to be considered a match, an element from an opera- tor’s composite element map must match at least one ele- ment from another operator’s composite element map. For each operator and part, the total potential matches, MRDMC
,
is found by Equation 3. MRDMC
= C*(P-1)! Equation 3
Where C is the number of master clusters defined for a part and P is the number of operators. It is important to note that the composite element maps for each part are the union of all of the element maps for each operator. Therefore, an ele- ment from one trial of the first operator only requires the same location as one element from any trial of any other operator for a master cluster to be considered a match.
Since the size and shape of the areas identified by operators could be grossly different in size, it is also important to have an indication of how the size and shape correspond. The second percentage value indicates how well the operators perform in defining the same size and shape of the defect regions. These comparisons are done between each operator and for each part and reported as element match percentage. Each element for a particular operator is checked to see if it matches an element in the composite element map for each other operator. The total potential matches, MRDEl
, for each
operator and part combination are found by the following. MRDEl
= Ej*(P-1) Methodology Implementation
The experimental data were collected at three steel casting producers, which collectively represent a broad spectrum of the North American steel casting industry. This experiment had three stages. The first was the inspection of the castings and the collection of images of the castings. The next stage was the extraction of the coordinates of the elements from the images collected. The final stage was the analysis of the coor- dinate data. At each company, a particular casting design was chosen for the study, and six to ten parts of the chosen design were then picked to be used in this experiment. Two operators at each of the three locations participated in the experiment. The overall size of the casting at foundry 1 was 350 mm (14 in.) and those at the other two foundries were 600 mm (24 in.). Some of the results of the case study without the methodology were previously reported by the authors.13-14
12 Equation 4
Data Collection and Analysis
The parts were marked for defects by the operators employing the same method that they typically use to inspect castings, except that only one side of the castings was inspected for this study. This study wanted to measure the actual variabil- ity that existed in the inspection operations, while minimiz- ing the influence of the study on the current process. At the three companies, each of two operators inspected each part twice. To reduce bias, the inspections were done on differ- ent days and the order of the parts was randomly selected by the experiment moderator. After the parts were marked by the inspectors with industrial crayons per their normal protocol, round stickers of 19 mm (¾ in.) diameter were used to cover the markings, as previously shown in Figure 3. These stickers became the elements that were used in the measurement error analysis. Careful attention was paid to carry out the sticker placement process as consistently as possible. Digital pictures of the sticker-covered parts were then taken. Between trials, the parts were shot blasted to remove all markings. There were initial concerns that the shot blasting between trials could af- fect the results, but this was ruled out through analysis.
The digital pictures were cleaned using photo software to eliminate noise and to delineate the element (sticker) bound- aries. This process did not change the location of the ele- ments. A cleaned image with elements identified is shown in Figure 11. These images were then input into DVT Frame- Work software to determine the center coordinates of each element (sticker) which were recorded in a spreadsheet. (Other software would have worked equally as well)
The algorithms presented in the previous sections were im- plemented via macros in the spreadsheet. The master clus- ter operation was used to take the element coordinates and group the elements into master clusters. The nominal search zone coefficient for the master cluster search was set at 2.5 times the element radius. However, for Companies 2 and 3, a search zone of 3.0 times the element radius was used be- cause of lower image quality and a high percentage of ele- ments that were at an angle to the image view.
Figure 11. Cleaned image created from the steel casting shown in Figure 3.
International Journal of Metalcasting/Summer 2011
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