In a typical GR&R study a number of parts are chosen to be measured in some way. Every part is measured a set number of times each by a number of different appraisers. This is done for all parts. My question arises from the assumption that the measurement being taken is assumed to be the same between all parts. I will use two examples to illustrate what I mean: In the first example, let's say there is a measurement system that measures the diameter of golf balls. You have 100 golf balls and each ball is measured 3 times by 3 appraisers using the same instrument. In this example, it is assumed that between the different parts, the measurements should be similar since all golf balls should have roughly identical diameters (i.e. the diameter of ball #54 should be very similiar to the diameter measured for ball #80, even when measured by different appraisers). In addition to taking the average measurement value across all trials for a single part, taking the average measurements across 100 parts is completely sensible . The equipment/appraiser variations should be rather straighforward to calculate. In a different example let's say we are trying to qualify an inspection system's ability to detect a variety of surface defects on some product. So let's say we again have 100 parts each being measured 3 times each by 3 appraisers. This time the thing being measured on each part are the dimensions of the defect that part has. The problem with this is that no two defects are identical (i.e. part #54 could have a defect that is 0.04mm^2 while part #80 could have a defect that is 0.25mm^2) . So as you move from part to part the inspection system / appraiser is measuring completely different things. It would still be sensible to take the average measurement values within each part for all tirals and appraisers because the same defect is being measured each time. However it would seem that taking the average measurements across all parts loses all meaning and credibility. It seems to me that the problem the second example illustrates makes it impossible to calculate variance values as you need average the measurements from all parts together. Am I missing something obvious or is there another approach one could take with this kind of example? Hopefully I have illustrated my question well enough. I'd be happy to clarify if needed. Thanks!
