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A gear inspection common-region comparison evaluates repeated surface observations on the same registered portion of a tooth flank. It prevents a changed gear pitting inspection mask from being mistaken for a change in damage. The region must be common in surface coordinates, not merely occupy the same pixel positions in two camera images.

After image registration, let $m_i^{(0)}$ and $m_i^{(1)}$ be inspection-mask indicator functions on one reference grid. Their common mask isIf $p_i^{(t)}$ classifies pitting at time $t$ and $a_i$ is represented surface area, defineThe identical denominator makes the difference a comparison within the same eligible area. It does not eliminate errors in registration or image segmentation.

An original example has 10000 eligible equal-area pixels at the first inspection and 8000 at the second, with 7000 in common. In the common region, pitted counts rise from 140 to 210: fractions rise from $2\%$ to $3\%$, a change of one percentage point or $50\%$ relative to the original fraction. Suppose total pitted counts were 200 and 240 across the separate full masks. Their raw difference, 40 pixels, is not the same quantity as the 70-pixel increase within the common region.

A gear inspection coverage audit should also record the excluded areas and why they disappeared or became newly visible. An intersection-only result can miss damage on an edge that the second camera view no longer captures. Keeping the original images makes that loss of coverage visible to a later reviewer.

Common inputs can correlate the two estimated fractions. In general,This is the usual correlated-input uncertainty propagation, not an assumption that neighboring image pixels are independent.^[ref] A primary NASA endurance study linked repeated physical inspections with vibration and debris observations; the common-region formalism specifies one way to make such repeated surface measurements comparable.^[ref]

A gear inspection coverage audit records which parts of a tooth surface were eligible for observation, which were excluded and why. It accompanies a gear pitting area fraction or gear inspection common-region comparison so that a numerical damage statistic can be interpreted against the area actually inspected.

A useful record retains the original image, gear pitting inspection mask, surface-coordinate map from image registration, represented pixel areas and exclusion reasons. Shadow, occlusion and an out-of-frame edge are different from a visible region classified as intact. An audit also distinguishes changes in viewing coverage from changes in the image segmentation rule.

An original calculation shows how missing area limits interpretation. Let inspected fraction $c=A_{\mathrm{seen}}/A_{\mathrm{target}}$ and observed pitting fraction ${\varphi }_{\mathrm{seen}}$ both refer to the same target surface. If unseen area has unknown pitting fraction $0\le {\varphi }_{\mathrm{unseen}}\le 1$, thenso the gear inspection missing-area bound isAt $c=0.8$ and ${\varphi }_{\mathrm{seen}}=0.02$, the whole-target fraction lies between $0.016$ and $0.216$ without further information. This is a deterministic range over missing data, not a statistical confidence interval. A small observed fraction does not alone establish a small whole-target fraction.

For repeated inspections, record areas visible only initially, only later and at both times. A common-region result can be valid for its intersection while becoming less representative of the full target if a damaged edge is systematically lost. Increasing pixel count inside the retained region does not recover information about the missing region.

The primary NASA gear-endurance study connected inspection history to vibration and oil-debris observations, illustrating the importance of tying a damage interpretation to physical inspection rather than a signal label alone.^[ref] The audit and bound above specify an explicit measurement convention; they do not assert that the historical study used this digital-mask procedure.

The gear pitting area fraction measures how much of a stated tooth-flank inspection region is classified as affected by gear surface pitting:Both areas must use the same geometric convention. A projected photograph, an unwrapped flank map and an actual curved surface need not assign the same areas. The gear pitting inspection mask specifies which part of the flank is included, so that an apparent change of damage is not merely a change of inspected region.

For an original image-counting example, let the inspected region contain $N$ equal-area pixels and let $n$ be classified as pitted. If their common scale is $s$ length units per pixel,Thus $n=2400$ out of $N=120000$ gives $\varphi =0.02$, or $2\%$. The common scale cancels from the ratio; uncertainty in the classification boundary, perspective distortion or the inspection mask does not. Image segmentation should therefore be checked against the actual surface, with consistent illumination and a recorded threshold or classification rule.

Combining regions requires area weighting. Suppose one region has $0.6\mathrm{m}{\mathrm{m}}^2$ of pits within $30\mathrm{m}{\mathrm{m}}^2$ and another has $1.2\mathrm{m}{\mathrm{m}}^2$ within $120\mathrm{m}{\mathrm{m}}^2$. Their fractions are $2\%$ and $1\%$, but the combined fraction is $1.8/150=1.2\%$, rather than the unweighted average $1.5\%$.

The ratio measures extent under its chosen convention, not pit depth, lost volume or a universal remaining life. A 2009 NASA endurance study paired repeated gear inspection with vibration and oil-debris monitoring. Its test rig used accelerometers, shaft timing signals and an inductive debris sensor, giving observations of different aspects of the evolving damage.^[ref] A surface fraction can complement these measurements, but it does not make their signals interchangeable.