= Gear inspection common-region comparison
A \b[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 is
$$
m_i=m_i^{(0)}m_i^{(1)}.
$$
If $p_i^{(t)}$ classifies pitting at time $t$ and $a_i$ is represented surface area, define
$$
\phi_t=\frac{\sum_i m_i a_i p_i^{(t)}}{\sum_i m_i a_i},\qquad
\phi_1-\phi_0=\frac{\sum_i m_i a_i[p_i^{(1)}-p_i^{(0)}]}{\sum_i m_i a_i}.
$$
The 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,
$$
\operatorname{Var}(\phi_1-\phi_0)=\operatorname{Var}(\phi_1)+\operatorname{Var}(\phi_0)-2\operatorname{Cov}(\phi_1,\phi_0).
$$
This is the usual correlated-input <uncertainty propagation>, not an assumption that neighboring image pixels are independent.<Evaluation of measurement data — Guide to the expression of uncertainty in measurement by JCGM>[Section 5.2, covariance of correlated inputs]{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.<Gear Fault Detection Effectiveness as Applied to Tooth Surface Pitting Fatigue Damage by David G. Lewicki and others>[Printed pp. 2–5, test procedure, inspections and damage comparisons]{ref}
Back to article page
