Gear inspection coverage audit

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.

A gear inspection missing-area bound limits the whole-target pitting fraction using the area actually observed and explicit constraints on the unseen area. It formalizes what a gear inspection coverage audit can establish without assuming that excluded regions resemble visible ones.

Let $c=A_{\mathrm{seen}}/A_{\mathrm{target}}$, let $p$ be the observed gear pitting area fraction, and let $u$ be the unseen fraction affected by pitting. For a consistent surface-area convention,With only $0\le u\le 1$ known,The interval width is exactly $1-c$. Improving classification precision within the visible area cannot by itself remove uncertainty from a completely unseen region.

For an original example with $c=0.9$ and $p=0.02$, the possible whole-target fraction ranges from $0.018$ to $0.118$. The observed $2\%$ therefore does not prove that the whole surface is below an illustrative $5\%$ criterion. That chosen criterion is not a gear safety or acceptance standard.

The worst-case upper bound meets a target $\theta <1$ only iffor $p<1$. At $p=0.02$ and $\theta =0.05$, at least about $96.94\%$ coverage is required for this particular worst-case guarantee.

Additional justified information can narrow the range. If a separate observation establishes $0\le u\le 0.1$, then $cp\le \Phi \le cp+0.1(1-c)$. At $c=0.8$ and $p=0.02$, this gives $0.016\le \Phi \le 0.036$. The tighter bound depends on the new evidence about the unseen region, not on a mathematical preference for a smaller interval.

These deterministic bounds assume the observed classification and represented areas are correct. Image registration, image segmentation and geometric uncertainties can require additional allowances. They are not confidence intervals and do not describe pit depth or remaining fatigue life. The primary NASA endurance study combined inspection with vibration and debris monitoring; these different observations constrain different aspects of damage.^[ref]