Vision Math

How to Calculate Machine Vision Inspection Metrics: Coverage, Detection Rate, and Cycle Time

A step by step walkthrough of the five formulas that govern industrial vision inspection, with real units and worked examples you can reproduce.

Start with camera coverage rate, because it sets everything downstream. Coverage rate in parts per minute equals line speed divided by part pitch, capped by the camera field of view. If a conveyor runs at 30 meters per minute and parts sit on a 0.15 meter pitch, that is 200 parts per minute. A camera with a 0.10 meter field of view at that speed sees each part for 0.10 divided by 0.5 meters per second, or 0.2 seconds. The Camera Coverage Rate calculator resolves whether one camera keeps up or you need a second station tiled across the web width.

Detection rate is the metric quality owners actually sign off on. Vision Defect Detection Rate equals true positives divided by the sum of true positives and false negatives. Run a seeded sample of 500 parts with 50 known defects. If the system flags 47 of them, detection rate is 47 divided by 50, or 94 percent. Escape rate is the complement, 6 percent, meaning 3 defective parts per 50 pass through. Always report detection against a known defect population, not against total parts, or you will overstate performance by an order of magnitude.

Cycle time is a chain of fixed stages, not a single number. Camera Cycle Time equals exposure time plus readout time plus image transfer plus inference plus reject actuation. A 2 millisecond exposure, 8 millisecond sensor readout, 5 millisecond transfer over GigE, 22 millisecond CNN inference, and 4 millisecond reject pulse sum to 41 milliseconds. That ceiling is 1000 divided by 41, or roughly 24 parts per second. If your line demands 30 parts per second, you have a 6 part deficit and must cut inference time or parallelize cameras before the project is feasible.

Sizing the training set is a real calculation, not a guess. A workable rule for supervised defect models is 150 to 1000 labeled images per defect class, scaled by class imbalance. If your rarest defect appears on 0.5 percent of parts, capturing 200 examples of it requires 200 divided by 0.005, or 40,000 total images collected. The Image Dataset Size calculator converts defect rate and target examples per class into the raw capture volume, which is the input nobody remembers to budget for and the reason pilots stall.

Annotation workload follows directly from dataset size. Annotation Workload equals image count times regions per image times seconds per region, divided by 3600 for hours. Bounding boxes run 8 to 15 seconds each; pixel-accurate segmentation masks run 60 to 240 seconds each. For 40,000 images at an average 3 regions each and 20 seconds per region, that is 40,000 times 3 times 20, or 2.4 million seconds, which is 667 labeling hours. At a sustained 6 productive hours per day, that is about 111 working days for one annotator, so plan the team accordingly.

Confusion between false reject and false accept trips up the math, so pin the definitions. False reject rate is good parts scrapped divided by good parts inspected. False accept rate is defective parts passed divided by defective parts inspected. At a 2 percent underlying defect rate and 94 percent detection, inspecting 100,000 parts yields 2000 true defects, of which 120 escape as false accepts. If the false reject rate is 1.5 percent on the 98,000 good parts, that is 1470 good parts wrongly scrapped, a number that feeds directly into any downstream cost model.

Lighting and resolution are the inputs that quietly break every other formula. Defect detectability requires the smallest feature to span at least 3 to 4 pixels. If a 0.2 millimeter crack must be caught across a 200 millimeter field on a 4000 pixel sensor, each pixel covers 0.05 millimeters, so the crack spans 4 pixels, which is marginal but workable. Drop to a 2000 pixel sensor and each pixel covers 0.1 millimeters, the crack spans 2 pixels, and detection rate collapses regardless of how good the model is.

Chain the formulas to validate a station before you order hardware. Coverage rate sets throughput demand, cycle time sets throughput capacity, and if capacity is below demand the station fails on paper. Resolution sets the minimum detectable defect, which caps achievable detection rate. Dataset size and annotation workload set the schedule to reach that detection rate. Run all five through the Camera Coverage Rate, Camera Cycle Time, Vision Defect Detection Rate, Image Dataset Size, and Annotation Workload calculators together, and you get a feasibility answer in numbers rather than a vendor promise.

Published 2026-07-01.