Machine Analytics
At 36,000 picks an hour, a one-in-a-hundred-thousand false alarm is still a stop every three hours. Rare events are not rare when you sample them constantly.
— no.
Spurious stop-motion trips on intact weft
Gaussian tails are assumed, and that assumption is doing a great deal of work several standard deviations out where these probabilities live — real sensor noise has heavier tails than a normal distribution, driven by lint, vibration and stray light, so measured false-stop rates routinely exceed what this predicts. The normal integral itself uses a standard series approximation whose absolute accuracy is around 1e-7, which is a large relative error once the probability is smaller than that. Both distributions must be characterised from logged sensor data on the actual style, since yarn colour, count and hairiness all shift them. Use the separation index as the honest diagnostic: below about 4 sigma, no threshold gives a good answer and the sensor or its optics need attention.
IoT Weft Stop-Motion Sensor False Positive Rate — free, with the formula and a worked example, at Textile School.