IoT Weft Stop-Motion Sensor False Positive Rate

The formula

This is the expression the tool evaluates. Every term is named underneath, with the unit it must be supplied in.

How the result is derived

Step by step, from the values you type to the figure on screen.

1. The 8 inputs are read from the form on every keystroke: Mean Signal, Weft Present, Signal Standard Deviation, Mean Signal, Weft Broken, Break Standard Deviation, Detection Threshold, Picks per Hour, Shift Length and Time Lost per False Stop.
2. Each value is checked against the accepted range in the input table below. A value outside its range stops the calculation rather than producing a misleading figure — the results blank out and a message appears.
3. The validated values are substituted into the expression above, which resolves False Stops per Hour together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — False Positive Probability, Missed Detection Rate, Distribution Separation, Threshold Below Signal Mean, False Stops per Shift and Production Time Lost — come from the same pass, so they always describe the same case as the headline figure.
5. Results are rounded for display only. The full-precision value is used throughout the chain, so reading a rounded intermediate figure back into the tool by hand can shift the last digit.

What each input means

Where to read each value on the floor, the unit it must be in, and the range the tool accepts.

What the tool returns

The headline figure and every supporting value it is built from.

Worked example

The tool loads with this case already solved — the False Stops per Hour shown above is its answer. Change one value and the difference from this baseline is the sensitivity of the result to that variable.

How to use it

1. Work through the input groups in order — Signal Distributions and Loom Operation. The defaults are a realistic case, so you can change one value at a time and watch what moves.
2. There is no calculate button. Every figure recalculates as you type or drag, which is what makes this usable for a what-if sweep rather than a single answer.
3. Read False Stops per Hour in the dark results panel — that is the headline figure, expressed in no..
4. Check the supporting rows underneath (False Positive Probability, Missed Detection Rate, Distribution Separation, Threshold Below Signal Mean, False Stops per Shift and Production Time Lost) before acting on the headline — they are where an implausible input usually shows itself first.
5. Reset to defaults returns every field to the reference case, which is the quickest way to check whether a surprising result came from the tool or from an input you had changed earlier.

Where this is used

• Process planning — establishing False Stops per Hour before a trial is booked, so machine time and material in Textile Machinery Kinematics & IoT Analytics are committed against a calculated figure rather than an estimate.
• Costing and quotation — False Stops per Hour is an input to the cost sheet, and quoting from a worked number rather than a remembered one is what keeps a margin intact.
• Troubleshooting — when the floor result drifts from plan, entering the measured values (starting with Mean Signal, Weft Present) shows how much of the gap in False Stops per Hour each variable explains.
• Teaching and study — the accepted ranges bracket normal Textile Machinery Kinematics & IoT Analytics practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• 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.
• Every input is bounded to the range normal practice occupies (Mean Signal, Weft Present 10 to 1000 units, Signal Standard Deviation 0.5 to 200 units and Mean Signal, Weft Broken 0 to 500 units, and so on for the rest). Those bounds are guard rails against typing errors, not a claim that the formula fails one unit outside them.
• The calculation is deterministic: the same inputs always give the same result. It carries no allowance for machine condition, operator skill, ambient conditions or lot-to-lot material variation unless an input above explicitly represents one.
• Nothing is sent anywhere. The maths runs in your browser, so the numbers you type never leave the page.

Questions people ask