Colour Measurement Uncertainty & Tolerance Guard Band

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 6 inputs are read from the form on every keystroke: Shade Tolerance, Coverage Factor, Drift Against White Tile, Repeatability, Inter-Instrument Agreement and Readings Averaged.
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 Usable Shade Latitude together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Repeatability of the Mean, Combined Standard Uncertainty, Expanded Uncertainty, Tolerance Consumed, Measurement Capability Ratio, Share from Drift, Share from Repeatability and Share from Inter-Instrument Agreement — 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 Usable Shade Latitude 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 — Specification and Instrument. 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 Usable Shade Latitude in the dark results panel — that is the headline figure, expressed in dE.
4. Check the supporting rows underneath (Repeatability of the Mean, Combined Standard Uncertainty, Expanded Uncertainty, Tolerance Consumed, Measurement Capability Ratio, Share from Drift, Share from Repeatability and Share from Inter-Instrument Agreement) 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 Usable Shade Latitude before a trial is booked, so machine time and material in Dyeing, Printing, Color Management & Chemical Control are committed against a calculated figure rather than an estimate.
• Costing and quotation — Usable Shade Latitude 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 Shade Tolerance) shows how much of the gap in Usable Shade Latitude each variable explains.
• Teaching and study — the accepted ranges bracket normal Dyeing, Printing, Color Management & Chemical Control practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• Quadrature addition assumes the three contributions are independent, which is a fair description of drift, presentation repeatability and inter-instrument disagreement but understates the total where a single cause feeds two of them - a failing lamp, for example, degrades repeatability and drift together, and the combined figure will then be optimistic. The shares are variance shares rather than shares of the DE figure, which is why they sum to a hundred while the DE contributions do not; that is the correct way to read an uncertainty budget and it is also why reducing the largest share is worth so much more than reducing the smallest. A capability ratio below about one means the measurement system cannot reliably distinguish a pass from a fail at this tolerance, and the honest responses are to agree a wider tolerance, to move both parties onto instruments with better agreement, or to exchange physical standards rather than numbers. Averaging readings helps only the random term, and it helps as the square root, so going from three readings to twelve halves a contribution that is usually the smallest of the three to begin with. Nothing here covers sample presentation - aperture size, backing, folding and directionality on a napped or corduroy fabric routinely dwarf every instrument term in this budget.
• Every input is bounded to the range normal practice occupies (Shade Tolerance 0.05 to 5 dE, Coverage Factor 1 to 3 k and Drift Against White Tile 0 to 2 dE, 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