Fibre Blend Homogeneity Index Across Process Stages

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: Bale Laydown CV, Chute Feed CV, Finisher Sliver CV, Yarn CV, Target Blend (Major Component), Measured Blend in Yarn, Number of Yarn Samples and Contract Tolerance (±).
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 Blend Homogeneity Index together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Variance Removed: Laydown to Chute, Variance Removed: Chute to Sliver, Variance Removed: Sliver to Yarn, Blend Deviation from Target, Deviation in Standard Errors and Margin Left in Tolerance — 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 Blend Homogeneity Index 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 — Blend Variation by Stage and Ratio Check. 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 Blend Homogeneity Index in the dark results panel — that is the headline figure, expressed in %.
4. Check the supporting rows underneath (Variance Removed: Laydown to Chute, Variance Removed: Chute to Sliver, Variance Removed: Sliver to Yarn, Blend Deviation from Target, Deviation in Standard Errors and Margin Left in Tolerance) 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 Blend Homogeneity Index before a trial is booked, so machine time and material in Fiber Testing, Bale Management & Laboratory Sampling are committed against a calculated figure rather than an estimate.
• Costing and quotation — Blend Homogeneity Index 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 Bale Laydown CV) shows how much of the gap in Blend Homogeneity Index each variable explains.
• Teaching and study — the accepted ranges bracket normal Fiber Testing, Bale Management & Laboratory Sampling practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• A negative stage reduction is the finding, not an error: it means that stage added blend variation rather than removing it, which is what a starved chute, an uneven creel or a draw frame running with a missing end actually looks like in the data. The default case is deliberately one of these — sliver CV is lower than yarn CV, so spinning undid part of what drawing achieved. Variance falls with the square root of the number of doublings only when the components are fed independently; correlated feed, such as bales from one origin sitting together in the laydown, defeats the arithmetic entirely and is the usual reason a mill's measured reduction lags the textbook figure. The deviation test assumes the samples are independent and representative, so taking twelve samples from one cone tests the cone, not the lot. And a deviation inside tolerance but beyond two standard errors is a real shift the contract simply happens to permit — it will drift further.
• Every input is bounded to the range normal practice occupies (Bale Laydown CV 0.01 to 100 %, Chute Feed CV 0.01 to 100 % and Finisher Sliver CV 0.01 to 100 %, 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