Fibre Blend Homogeneity Index Across Process Stages

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.