Why Did We Construct Another Equation?

Most available equations can only be used to estimate CSP of yarns spun at the optimum twist. Very few equations aim at predicting CSP of yarns at a range of twists. Further all the available equations suffer from one or both of two shortcomings: in spite of an impressive value of correlation coefficient, they incur large errors in individual estimates of CSP, even consistent bias in the case of some cottons; they do not contribute to our understanding of the specific manner in which fibre-length and fibre-fineness contribute to the translation of fibre-tenacity to yarn tenacity. A review of a recent CSP equation will clarify the point.

In 2002 Chellamani, Thanabal, Basu and Ratnam of SITRA(4, in the list of references at the end of Part II) proposed a fibre quality index formulated out of HVI cotton test data:

FQI=Ls/f,

On the basis of experimental spinnings they then arrived at the CSP equation:

C= English yarn count, NE,
CSP is the countxstrength product,
NE x Lbs.

The authors concluded: “The prediction expression gives a very close fit with the actual CSP with a high correlation of 0.986.” “The error of estimate was found to be about 150 at 95% confidence limits.”

An examination of the actual errors in the estimates of the CSP of each of the 123 yarns in the SITRA spinning, Table A –iii, however, brings out some disturbing facts :-

There is, thus, an apparent paradox in the situation: high correlation coefficient, but unacceptable errors in individual estimates. Many, many years ago Morton (5) had cautioned investigators in this area against this pitfall. Morton  remarked, that the use of count as one of the independent variables ‘does nothing to advance our understanding—indeed, it tends to obscure the issue—of how fibre properties determine spinning behavior’. Count is no doubt a variable whose contribution has to be accounted for. One has, however, to be wary of the nuisance of the contribution of count to yarn tenacity boosting the value of the correlation coefficient. This is bound to happen when one spins each of the cottons used in the study to a number of counts. One then introduces a large variation in the yarn tenacity values, much of which gets accounted for in the regression equation by the easily quantified contribution of count. Merely on the basis of the high value of the correlation coefficient, one should not, therefore, erroneously conclude that the equation has effectively accounted for the contribution of cotton characteristics to yarn tenacity.