Question

A ring spun yarn with mean linear density of 32 tex is produced from 2 denier polyester staple fibre. If the standard deviation of the yarn linear density is 3.2 tex, then the index of irregularity of the yarn (up to 1 decimal place) is:

Hint:

- The index of irregularity measures the variation in yarn linear density. It is calculated as the ratio of the standard deviation to the mean, expressed as a percentage.

Answer 1

Correct Answer: 1.1

The index of irregularity \( U \) of the yarn is given by the formula: \[ U = \frac{\sigma}{\mu} \times 100 \] where \( \sigma \) is the standard deviation of the yarn linear density, and \( \mu \) is the mean linear density. Substituting the given values: \[ U = \frac{3.2}{32} \times 100 = 10% \] Thus, the index of irregularity of the yarn is between 1.1 and 1.3.