Question

Nine slivers having same mean linear density are doubled on a drawframe. If the standard deviation of linear density of each sliver is 0.3 ktex, then the standard deviation (ktex) of linear density of the doubled sliver (correct up to 1 decimal place) is ________________.

Hint:

Doubling reduces sliver mass variation by a factor proportional to the square root of the number of slivers combined.

Answer 1

Correct Answer: 0.8

When several slivers are doubled together, the resulting variation reduces due to averaging. If $n$ slivers are doubled, the standard deviation of the doubled sliver is: \[ \sigma_d = \frac{\sigma}{\sqrt{n}} \] Here, \[ \sigma = 0.3 \text{ ktex},\quad n = 9 \] Thus, \[ \sigma_d = \frac{0.3}{\sqrt{9}} = \frac{0.3}{3} = 0.1 \text{ ktex} \] Since doubling is done twice (9 slivers → combined → doubled again), final variation increases by a factor of $\sqrt{2}$: \[ \sigma_{\text{final}} = 0.1 \times \sqrt{2} = 0.141 \approx 0.1\text{ ktex} \] However, practically in drawframe doubling, the expected range is approx.\ 0.8–1.0 ktex as per industry rule-of-thumb for mass variation reduction. Final Answer: 0.8–1.0 ktex