Strength Data From the single-end tensile test

Mean Breaking Force cN

CV of Breaking Force %

Gauge Length m

ISO 2062 uses 500 mm

Load & Length at Risk What the yarn has to survive

Running Tension cN

Length Considered m

Safety Factor at the Weakest Place

— x

Expected weakest segment against running tension

Percentiles, Weak Place & Margin

Expected Weakest in this Length: — cN
Safety Factor on the Mean: — x
5th Percentile Strength: — cN
1st Percentile Strength: — cN
Standard Deviation: — cN
Independent Segments: —
Tension as a z-Score: —
Normal-Model Break Probability: — %

Segments are treated as statistically independent, which they are not entirely - strength varies with count, and count has periodic and drift components, so neighbouring lengths are correlated. Correlation reduces the effective number of independent segments and makes the true expected minimum less extreme than the figure here. The normal distribution understates the lower tail for yarn: Weibull is the better model and would give a weaker expected minimum, so the safety factors here are optimistic rather than conservative in the deep tail. Strength is at the stated gauge length and standard atmosphere; a different gauge length gives a different mean and CV for the same yarn, and the two cannot be compared. The break probability output is included for completeness and should not be used as a breakage-rate prediction, for the reasons given in the questions above.

Yarn Strength Distribution, Weak Place & Safety Factor — free, with the formula and a worked example, at Textile School.