Step 1: Understand the concept being described. This is known as the "weakest link theory" as it applies to textiles. A yarn is like a chain; its overall strength is determined by the strength of its weakest link.
Step 2: Analyze the effect of specimen length. A yarn is never perfectly uniform; it has natural variations in thickness and strength along its length. It contains thin, weak places as well as thick, strong places. - A short specimen of yarn has a certain probability of containing a weak spot. - A longer specimen of yarn has a statistically higher probability of containing an even weaker spot somewhere along its greater length.
Step 3: Apply the weakest link theory. When the yarn is tested for strength, it will always break at its weakest point. Since a longer specimen is more likely to contain a very weak point than a shorter specimen, the average breaking strength measured for longer specimens will be lower than that for shorter specimens.
Conclusion: The strength of yarn decreases with increasing specimen length because there is a higher probability of finding exceptionally weak places in a longer length.