Concept:
No yarn is perfectly uniform. Yarn irregularity (unevenness) is a measure of the variation in weight per unit length along the yarn. This variation is caused by both mechanical faults and the fundamental nature of fibers.
Step 1: The Theoretical Minimum.
Even if a spinning machine were mechanically perfect, the yarn would still show some level of unevenness. This is because fibers are discrete units that are arranged randomly throughout the yarn's cross-section.
Step 2: Defining Limit Irregularity.
The theoretical minimum level of irregularity achievable for a given fiber and yarn count, assuming a Poisson distribution of fiber ends, is called the limit irregularity. It represents the unavoidable variation caused solely by the random arrangement of fibres. Any actual yarn will have an irregularity higher than this limit due to additional mechanical "drafting waves" and faults.