Trims & Fasteners
If the button comes off below the thread's own capacity, more stitches will not fix it — the fabric or the shank is the weak link.
— N
Average across the three specimens
A capacity ratio well below 1 means the thread is not the limit — look at the fabric behind the button, the shank, or a reinforcement patch. Childrenswear button security is a regulated safety requirement: the lowest specimen, not the mean, is what a child will find, and compliance rests on the governing standard.
Button Pull-out Force & Attachment Capacity (ASTM D6644) — free, with the formula and a worked example, at Textile School.